SAS Output

MCMC analysis of regions

The MCMC Procedure

country=ENG region_code=' ' region_name=London

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000200
2	1	0.5981	0.000360
3	1	0.1567	0.2308
4	1	0.1222	0.3950

Burn-In History
Block	Scale	Acceptance Rate
1	0.1222	0.3931

Sampling History
Block	Scale	Acceptance Rate
1	0.1222	0.3919

MCMC analysis of regions

The MCMC Procedure

country=ENG region_code=' ' region_name=London

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.000640	0.000028	0.000597	0.000694
i0	2000	0.1094	0.0155	0.0794	0.1400
R0	2000	2.5809	0.3538	1.8904	3.2661
beta	2000	0.3055	0.00849	0.2895	0.3223
gamma	2000	0.1206	0.0176	0.0886	0.1537

MCMC analysis of regions

The MCMC Procedure

country=ENG region_code=' ' region_name=London

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	9.727E-7	0.000028	0.0343
i0	0.000521	0.0155	0.0336
R0	0.0128	0.3538	0.0361
beta	0.000215	0.00849	0.0253
gamma	0.000631	0.0176	0.0359

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.3641	0.0135	0.0208	-0.0461
i0	0.3555	0.0165	0.0163	-0.0051
R0	0.4667	0.0097	0.0103	-0.0188
beta	0.0993	0.0122	-0.0396	0.0457
gamma	0.4290	0.0230	0.0134	-0.0304

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	-0.7409	0.4587
i0	1.1640	0.2444
R0	1.2289	0.2191
beta	0.6556	0.5121
gamma	-0.9893	0.3225

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	0.0827	0.6763	Passed	0	2.073E-6	0.000640	0.00324	Passed
i0	0.1578	0.3666	Passed	0	0.00107	0.1094	0.00977	Passed
R0	0.2377	0.2050	Passed	0	0.0247	2.5809	0.00958	Passed
beta	0.0680	0.7636	Passed	0	0.000402	0.3055	0.00131	Passed
gamma	0.1729	0.3266	Passed	0	0.00125	0.1206	0.0104	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	851.1	2.3500	0.4255
i0	887.0	2.2548	0.4435
R0	768.2	2.6035	0.3841
beta	1563.2	1.2794	0.7816
gamma	776.2	2.5768	0.3881

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	73.6840	9.7032	57.0000	94.0000
int_dec_avg_dot_2	2000	84.9495	10.2928	64.0000	104.0
int_dec_avg_dot_3	2000	96.6495	10.7576	76.0000	118.0
int_dec_avg_dot_4	2000	109.7	11.0135	87.0000	130.0
int_dec_avg_dot_5	2000	122.9	11.8686	99.0000	145.0
int_dec_avg_dot_6	2000	136.6	12.3441	114.0	161.0
int_dec_avg_dot_7	2000	149.4	12.8110	122.0	172.0
int_dec_avg_dot_8	2000	162.1	13.3479	136.0	187.0
int_dec_avg_dot_9	2000	173.0	13.9347	146.0	199.0
int_dec_avg_dot_10	2000	182.9	14.4603	152.0	209.0
int_dec_avg_dot_11	2000	190.5	14.5568	160.0	217.0
int_dec_avg_dot_12	2000	196.3	14.7090	166.0	223.0
int_dec_avg_dot_13	2000	199.6	14.6708	172.0	228.0
int_dec_avg_dot_14	2000	200.0	15.1463	170.0	229.0
int_dec_avg_dot_15	2000	198.7	14.7928	170.0	227.0
int_dec_avg_dot_16	2000	195.0	14.8620	164.0	221.0
int_dec_avg_dot_17	2000	189.9	14.6107	159.0	216.0
int_dec_avg_dot_18	2000	183.4	14.3937	156.0	212.0
int_dec_avg_dot_19	2000	176.0	13.5747	149.0	202.0
int_dec_avg_dot_20	2000	167.3	13.5253	140.0	193.0
int_dec_avg_dot_21	2000	158.8	12.9909	135.0	185.0
int_dec_avg_dot_22	2000	149.3	12.5433	123.0	171.0
int_dec_avg_dot_23	2000	140.1	12.2500	116.0	163.0
int_dec_avg_dot_24	2000	130.4	11.7038	109.0	154.0
int_dec_avg_dot_25	2000	121.6	11.0285	99.0000	141.0
int_dec_avg_dot_26	2000	113.1	10.8524	93.0000	134.0
int_dec_avg_dot_27	2000	104.0	10.4681	83.0000	123.0
int_dec_avg_dot_28	2000	96.2710	10.1171	74.0000	113.0
int_dec_avg_dot_29	2000	88.8250	9.7042	69.0000	106.0
int_dec_avg_dot_30	2000	82.1450	9.2358	64.0000	99.0000
int_dec_avg_dot_31	2000	74.3305	8.8819	56.0000	90.0000
int_dec_avg_dot_32	2000	68.7030	8.3790	52.0000	85.0000
int_dec_avg_dot_33	2000	62.9705	8.1016	46.0000	77.0000
int_dec_avg_dot_34	2000	57.2585	7.9027	41.0000	71.0000
int_dec_avg_dot_35	2000	52.2605	7.3484	36.0000	65.0000
int_dec_avg_dot_36	2000	47.5930	6.9723	33.0000	60.0000
int_dec_avg_dot_37	2000	43.7620	6.8490	30.0000	56.0000
int_dec_avg_dot_38	2000	39.5985	6.4779	27.0000	52.0000
int_dec_avg_dot_39	2000	36.0770	6.3867	22.0000	47.0000
int_dec_avg_dot_40	2000	32.8470	5.9782	21.0000	44.0000
int_dec_avg_dot_41	2000	29.7030	5.9092	17.0000	40.0000
int_dec_avg_dot_42	2000	27.1050	5.4301	17.0000	37.0000
int_dec_avg_dot_43	2000	24.6560	5.4078	13.0000	34.0000

MCMC analysis of regions

The MCMC Procedure

country=ENG region_code=' ' region_name=London

MCMC analysis of regions

The MCMC Procedure

country=ENG region_code=' ' region_name=Midlands

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000600
2	1	0.6482	0.00246
3	1	0.2000	0.1550
4	1	0.1315	0.5322
5	1	0.1967	0.6310
6	1	0.3827	0.6172
7	1	0.7157	0.5688
8	1	1.1737	0.4914
9	1	1.5942	0.4248

Burn-In History
Block	Scale	Acceptance Rate
1	1.5942	0.4246

Sampling History
Block	Scale	Acceptance Rate
1	1.5942	0.4243

MCMC analysis of regions

The MCMC Procedure

country=ENG region_code=' ' region_name=Midlands

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.000455	9.775E-6	0.000435	0.000473
i0	2000	0.1260	0.0110	0.1039	0.1470
R0	2000	4.6868	0.7222	3.2744	6.0624
beta	2000	0.2868	0.0154	0.2562	0.3150
gamma	2000	0.0622	0.00731	0.0493	0.0774

MCMC analysis of regions

The MCMC Procedure

country=ENG region_code=' ' region_name=Midlands

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	2.297E-7	9.775E-6	0.0235
i0	0.000240	0.0110	0.0219
R0	0.0165	0.7222	0.0229
beta	0.000345	0.0154	0.0224
gamma	0.000163	0.00731	0.0224

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.0182	-0.0129	-0.0144	-0.0142
i0	-0.0195	0.0087	0.0198	-0.0086
R0	0.0190	0.0030	-0.0015	-0.0164
beta	0.0008	0.0186	0.0023	-0.0020
gamma	0.0094	-0.0079	0.0054	-0.0082

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	.	.
i0	-3.0543	0.0023
R0	-1.3496	0.1771
beta	0.2651	0.7909
gamma	2.3974	0.0165

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	.	.	Failed	.	.	.	.
i0	0.3349	0.1081	Passed	0	0.000478	0.1260	0.00379	Passed
R0	0.1704	0.3329	Passed	0	0.0352	4.6868	0.00751	Passed
beta	0.0671	0.7695	Passed	0	0.000736	0.2868	0.00257	Passed
gamma	0.3244	0.1156	Passed	0	0.000354	0.0622	0.00569	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	1811.4	1.1041	0.9057
i0	2081.1	0.9610	1.0406
R0	1908.4	1.0480	0.9542
beta	2000.0	1.0000	1.0000
gamma	2000.0	1.0000	1.0000

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	37.6675	7.0408	23.0000	50.0000
int_dec_avg_dot_2	2000	45.0110	7.3347	32.0000	59.0000
int_dec_avg_dot_3	2000	53.0970	7.8103	37.0000	67.0000
int_dec_avg_dot_4	2000	62.1460	8.2664	46.0000	78.0000
int_dec_avg_dot_5	2000	71.8755	8.9847	53.0000	88.0000
int_dec_avg_dot_6	2000	82.2225	9.4694	62.0000	99.0000
int_dec_avg_dot_7	2000	92.8650	9.6903	73.0000	110.0
int_dec_avg_dot_8	2000	103.1	10.7922	81.0000	123.0
int_dec_avg_dot_9	2000	113.8	11.3972	91.0000	135.0
int_dec_avg_dot_10	2000	123.1	11.8388	101.0	147.0
int_dec_avg_dot_11	2000	131.3	12.3097	107.0	155.0
int_dec_avg_dot_12	2000	138.6	12.3160	115.0	162.0
int_dec_avg_dot_13	2000	143.4	12.4679	118.0	166.0
int_dec_avg_dot_14	2000	146.4	12.9063	122.0	171.0
int_dec_avg_dot_15	2000	148.5	12.7611	125.0	174.0
int_dec_avg_dot_16	2000	149.4	12.6813	124.0	173.0
int_dec_avg_dot_17	2000	147.9	12.7483	126.0	175.0
int_dec_avg_dot_18	2000	146.2	12.5733	121.0	169.0
int_dec_avg_dot_19	2000	143.2	12.7191	117.0	166.0
int_dec_avg_dot_20	2000	139.1	12.3539	114.0	162.0
int_dec_avg_dot_21	2000	135.1	11.9184	112.0	157.0
int_dec_avg_dot_22	2000	130.2	11.9161	106.0	152.0
int_dec_avg_dot_23	2000	125.0	11.4875	102.0	146.0
int_dec_avg_dot_24	2000	119.8	11.5820	99.0000	143.0
int_dec_avg_dot_25	2000	115.0	10.9543	91.0000	134.0
int_dec_avg_dot_26	2000	110.2	11.1069	87.0000	130.0
int_dec_avg_dot_27	2000	103.7	10.4914	82.0000	122.0
int_dec_avg_dot_28	2000	99.1235	10.5392	77.0000	118.0
int_dec_avg_dot_29	2000	94.4385	9.8353	76.0000	113.0
int_dec_avg_dot_30	2000	89.3620	9.8033	69.0000	107.0
int_dec_avg_dot_31	2000	84.7030	9.4469	67.0000	103.0
int_dec_avg_dot_32	2000	80.1735	9.2077	61.0000	97.0000
int_dec_avg_dot_33	2000	75.8320	9.0382	59.0000	93.0000
int_dec_avg_dot_34	2000	71.8385	8.4056	55.0000	87.0000
int_dec_avg_dot_35	2000	67.6050	8.3506	51.0000	83.0000
int_dec_avg_dot_36	2000	64.0725	8.3786	46.0000	79.0000
int_dec_avg_dot_37	2000	60.7705	7.9144	44.0000	75.0000
int_dec_avg_dot_38	2000	57.3140	7.6392	42.0000	72.0000
int_dec_avg_dot_39	2000	53.9140	7.6784	38.0000	68.0000
int_dec_avg_dot_40	2000	50.7990	7.2222	38.0000	65.0000
int_dec_avg_dot_41	2000	48.2560	7.1867	35.0000	62.0000
int_dec_avg_dot_42	2000	45.4280	7.1386	31.0000	59.0000
int_dec_avg_dot_43	2000	42.8660	7.0674	29.0000	56.0000

MCMC analysis of regions

The MCMC Procedure

country=ENG region_code=' ' region_name=Midlands

MCMC analysis of regions

The MCMC Procedure

country=ENG region_code=' ' region_name=North West

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000600
2	1	0.6482	0.00366
3	1	0.2085	0.1728
4	1	0.1429	0.5444
5	1	0.2203	0.6232
6	1	0.4191	0.6204
7	1	0.7908	0.5582
8	1	1.2621	0.4837
9	1	1.6843	0.4125

Burn-In History
Block	Scale	Acceptance Rate
1	1.6843	0.4124

Sampling History
Block	Scale	Acceptance Rate
1	1.6843	0.4120

MCMC analysis of regions

The MCMC Procedure

country=ENG region_code=' ' region_name=North West

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.000514	0.000013	0.000488	0.000537
i0	2000	0.0592	0.00585	0.0479	0.0704
R0	2000	4.4788	0.6322	3.3443	5.8111
beta	2000	0.3097	0.0122	0.2871	0.3346
gamma	2000	0.0703	0.00859	0.0546	0.0882

MCMC analysis of regions

The MCMC Procedure

country=ENG region_code=' ' region_name=North West

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	2.817E-7	0.000013	0.0224
i0	0.000131	0.00585	0.0224
R0	0.0148	0.6322	0.0233
beta	0.000278	0.0122	0.0229
gamma	0.000200	0.00859	0.0233

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	-0.0283	0.0129	-0.0359	0.0021
i0	-0.0016	0.0021	-0.0015	0.0037
R0	0.0213	0.0192	-0.0092	-0.0187
beta	0.0224	0.0191	0.0496	0.0035
gamma	0.0272	0.0180	-0.0144	-0.0218

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	0.2261	0.8211
i0	0.8594	0.3901
R0	0.3857	0.6997
beta	-0.6626	0.5076
gamma	-0.4093	0.6823

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	.	.	Failed	.	.	.	.
i0	0.1413	0.4172	Passed	0	0.000268	0.0592	0.00453	Passed
R0	0.0697	0.7537	Passed	0	0.0280	4.4788	0.00624	Passed
beta	0.0474	0.8919	Passed	0	0.000573	0.3097	0.00185	Passed
gamma	0.1014	0.5783	Passed	0	0.000395	0.0703	0.00562	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	1987.2	1.0065	0.9936
i0	2000.0	1.0000	1.0000
R0	1835.2	1.0898	0.9176
beta	1914.3	1.0448	0.9571
gamma	1838.5	1.0879	0.9192

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	15.4330	4.2997	7.0000	24.0000
int_dec_avg_dot_2	2000	18.7175	4.4452	10.0000	27.0000
int_dec_avg_dot_3	2000	22.9870	5.2244	12.0000	32.0000
int_dec_avg_dot_4	2000	27.6775	5.5639	17.0000	38.0000
int_dec_avg_dot_5	2000	33.0875	6.1159	20.0000	44.0000
int_dec_avg_dot_6	2000	39.5445	6.6278	26.0000	52.0000
int_dec_avg_dot_7	2000	46.9465	7.2200	32.0000	60.0000
int_dec_avg_dot_8	2000	54.7310	7.4346	39.0000	68.0000
int_dec_avg_dot_9	2000	63.5690	8.5784	46.0000	80.0000
int_dec_avg_dot_10	2000	72.4930	8.7636	54.0000	88.0000
int_dec_avg_dot_11	2000	81.3675	9.5110	64.0000	101.0
int_dec_avg_dot_12	2000	90.0760	9.9177	71.0000	109.0
int_dec_avg_dot_13	2000	98.5580	10.5303	77.0000	118.0
int_dec_avg_dot_14	2000	106.3	10.7423	85.0000	127.0
int_dec_avg_dot_15	2000	112.3	11.1679	90.0000	133.0
int_dec_avg_dot_16	2000	116.6	11.5280	94.0000	139.0
int_dec_avg_dot_17	2000	119.7	11.7629	94.0000	140.0
int_dec_avg_dot_18	2000	121.3	10.8262	104.0	145.0
int_dec_avg_dot_19	2000	121.1	11.3989	100.0	143.0
int_dec_avg_dot_20	2000	120.4	11.1644	97.0000	141.0
int_dec_avg_dot_21	2000	118.4	11.2092	97.0000	139.0
int_dec_avg_dot_22	2000	115.2	11.5332	93.0000	136.0
int_dec_avg_dot_23	2000	111.6	10.9934	90.0000	132.0
int_dec_avg_dot_24	2000	107.9	10.8357	83.0000	126.0
int_dec_avg_dot_25	2000	103.8	10.6028	82.0000	123.0
int_dec_avg_dot_26	2000	98.8585	10.7618	78.0000	120.0
int_dec_avg_dot_27	2000	94.3360	10.0106	74.0000	113.0
int_dec_avg_dot_28	2000	89.1400	9.6701	69.0000	106.0
int_dec_avg_dot_29	2000	84.6750	9.4636	64.0000	101.0
int_dec_avg_dot_30	2000	80.0810	9.1721	63.0000	98.0000
int_dec_avg_dot_31	2000	75.5270	8.8606	59.0000	93.0000
int_dec_avg_dot_32	2000	71.9060	8.6640	53.0000	87.0000
int_dec_avg_dot_33	2000	67.6270	8.2750	51.0000	83.0000
int_dec_avg_dot_34	2000	63.5005	8.3439	46.0000	78.0000
int_dec_avg_dot_35	2000	59.5425	7.9931	43.0000	74.0000
int_dec_avg_dot_36	2000	55.9960	7.7458	40.0000	70.0000
int_dec_avg_dot_37	2000	52.3885	7.6022	36.0000	66.0000
int_dec_avg_dot_38	2000	49.3175	7.2715	35.0000	63.0000
int_dec_avg_dot_39	2000	46.4410	7.0175	34.0000	60.0000
int_dec_avg_dot_40	2000	43.2245	6.9295	29.0000	56.0000
int_dec_avg_dot_41	2000	40.6385	6.8285	27.0000	53.0000
int_dec_avg_dot_42	2000	37.9745	6.5620	24.0000	49.0000
int_dec_avg_dot_43	2000	35.4265	6.3699	24.0000	48.0000

MCMC analysis of regions

The MCMC Procedure

country=ENG region_code=' ' region_name=North West

MCMC analysis of regions

The MCMC Procedure

country=ESP region_code=CL region_name=Castile and León

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000400
2	1	0.6283	0.0204
3	1	0.2532	0.3419

Burn-In History
Block	Scale	Acceptance Rate
1	0.2532	0.3442

Sampling History
Block	Scale	Acceptance Rate
1	0.2532	0.3439

MCMC analysis of regions

The MCMC Procedure

country=ESP region_code=CL region_name=Castile and León

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.000871	0.000027	0.000820	0.000925
i0	2000	0.0339	0.00573	0.0230	0.0452
R0	2000	8.4515	1.0105	6.5409	10.4934
beta	2000	0.4115	0.0274	0.3609	0.4658
gamma	2000	0.0491	0.00368	0.0420	0.0562

MCMC analysis of regions

The MCMC Procedure

country=ESP region_code=CL region_name=Castile and León

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	6.957E-7	0.000027	0.0257
i0	0.000132	0.00573	0.0230
R0	0.0226	1.0105	0.0224
beta	0.000667	0.0274	0.0243
gamma	0.000082	0.00368	0.0224

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.0279	0.0331	0.0039	0.0021
i0	0.0276	-0.0169	0.0357	0.0043
R0	0.0088	0.0148	0.0551	0.0388
beta	0.0119	-0.0212	0.0646	0.0282
gamma	0.0009	0.0379	0.0188	-0.0038

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	-1.2518	0.2106
i0	0.3734	0.7088
R0	-1.4991	0.1338
beta	-0.7907	0.4291
gamma	1.6485	0.0992

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	0.3957	0.0742	Passed	0	0	0.000871	0	Passed
i0	0.3959	0.0741	Passed	0	0.000259	0.0339	0.00762	Passed
R0	0.3520	0.0971	Passed	400	0.0658	8.4751	0.00776	Passed
beta	0.4596	0.0505	Passed	0	0.00155	0.4115	0.00377	Passed
gamma	0.1845	0.2995	Passed	400	0.000206	0.0490	0.00421	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	1512.6	1.3222	0.7563
i0	1895.5	1.0552	0.9477
R0	2000.0	1.0000	1.0000
beta	1689.5	1.1838	0.8448
gamma	2000.0	1.0000	1.0000

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	3.5305	1.9837	0	7.0000
int_dec_avg_dot_2	2000	4.7975	2.2676	1.0000	9.0000
int_dec_avg_dot_3	2000	6.2780	2.6590	1.0000	11.0000
int_dec_avg_dot_4	2000	8.2810	3.0517	2.0000	14.0000
int_dec_avg_dot_5	2000	11.0105	3.4712	4.0000	17.0000
int_dec_avg_dot_6	2000	14.4355	4.1543	6.0000	22.0000
int_dec_avg_dot_7	2000	18.5735	4.6303	9.0000	27.0000
int_dec_avg_dot_8	2000	23.7675	5.0240	14.0000	33.0000
int_dec_avg_dot_9	2000	29.9350	5.7386	18.0000	40.0000
int_dec_avg_dot_10	2000	36.7815	6.4867	23.0000	48.0000
int_dec_avg_dot_11	2000	43.8690	6.8567	29.0000	56.0000
int_dec_avg_dot_12	2000	50.6690	7.5521	35.0000	64.0000
int_dec_avg_dot_13	2000	56.5610	8.0991	41.0000	72.0000
int_dec_avg_dot_14	2000	60.9555	8.3766	44.0000	76.0000
int_dec_avg_dot_15	2000	64.1875	8.3321	49.0000	81.0000
int_dec_avg_dot_16	2000	66.1515	8.6090	48.0000	81.0000
int_dec_avg_dot_17	2000	66.8835	8.5978	50.0000	83.0000
int_dec_avg_dot_18	2000	66.2870	8.6161	48.0000	82.0000
int_dec_avg_dot_19	2000	65.4195	8.3572	49.0000	81.0000
int_dec_avg_dot_20	2000	63.5205	8.1863	46.0000	78.0000
int_dec_avg_dot_21	2000	61.6885	8.1841	45.0000	77.0000
int_dec_avg_dot_22	2000	59.5240	7.9374	44.0000	75.0000
int_dec_avg_dot_23	2000	57.1195	7.8190	42.0000	72.0000
int_dec_avg_dot_24	2000	54.6270	7.6020	39.0000	69.0000
int_dec_avg_dot_25	2000	52.5220	7.3610	39.0000	67.0000
int_dec_avg_dot_26	2000	50.0100	7.1594	35.0000	63.0000
int_dec_avg_dot_27	2000	47.8610	7.0886	33.0000	60.0000
int_dec_avg_dot_28	2000	45.7015	6.8128	32.0000	58.0000
int_dec_avg_dot_29	2000	43.5415	7.0038	30.0000	57.0000
int_dec_avg_dot_30	2000	41.6490	6.3815	29.0000	53.0000
int_dec_avg_dot_31	2000	39.2110	6.1902	27.0000	50.0000
int_dec_avg_dot_32	2000	37.7795	6.3538	26.0000	50.0000
int_dec_avg_dot_33	2000	35.9740	5.9837	23.0000	46.0000
int_dec_avg_dot_34	2000	34.1495	6.1400	23.0000	46.0000
int_dec_avg_dot_35	2000	32.6005	5.7262	21.0000	43.0000
int_dec_avg_dot_36	2000	30.5930	5.7016	18.0000	40.0000
int_dec_avg_dot_37	2000	29.3030	5.4340	20.0000	40.0000
int_dec_avg_dot_38	2000	28.0105	5.3394	17.0000	37.0000
int_dec_avg_dot_39	2000	26.6575	5.2657	16.0000	36.0000
int_dec_avg_dot_40	2000	25.1260	4.8731	15.0000	34.0000
int_dec_avg_dot_41	2000	24.1505	5.0234	14.0000	33.0000
int_dec_avg_dot_42	2000	22.9470	4.9158	14.0000	32.0000
int_dec_avg_dot_43	2000	21.7740	4.9241	11.0000	30.0000
int_dec_avg_dot_44	2000	20.7795	4.6768	11.0000	29.0000
int_dec_avg_dot_45	2000	19.7650	4.5243	11.0000	28.0000
int_dec_avg_dot_46	2000	18.8675	4.4231	10.0000	27.0000
int_dec_avg_dot_47	2000	17.8185	4.3939	9.0000	26.0000
int_dec_avg_dot_48	2000	16.9095	4.2822	7.0000	24.0000
int_dec_avg_dot_49	2000	16.1180	4.2842	8.0000	24.0000
int_dec_avg_dot_50	2000	15.3660	4.0949	6.0000	22.0000
int_dec_avg_dot_51	2000	14.6750	4.0214	7.0000	22.0000

MCMC analysis of regions

The MCMC Procedure

country=ESP region_code=CL region_name=Castile and León

MCMC analysis of regions

The MCMC Procedure

country=ESP region_code=CT region_name=Catalonia

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000720
2	1	0.6577	0.00164
3	1	0.1952	0.1421
4	1	0.1243	0.5287
5	1	0.1844	0.6274
6	1	0.3550	0.6242
7	1	0.6772	0.5805
8	1	1.1453	0.5148
9	1	1.6432	0.4284
10	1	1.9392	0.3792

Burn-In History
Block	Scale	Acceptance Rate
1	1.9392	0.3769

Sampling History
Block	Scale	Acceptance Rate
1	1.9392	0.3810

MCMC analysis of regions

The MCMC Procedure

country=ESP region_code=CT region_name=Catalonia

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.000992	0.000033	0.000935	0.00106
i0	2000	0.0286	0.00381	0.0217	0.0365
R0	2000	15.9582	1.6285	12.8363	19.1596
beta	2000	0.4468	0.0256	0.3979	0.4960
gamma	2000	0.0282	0.00174	0.0249	0.0317

MCMC analysis of regions

The MCMC Procedure

country=ESP region_code=CT region_name=Catalonia

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	7.166E-7	0.000033	0.0216
i0	0.000080	0.00381	0.0209
R0	0.0341	1.6285	0.0209
beta	0.000526	0.0256	0.0205
gamma	0.000038	0.00174	0.0220

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	-0.0166	-0.0267	-0.0234	0.0104
i0	-0.0371	0.0168	0.0006	0.0129
R0	-0.0156	-0.0100	-0.0037	-0.0122
beta	-0.0133	0.0035	-0.0029	-0.0006
gamma	-0.0211	-0.0165	-0.0028	-0.0037

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	0.7002	0.4838
i0	-1.0086	0.3132
R0	0.6128	0.5400
beta	0.5850	0.5586
gamma	-0.6564	0.5116

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	0.0374	0.9459	Passed	0	0	0.000992	0	Passed
i0	0.1620	0.3551	Passed	0	0.000149	0.0286	0.00521	Passed
R0	0.0457	0.9016	Passed	0	0.0664	15.9582	0.00416	Passed
beta	0.0805	0.6890	Passed	0	0.00110	0.4468	0.00245	Passed
gamma	0.0234	0.9926	Passed	0	0.000070	0.0282	0.00250	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	2148.8	0.9308	1.0744
i0	2283.4	0.8759	1.1417
R0	2284.1	0.8756	1.1420
beta	2373.8	0.8425	1.1869
gamma	2062.0	0.9699	1.0310

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	6.0870	2.6088	0	10.0000
int_dec_avg_dot_2	2000	8.5925	3.2038	2.0000	14.0000
int_dec_avg_dot_3	2000	12.1530	3.6691	5.0000	19.0000
int_dec_avg_dot_4	2000	16.7705	4.3835	7.0000	24.0000
int_dec_avg_dot_5	2000	22.9700	5.3104	13.0000	33.0000
int_dec_avg_dot_6	2000	31.7720	5.9789	20.0000	43.0000
int_dec_avg_dot_7	2000	42.6945	6.7773	28.0000	54.0000
int_dec_avg_dot_8	2000	56.2225	7.8411	40.0000	70.0000
int_dec_avg_dot_9	2000	72.9660	9.1841	53.0000	89.0000
int_dec_avg_dot_10	2000	91.5860	10.4695	68.0000	110.0
int_dec_avg_dot_11	2000	110.3	11.3524	87.0000	131.0
int_dec_avg_dot_12	2000	128.9	12.6841	105.0	153.0
int_dec_avg_dot_13	2000	144.4	12.8721	119.0	168.0
int_dec_avg_dot_14	2000	156.3	13.4240	132.0	184.0
int_dec_avg_dot_15	2000	163.5	13.6111	135.0	188.0
int_dec_avg_dot_16	2000	167.7	13.3578	142.0	193.0
int_dec_avg_dot_17	2000	168.2	13.5267	141.0	194.0
int_dec_avg_dot_18	2000	167.2	13.2639	140.0	193.0
int_dec_avg_dot_19	2000	165.2	13.5495	138.0	190.0
int_dec_avg_dot_20	2000	161.9	13.2282	137.0	187.0
int_dec_avg_dot_21	2000	158.8	12.9415	133.0	183.0
int_dec_avg_dot_22	2000	154.4	12.7453	130.0	180.0
int_dec_avg_dot_23	2000	150.8	12.4133	125.0	173.0
int_dec_avg_dot_24	2000	147.0	12.3006	123.0	170.0
int_dec_avg_dot_25	2000	143.3	11.9935	118.0	165.0
int_dec_avg_dot_26	2000	138.9	11.6448	115.0	160.0
int_dec_avg_dot_27	2000	135.1	12.0834	109.0	156.0
int_dec_avg_dot_28	2000	131.6	11.6686	110.0	155.0
int_dec_avg_dot_29	2000	127.8	11.6013	106.0	151.0
int_dec_avg_dot_30	2000	124.2	11.4194	103.0	147.0
int_dec_avg_dot_31	2000	120.8	11.1420	96.0000	140.0
int_dec_avg_dot_32	2000	117.4	11.3047	94.0000	138.0
int_dec_avg_dot_33	2000	113.9	10.4344	94.0000	134.0
int_dec_avg_dot_34	2000	110.8	10.8691	88.0000	130.0
int_dec_avg_dot_35	2000	107.3	10.5408	87.0000	127.0
int_dec_avg_dot_36	2000	104.4	10.1826	84.0000	123.0
int_dec_avg_dot_37	2000	102.0	10.1629	81.0000	120.0
int_dec_avg_dot_38	2000	98.7225	10.1573	77.0000	117.0
int_dec_avg_dot_39	2000	96.1940	10.0630	76.0000	114.0
int_dec_avg_dot_40	2000	93.3310	9.6901	75.0000	112.0
int_dec_avg_dot_41	2000	90.6900	9.5688	71.0000	108.0
int_dec_avg_dot_42	2000	88.0295	9.5607	69.0000	105.0
int_dec_avg_dot_43	2000	85.4425	9.6238	66.0000	103.0
int_dec_avg_dot_44	2000	83.1800	9.4974	64.0000	101.0
int_dec_avg_dot_45	2000	80.9160	9.2183	63.0000	99.0000
int_dec_avg_dot_46	2000	78.6915	9.1943	61.0000	96.0000
int_dec_avg_dot_47	2000	76.6875	9.0944	58.0000	94.0000
int_dec_avg_dot_48	2000	74.4050	9.2059	55.0000	90.0000
int_dec_avg_dot_49	2000	72.4230	8.9938	55.0000	90.0000
int_dec_avg_dot_50	2000	69.8870	8.8674	50.0000	85.0000
int_dec_avg_dot_51	2000	68.2855	8.6506	51.0000	85.0000

MCMC analysis of regions

The MCMC Procedure

country=ESP region_code=CT region_name=Catalonia

MCMC analysis of regions

The MCMC Procedure

country=ESP region_code=MD region_name=Community of Madrid

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000300
2	1	0.6153	0.00222
3	1	0.1880	0.1971
4	1	0.1362	0.5745
5	1	0.2267	0.6285
6	1	0.4379	0.6139
7	1	0.8114	0.5637
8	1	1.3135	0.4889
9	1	1.7737	0.4051

Burn-In History
Block	Scale	Acceptance Rate
1	1.7737	0.4054

Sampling History
Block	Scale	Acceptance Rate
1	1.7737	0.4065

MCMC analysis of regions

The MCMC Procedure

country=ESP region_code=MD region_name=Community of Madrid

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.00136	0.000017	0.00133	0.00139
i0	2000	0.1183	0.00680	0.1050	0.1309
R0	2000	6.8405	0.4470	6.0063	7.7180
beta	2000	0.3782	0.0151	0.3485	0.4065
gamma	2000	0.0554	0.00189	0.0518	0.0590

MCMC analysis of regions

The MCMC Procedure

country=ESP region_code=MD region_name=Community of Madrid

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	3.91E-7	0.000017	0.0224
i0	0.000144	0.00680	0.0211
R0	0.01000	0.4470	0.0224
beta	0.000338	0.0151	0.0224
gamma	0.000042	0.00189	0.0224

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.0013	-0.0146	0.0006	0.0134
i0	0.0384	-0.0664	-0.0218	-0.0194
R0	-0.0009	0.0096	0.0255	0.0419
beta	0.0030	-0.0009	0.0033	0.0349
gamma	0.0035	-0.0050	0.0471	0.0088

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	-1.5177	0.1291
i0	0.9190	0.3581
R0	-1.1813	0.2375
beta	-1.4630	0.1435
gamma	0.4276	0.6689

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	.	.	Failed	.	.	.	.
i0	0.1711	0.3313	Passed	0	0.000289	0.1183	0.00245	Passed
R0	0.1091	0.5422	Passed	0	0.0199	6.8405	0.00291	Passed
beta	0.1684	0.3381	Passed	0	0.000654	0.3782	0.00173	Passed
gamma	0.0440	0.9116	Passed	0	0.000082	0.0554	0.00149	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	2000.0	1.0000	1.0000
i0	2241.9	0.8921	1.1210
R0	2000.0	1.0000	1.0000
beta	2000.0	1.0000	1.0000
gamma	2000.0	1.0000	1.0000

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	58.9395	8.5215	41.0000	74.0000
int_dec_avg_dot_2	2000	75.1580	9.7840	56.0000	93.0000
int_dec_avg_dot_3	2000	95.7240	10.4509	76.0000	116.0
int_dec_avg_dot_4	2000	118.8	12.0444	93.0000	140.0
int_dec_avg_dot_5	2000	145.7	12.5053	121.0	170.0
int_dec_avg_dot_6	2000	174.5	14.0871	148.0	202.0
int_dec_avg_dot_7	2000	203.8	15.1448	172.0	231.0
int_dec_avg_dot_8	2000	232.6	16.1678	198.0	261.0
int_dec_avg_dot_9	2000	258.0	17.3035	224.0	291.0
int_dec_avg_dot_10	2000	279.7	18.0608	243.0	314.0
int_dec_avg_dot_11	2000	293.9	18.2835	256.0	327.0
int_dec_avg_dot_12	2000	303.5	18.0966	266.0	336.0
int_dec_avg_dot_13	2000	306.8	18.2334	272.0	342.0
int_dec_avg_dot_14	2000	306.2	18.4079	270.0	342.0
int_dec_avg_dot_15	2000	301.2	17.9341	264.0	334.0
int_dec_avg_dot_16	2000	293.5	17.7548	259.0	328.0
int_dec_avg_dot_17	2000	284.8	17.7157	250.0	319.0
int_dec_avg_dot_18	2000	273.7	17.1929	238.0	306.0
int_dec_avg_dot_19	2000	263.5	16.8369	228.0	294.0
int_dec_avg_dot_20	2000	251.2	16.6500	219.0	283.0
int_dec_avg_dot_21	2000	240.2	16.0391	209.0	271.0
int_dec_avg_dot_22	2000	227.9	15.4453	198.0	257.0
int_dec_avg_dot_23	2000	217.6	15.4447	186.0	245.0
int_dec_avg_dot_24	2000	206.3	14.7829	178.0	235.0
int_dec_avg_dot_25	2000	195.2	14.6239	167.0	224.0
int_dec_avg_dot_26	2000	185.0	13.9460	158.0	212.0
int_dec_avg_dot_27	2000	176.3	13.5971	149.0	201.0
int_dec_avg_dot_28	2000	166.6	13.0294	141.0	191.0
int_dec_avg_dot_29	2000	157.7	12.8807	132.0	182.0
int_dec_avg_dot_30	2000	149.0	12.7909	123.0	172.0
int_dec_avg_dot_31	2000	141.2	11.8993	117.0	163.0
int_dec_avg_dot_32	2000	133.9	11.9353	110.0	156.0
int_dec_avg_dot_33	2000	126.8	11.1592	104.0	148.0
int_dec_avg_dot_34	2000	120.0	10.9221	98.0000	140.0
int_dec_avg_dot_35	2000	113.4	11.0052	92.0000	134.0
int_dec_avg_dot_36	2000	106.9	10.4968	87.0000	128.0
int_dec_avg_dot_37	2000	101.1	10.4016	81.0000	122.0
int_dec_avg_dot_38	2000	95.8935	9.9835	75.0000	113.0
int_dec_avg_dot_39	2000	90.7310	9.7387	72.0000	109.0
int_dec_avg_dot_40	2000	85.7015	9.3363	68.0000	103.0
int_dec_avg_dot_41	2000	80.9465	9.0720	65.0000	99.0000
int_dec_avg_dot_42	2000	76.5290	8.7965	59.0000	93.0000
int_dec_avg_dot_43	2000	72.0850	8.4377	56.0000	88.0000
int_dec_avg_dot_44	2000	68.4505	8.4302	53.0000	85.0000
int_dec_avg_dot_45	2000	64.3940	8.4544	47.0000	79.0000
int_dec_avg_dot_46	2000	61.2255	8.1130	45.0000	77.0000
int_dec_avg_dot_47	2000	57.7725	7.7966	43.0000	73.0000
int_dec_avg_dot_48	2000	54.7285	7.5206	39.0000	68.0000
int_dec_avg_dot_49	2000	51.6795	7.5941	35.0000	65.0000
int_dec_avg_dot_50	2000	48.7055	7.2837	34.0000	62.0000
int_dec_avg_dot_51	2000	46.1540	6.9016	31.0000	58.0000

MCMC analysis of regions

The MCMC Procedure

country=ESP region_code=MD region_name=Community of Madrid

MCMC analysis of regions

The MCMC Procedure

country=FRA region_code=11 region_name=Île-de-France

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000280
2	1	0.6122	0.00382
3	1	0.1978	0.2226
4	1	0.1516	0.5720
5	1	0.2507	0.6288
6	1	0.4847	0.6060
7	1	0.8782	0.5554
8	1	1.3921	0.4648
9	1	1.7799	0.3957

Burn-In History
Block	Scale	Acceptance Rate
1	1.7799	0.3943

Sampling History
Block	Scale	Acceptance Rate
1	1.7799	0.3968

MCMC analysis of regions

The MCMC Procedure

country=FRA region_code=11 region_name=Île-de-France

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.000565	0.000013	0.000542	0.000592
i0	2000	0.2403	0.0154	0.2104	0.2697
R0	2000	6.5734	1.1141	4.4018	8.7178
beta	2000	0.3415	0.0323	0.2812	0.4040
gamma	2000	0.0527	0.00451	0.0448	0.0620

MCMC analysis of regions

The MCMC Procedure

country=FRA region_code=11 region_name=Île-de-France

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	3.282E-7	0.000013	0.0249
i0	0.000344	0.0154	0.0224
R0	0.0254	1.1141	0.0228
beta	0.000722	0.0323	0.0224
gamma	0.000104	0.00451	0.0232

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.0437	0.0021	0.0171	0.0181
i0	0.0063	-0.0066	0.0033	-0.0224
R0	0.0179	-0.0131	0.0272	0.0432
beta	-0.0012	-0.0051	0.0522	0.0465
gamma	0.0360	-0.0383	-0.0110	0.0291

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	-0.4609	0.6449
i0	0.3581	0.7203
R0	-1.3527	0.1762
beta	-1.2207	0.2222
gamma	1.3185	0.1873

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	.	.	Failed	.	.	.	.
i0	0.2112	0.2469	Passed	0	0.000632	0.2403	0.00263	Passed
R0	0.0624	0.7992	Passed	0	0.0501	6.5734	0.00762	Passed
beta	0.1048	0.5617	Passed	0	0.00143	0.3415	0.00418	Passed
gamma	0.0632	0.7938	Passed	0	0.000197	0.0527	0.00375	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	1612.4	1.2404	0.8062
i0	2000.0	1.0000	1.0000
R0	1930.8	1.0358	0.9654
beta	2000.0	1.0000	1.0000
gamma	1865.6	1.0721	0.9328

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	87.0790	11.3494	63.0000	108.0
int_dec_avg_dot_2	2000	104.7	11.6849	82.0000	127.0
int_dec_avg_dot_3	2000	124.0	11.9991	99.0000	145.0
int_dec_avg_dot_4	2000	144.1	12.5556	118.0	168.0
int_dec_avg_dot_5	2000	163.8	13.7353	136.0	189.0
int_dec_avg_dot_6	2000	181.6	14.7553	154.0	210.0
int_dec_avg_dot_7	2000	196.5	15.1446	166.0	227.0
int_dec_avg_dot_8	2000	208.8	15.5309	176.0	236.0
int_dec_avg_dot_9	2000	216.7	15.5917	185.0	247.0
int_dec_avg_dot_10	2000	221.2	15.4391	192.0	252.0
int_dec_avg_dot_11	2000	223.0	15.5209	195.0	255.0
int_dec_avg_dot_12	2000	221.0	15.4215	191.0	252.0
int_dec_avg_dot_13	2000	218.4	15.3058	190.0	249.0
int_dec_avg_dot_14	2000	213.1	14.9402	185.0	242.0
int_dec_avg_dot_15	2000	206.4	15.1645	176.0	234.0
int_dec_avg_dot_16	2000	199.7	15.3691	170.0	229.0
int_dec_avg_dot_17	2000	192.4	14.3747	163.0	218.0
int_dec_avg_dot_18	2000	184.8	14.3721	154.0	211.0
int_dec_avg_dot_19	2000	176.8	14.1078	148.0	203.0
int_dec_avg_dot_20	2000	169.7	13.6238	141.0	195.0
int_dec_avg_dot_21	2000	162.1	13.2822	135.0	186.0
int_dec_avg_dot_22	2000	153.9	12.9643	129.0	178.0
int_dec_avg_dot_23	2000	147.0	12.3889	124.0	172.0
int_dec_avg_dot_24	2000	139.6	12.1552	117.0	164.0
int_dec_avg_dot_25	2000	133.5	12.0186	110.0	156.0
int_dec_avg_dot_26	2000	127.2	11.4009	106.0	150.0
int_dec_avg_dot_27	2000	120.2	11.1646	98.0000	141.0
int_dec_avg_dot_28	2000	114.7	11.1145	94.0000	136.0
int_dec_avg_dot_29	2000	109.2	10.5654	89.0000	130.0
int_dec_avg_dot_30	2000	103.3	10.6075	81.0000	122.0
int_dec_avg_dot_31	2000	98.1800	10.1852	79.0000	118.0
int_dec_avg_dot_32	2000	93.1295	9.8269	73.0000	111.0
int_dec_avg_dot_33	2000	88.3060	9.5861	67.0000	104.0
int_dec_avg_dot_34	2000	83.8290	9.4829	66.0000	102.0
int_dec_avg_dot_35	2000	79.6955	9.3635	60.0000	97.0000
int_dec_avg_dot_36	2000	75.7950	9.0099	59.0000	94.0000
int_dec_avg_dot_37	2000	71.5545	8.9971	54.0000	88.0000
int_dec_avg_dot_38	2000	67.9040	8.7314	50.0000	84.0000
int_dec_avg_dot_39	2000	64.5390	8.5922	48.0000	81.0000
int_dec_avg_dot_40	2000	61.0985	8.4474	44.0000	77.0000

MCMC analysis of regions

The MCMC Procedure

country=FRA region_code=11 region_name=Île-de-France

MCMC analysis of regions

The MCMC Procedure

country=FRA region_code=32 region_name=Hauts-de-France

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000220
2	1	0.6020	0.0265
3	1	0.2536	0.3556

Burn-In History
Block	Scale	Acceptance Rate
1	0.2536	0.3496

Sampling History
Block	Scale	Acceptance Rate
1	0.2536	0.3542

MCMC analysis of regions

The MCMC Procedure

country=FRA region_code=32 region_name=Hauts-de-France

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.000273	0.000010	0.000255	0.000293
i0	2000	0.0387	0.00579	0.0271	0.0495
R0	2000	5.0371	0.8531	3.4261	6.7114
beta	2000	0.2916	0.0158	0.2624	0.3225
gamma	2000	0.0593	0.00883	0.0432	0.0765

MCMC analysis of regions

The MCMC Procedure

country=FRA region_code=32 region_name=Hauts-de-France

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	2.341E-7	0.000010	0.0232
i0	0.000135	0.00579	0.0234
R0	0.0183	0.8531	0.0214
beta	0.000351	0.0158	0.0223
gamma	0.000202	0.00883	0.0229

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.0381	-0.0391	-0.0060	-0.0048
i0	0.0265	-0.0311	-0.0171	-0.0092
R0	0.0483	0.0049	0.0096	0.0062
beta	0.0134	-0.0272	0.0019	0.0034
gamma	0.0730	0.0111	-0.0065	0.0041

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	0.4128	0.6797
i0	0.8427	0.3994
R0	0.3844	0.7007
beta	-0.2647	0.7912
gamma	-0.7820	0.4342

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	.	.	Failed	.	.	.	.
i0	0.1016	0.5772	Passed	0	0.000272	0.0387	0.00703	Passed
R0	0.0283	0.9814	Passed	0	0.0319	5.0371	0.00632	Passed
beta	0.0356	0.9544	Passed	0	0.000684	0.2916	0.00235	Passed
gamma	0.0688	0.7587	Passed	0	0.000375	0.0593	0.00632	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	1858.3	1.0763	0.9291
i0	1831.2	1.0922	0.9156
R0	2183.8	0.9158	1.0919
beta	2014.5	0.9928	1.0072
gamma	1909.3	1.0475	0.9547

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	3.7270	1.9787	0	7.0000
int_dec_avg_dot_2	2000	4.4825	2.2186	0	8.0000
int_dec_avg_dot_3	2000	5.6190	2.5016	1.0000	10.0000
int_dec_avg_dot_4	2000	6.6655	2.7281	1.0000	11.0000
int_dec_avg_dot_5	2000	8.0295	2.9942	2.0000	13.0000
int_dec_avg_dot_6	2000	9.7035	3.2462	4.0000	16.0000
int_dec_avg_dot_7	2000	11.6275	3.6208	4.0000	18.0000
int_dec_avg_dot_8	2000	13.9280	3.8986	6.0000	21.0000
int_dec_avg_dot_9	2000	16.1515	4.2187	8.0000	24.0000
int_dec_avg_dot_10	2000	19.2305	4.4803	10.0000	27.0000
int_dec_avg_dot_11	2000	22.1450	4.7908	13.0000	31.0000
int_dec_avg_dot_12	2000	25.5980	5.1847	14.0000	34.0000
int_dec_avg_dot_13	2000	28.8365	5.6547	18.0000	39.0000
int_dec_avg_dot_14	2000	32.1140	5.9968	20.0000	43.0000
int_dec_avg_dot_15	2000	35.4680	6.2574	23.0000	47.0000
int_dec_avg_dot_16	2000	38.3040	6.4929	25.0000	50.0000
int_dec_avg_dot_17	2000	41.3610	6.8120	28.0000	54.0000
int_dec_avg_dot_18	2000	43.2715	6.9633	30.0000	57.0000
int_dec_avg_dot_19	2000	45.3315	7.0086	31.0000	58.0000
int_dec_avg_dot_20	2000	46.7500	7.1048	33.0000	60.0000
int_dec_avg_dot_21	2000	47.6760	7.2612	33.0000	61.0000
int_dec_avg_dot_22	2000	47.8125	7.1852	34.0000	61.0000
int_dec_avg_dot_23	2000	47.3650	6.9993	34.0000	61.0000
int_dec_avg_dot_24	2000	46.8805	7.2438	32.0000	60.0000
int_dec_avg_dot_25	2000	46.0065	7.2664	32.0000	60.0000
int_dec_avg_dot_26	2000	45.1215	7.0079	30.0000	57.0000
int_dec_avg_dot_27	2000	43.3485	7.1947	28.0000	56.0000
int_dec_avg_dot_28	2000	42.3305	6.7371	28.0000	54.0000
int_dec_avg_dot_29	2000	40.9105	6.5501	26.0000	52.0000
int_dec_avg_dot_30	2000	38.9915	6.5310	26.0000	51.0000
int_dec_avg_dot_31	2000	37.6970	6.3533	25.0000	49.0000
int_dec_avg_dot_32	2000	35.9860	6.1486	23.0000	47.0000
int_dec_avg_dot_33	2000	34.4500	6.0388	24.0000	47.0000
int_dec_avg_dot_34	2000	32.7535	5.8541	22.0000	44.0000
int_dec_avg_dot_35	2000	31.2210	5.7162	19.0000	41.0000
int_dec_avg_dot_36	2000	29.7795	5.5093	19.0000	40.0000
int_dec_avg_dot_37	2000	28.1590	5.2748	18.0000	38.0000
int_dec_avg_dot_38	2000	26.6940	5.4903	16.0000	37.0000
int_dec_avg_dot_39	2000	25.4545	5.1138	16.0000	35.0000
int_dec_avg_dot_40	2000	23.9120	5.0498	15.0000	34.0000
int_dec_avg_dot_41	2000	22.8570	4.7813	13.0000	31.0000
int_dec_avg_dot_42	2000	21.5330	4.7654	12.0000	30.0000
int_dec_avg_dot_43	2000	20.4305	4.7329	11.0000	29.0000
int_dec_avg_dot_44	2000	19.4305	4.4153	10.0000	27.0000
int_dec_avg_dot_45	2000	18.3420	4.5139	10.0000	27.0000
int_dec_avg_dot_46	2000	17.3105	4.4347	8.0000	25.0000
int_dec_avg_dot_47	2000	16.4175	4.2133	8.0000	24.0000
int_dec_avg_dot_48	2000	15.5225	3.9762	8.0000	23.0000
int_dec_avg_dot_49	2000	14.6200	4.0305	5.0000	21.0000
int_dec_avg_dot_50	2000	13.9760	3.9624	6.0000	21.0000

MCMC analysis of regions

The MCMC Procedure

country=FRA region_code=32 region_name=Hauts-de-France

MCMC analysis of regions

The MCMC Procedure

country=FRA region_code=44 region_name=Grand Est

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000340
2	1	0.6208	0.00860
3	1	0.2208	0.2976

Burn-In History
Block	Scale	Acceptance Rate
1	0.2208	0.2973

Sampling History
Block	Scale	Acceptance Rate
1	0.2208	0.3008

MCMC analysis of regions

The MCMC Procedure

country=FRA region_code=44 region_name=Grand Est

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.000551	0.000011	0.000532	0.000572
i0	2000	0.3722	0.0252	0.3234	0.4214
R0	2000	6.0669	1.0298	4.2226	8.2106
beta	2000	0.3040	0.0332	0.2396	0.3675
gamma	2000	0.0507	0.00388	0.0436	0.0583

MCMC analysis of regions

The MCMC Procedure

country=FRA region_code=44 region_name=Grand Est

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	2.425E-7	0.000011	0.0224
i0	0.000534	0.0252	0.0212
R0	0.0230	1.0298	0.0224
beta	0.000673	0.0332	0.0203
gamma	0.000081	0.00388	0.0208

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.0093	-0.0143	0.0232	-0.0212
i0	-0.0139	0.0072	-0.0316	-0.0268
R0	-0.0063	-0.0191	-0.0099	-0.0072
beta	-0.0222	-0.0211	-0.0210	-0.0032
gamma	0.0147	-0.0116	0.0086	-0.0035

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	.	.
i0	0.3920	0.6950
R0	1.4600	0.1443
beta	1.5843	0.1131
gamma	-0.6158	0.5380

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	.	.	Failed	.	.	.	.
i0	0.1008	0.5808	Passed	0	0.000918	0.3722	0.00247	Passed
R0	0.1776	0.3154	Passed	0	0.0420	6.0669	0.00693	Passed
beta	0.1852	0.2981	Passed	0	0.00129	0.3040	0.00426	Passed
gamma	0.1167	0.5088	Passed	0	0.000160	0.0507	0.00315	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	2000.0	1.0000	1.0000
i0	2234.5	0.8951	1.1173
R0	2000.0	1.0000	1.0000
beta	2435.5	0.8212	1.2178
gamma	2302.0	0.8688	1.1510

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	57.8305	8.5359	41.0000	74.0000
int_dec_avg_dot_2	2000	57.5745	8.4257	41.0000	73.0000
int_dec_avg_dot_3	2000	65.4290	8.6248	49.0000	82.0000
int_dec_avg_dot_4	2000	65.1850	8.8438	48.0000	81.0000
int_dec_avg_dot_5	2000	73.2630	8.9188	56.0000	90.0000
int_dec_avg_dot_6	2000	73.1520	8.8773	56.0000	90.0000
int_dec_avg_dot_7	2000	79.8310	9.4684	60.0000	97.0000
int_dec_avg_dot_8	2000	79.9400	9.1954	62.0000	98.0000
int_dec_avg_dot_9	2000	86.1945	9.7576	66.0000	104.0
int_dec_avg_dot_10	2000	85.8695	9.6188	66.0000	103.0
int_dec_avg_dot_11	2000	90.8370	9.8033	71.0000	109.0
int_dec_avg_dot_12	2000	91.3000	9.7961	73.0000	110.0
int_dec_avg_dot_13	2000	94.2475	10.0104	74.0000	113.0
int_dec_avg_dot_14	2000	94.4790	9.9531	75.0000	113.0
int_dec_avg_dot_15	2000	96.1300	10.2320	76.0000	115.0
int_dec_avg_dot_16	2000	96.1535	10.0629	75.0000	114.0
int_dec_avg_dot_17	2000	96.9240	10.0633	78.0000	117.0
int_dec_avg_dot_18	2000	97.0635	10.2615	76.0000	116.0
int_dec_avg_dot_19	2000	96.3955	10.4501	74.0000	115.0
int_dec_avg_dot_20	2000	96.7400	10.0585	74.0000	114.0
int_dec_avg_dot_21	2000	95.8430	10.0329	78.0000	116.0
int_dec_avg_dot_22	2000	95.1015	10.0868	76.0000	114.0
int_dec_avg_dot_23	2000	93.7785	9.7170	72.0000	110.0
int_dec_avg_dot_24	2000	93.3830	10.0739	74.0000	113.0
int_dec_avg_dot_25	2000	91.2325	9.8106	73.0000	110.0
int_dec_avg_dot_26	2000	91.3665	9.6362	72.0000	109.0
int_dec_avg_dot_27	2000	88.5785	9.7658	69.0000	106.0
int_dec_avg_dot_28	2000	88.5770	9.5007	69.0000	106.0
int_dec_avg_dot_29	2000	85.6255	9.6739	64.0000	103.0
int_dec_avg_dot_30	2000	85.3400	9.5426	67.0000	103.0
int_dec_avg_dot_31	2000	82.7970	9.2480	66.0000	102.0
int_dec_avg_dot_32	2000	82.5905	9.2651	62.0000	98.0000
int_dec_avg_dot_33	2000	79.0420	9.0516	60.0000	95.0000
int_dec_avg_dot_34	2000	79.5075	9.1325	62.0000	97.0000
int_dec_avg_dot_35	2000	76.1510	9.1618	56.0000	92.0000
int_dec_avg_dot_36	2000	76.1965	9.1549	56.0000	92.0000
int_dec_avg_dot_37	2000	73.1040	8.4385	55.0000	88.0000
int_dec_avg_dot_38	2000	73.1785	8.4828	56.0000	89.0000
int_dec_avg_dot_39	2000	69.8950	8.5924	52.0000	86.0000
int_dec_avg_dot_40	2000	69.9610	8.5784	53.0000	86.0000
int_dec_avg_dot_41	2000	66.5425	8.3030	50.0000	82.0000
int_dec_avg_dot_42	2000	66.8040	8.2971	49.0000	82.0000
int_dec_avg_dot_43	2000	63.8955	8.1405	48.0000	79.0000
int_dec_avg_dot_44	2000	63.7580	8.0073	47.0000	78.0000
int_dec_avg_dot_45	2000	60.7300	7.8460	45.0000	75.0000
int_dec_avg_dot_46	2000	60.4725	8.0156	45.0000	76.0000
int_dec_avg_dot_47	2000	58.1160	7.7377	44.0000	73.0000
int_dec_avg_dot_48	2000	58.1310	7.7863	43.0000	73.0000
int_dec_avg_dot_49	2000	55.2755	7.6461	41.0000	70.0000
int_dec_avg_dot_50	2000	55.3060	7.3134	40.0000	69.0000
int_dec_avg_dot_51	2000	52.5970	7.5815	37.0000	66.0000
int_dec_avg_dot_52	2000	52.6040	7.1133	37.0000	65.0000
int_dec_avg_dot_53	2000	50.0265	7.2730	33.0000	62.0000
int_dec_avg_dot_54	2000	50.1315	7.1736	34.0000	62.0000
int_dec_avg_dot_55	2000	48.0225	7.0680	35.0000	62.0000
int_dec_avg_dot_56	2000	47.7700	6.9275	35.0000	62.0000
int_dec_avg_dot_57	2000	45.3985	7.0409	31.0000	58.0000
int_dec_avg_dot_58	2000	45.3540	6.7093	32.0000	58.0000
int_dec_avg_dot_59	2000	43.3440	6.4494	31.0000	55.0000
int_dec_avg_dot_60	2000	43.4250	6.6817	30.0000	56.0000
int_dec_avg_dot_61	2000	41.0905	6.7039	28.0000	54.0000
int_dec_avg_dot_62	2000	41.2185	6.7607	26.0000	53.0000
int_dec_avg_dot_63	2000	39.2990	6.4243	25.0000	50.0000
int_dec_avg_dot_64	2000	39.3715	6.3563	27.0000	51.0000
int_dec_avg_dot_65	2000	37.4680	6.2236	25.0000	49.0000
int_dec_avg_dot_66	2000	37.3115	6.1214	25.0000	48.0000
int_dec_avg_dot_67	2000	35.4200	6.0274	22.0000	46.0000
int_dec_avg_dot_68	2000	35.5190	6.1086	24.0000	47.0000
int_dec_avg_dot_69	2000	33.5790	5.8073	22.0000	44.0000
int_dec_avg_dot_70	2000	33.7630	5.9737	22.0000	45.0000
int_dec_avg_dot_71	2000	32.2620	5.7742	21.0000	43.0000
int_dec_avg_dot_72	2000	32.0720	5.7858	22.0000	44.0000
int_dec_avg_dot_73	2000	30.5775	5.8366	19.0000	41.0000
int_dec_avg_dot_74	2000	30.5995	5.6077	20.0000	41.0000
int_dec_avg_dot_75	2000	29.0000	5.4917	17.0000	38.0000
int_dec_avg_dot_76	2000	29.2175	5.5461	18.0000	39.0000
int_dec_avg_dot_77	2000	27.4645	5.4817	16.0000	37.0000
int_dec_avg_dot_78	2000	27.3285	5.5570	17.0000	38.0000
int_dec_avg_dot_79	2000	26.3050	5.2086	16.0000	36.0000
int_dec_avg_dot_80	2000	26.3815	5.2145	16.0000	36.0000
int_dec_avg_dot_81	2000	24.9960	5.1032	15.0000	34.0000
int_dec_avg_dot_82	2000	24.8375	5.1165	14.0000	34.0000
int_dec_avg_dot_83	2000	23.6875	5.1141	14.0000	33.0000
int_dec_avg_dot_84	2000	23.8355	5.0438	14.0000	33.0000
int_dec_avg_dot_85	2000	22.4000	4.9488	13.0000	32.0000
int_dec_avg_dot_86	2000	22.5920	4.8177	14.0000	32.0000

MCMC analysis of regions

The MCMC Procedure

country=FRA region_code=44 region_name=Grand Est

MCMC analysis of regions

The MCMC Procedure

country=GER region_code=5 region_name=Nordrhein-Westfalen

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000640
2	1	0.6515	0.00178
3	1	0.1949	0.0745
4	1	0.1021	0.4250

Burn-In History
Block	Scale	Acceptance Rate
1	0.1021	0.4044

Sampling History
Block	Scale	Acceptance Rate
1	0.1021	0.4263

MCMC analysis of regions

The MCMC Procedure

country=GER region_code=5 region_name=Nordrhein-Westfalen

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.000113	0.000023	0.000082	0.000162
i0	2000	0.00475	0.00162	0.00158	0.00775
R0	2000	1.6916	0.2301	1.2448	2.1053
beta	2000	0.5162	0.1012	0.3890	0.7356
gamma	2000	0.3185	0.1112	0.1628	0.5549

MCMC analysis of regions

The MCMC Procedure

country=GER region_code=5 region_name=Nordrhein-Westfalen

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	1.408E-6	0.000023	0.0608
i0	0.000087	0.00162	0.0536
R0	0.0122	0.2301	0.0530
beta	0.00634	0.1012	0.0627
gamma	0.00691	0.1112	0.0622

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.7368	0.2606	0.0748	-0.0334
i0	0.6057	0.1794	0.0583	-0.0165
R0	0.6308	0.1927	0.0366	-0.0152
beta	0.7555	0.2768	0.0961	-0.0406
gamma	0.7515	0.2743	0.0916	-0.0382

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	2.3084	0.0210
i0	-2.7632	0.0057
R0	-2.5643	0.0103
beta	2.1008	0.0357
gamma	2.1363	0.0327

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	0.2537	0.1837	Passed	0	2.965E-6	0.000113	0.0263	Passed
i0	0.2588	0.1775	Passed	0	0.000185	0.00475	0.0390	Passed
R0	0.1989	0.2696	Passed	0	0.0258	1.6916	0.0153	Passed
beta	0.2288	0.2180	Passed	0	0.0136	0.5162	0.0263	Passed
gamma	0.2270	0.2208	Passed	0	0.0148	0.3185	0.0464	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	270.7	7.3871	0.1354
i0	347.9	5.7495	0.1739
R0	355.4	5.6276	0.1777
beta	254.7	7.8524	0.1273
gamma	258.5	7.7361	0.1293

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	2.6745	1.6971	0	6.0000
int_dec_avg_dot_2	2000	3.2170	1.8143	0	6.0000
int_dec_avg_dot_3	2000	3.7615	2.0094	0	7.0000
int_dec_avg_dot_4	2000	4.4785	2.1626	0	8.0000
int_dec_avg_dot_5	2000	5.4760	2.4156	1.0000	10.0000
int_dec_avg_dot_6	2000	6.3295	2.5786	1.0000	11.0000
int_dec_avg_dot_7	2000	7.7940	2.8001	3.0000	13.0000
int_dec_avg_dot_8	2000	9.0220	3.0593	4.0000	15.0000
int_dec_avg_dot_9	2000	10.6075	3.4730	4.0000	17.0000
int_dec_avg_dot_10	2000	12.5370	3.6684	5.0000	19.0000
int_dec_avg_dot_11	2000	14.7215	4.0262	6.0000	22.0000
int_dec_avg_dot_12	2000	17.1845	4.2679	9.0000	25.0000
int_dec_avg_dot_13	2000	19.9195	4.4985	10.0000	28.0000
int_dec_avg_dot_14	2000	23.1115	4.8990	14.0000	32.0000
int_dec_avg_dot_15	2000	26.3480	5.3393	15.0000	36.0000
int_dec_avg_dot_16	2000	30.0485	5.7120	20.0000	42.0000
int_dec_avg_dot_17	2000	33.9285	6.0722	20.0000	44.0000
int_dec_avg_dot_18	2000	37.8290	6.3902	26.0000	50.0000
int_dec_avg_dot_19	2000	41.9250	7.0404	28.0000	55.0000
int_dec_avg_dot_20	2000	45.8795	7.0204	32.0000	59.0000
int_dec_avg_dot_21	2000	49.2590	7.3404	35.0000	63.0000
int_dec_avg_dot_22	2000	52.2245	7.4377	37.0000	66.0000
int_dec_avg_dot_23	2000	54.7345	7.7832	40.0000	69.0000
int_dec_avg_dot_24	2000	56.4175	7.7294	42.0000	71.0000
int_dec_avg_dot_25	2000	57.1545	8.0430	41.0000	72.0000
int_dec_avg_dot_26	2000	57.2480	7.9306	40.0000	71.0000
int_dec_avg_dot_27	2000	56.5580	7.7773	40.0000	70.0000
int_dec_avg_dot_28	2000	54.8480	7.5807	40.0000	69.0000
int_dec_avg_dot_29	2000	52.8505	7.5066	38.0000	67.0000
int_dec_avg_dot_30	2000	50.1485	7.4433	35.0000	64.0000
int_dec_avg_dot_31	2000	46.9110	7.1843	33.0000	60.0000
int_dec_avg_dot_32	2000	43.6255	6.8865	30.0000	56.0000
int_dec_avg_dot_33	2000	39.7550	6.7330	27.0000	52.0000
int_dec_avg_dot_34	2000	36.0585	6.2235	23.0000	47.0000
int_dec_avg_dot_35	2000	32.3905	5.7919	20.0000	42.0000
int_dec_avg_dot_36	2000	29.1260	5.5841	19.0000	40.0000
int_dec_avg_dot_37	2000	26.2020	5.1128	15.0000	35.0000
int_dec_avg_dot_38	2000	23.1040	4.9547	13.0000	32.0000
int_dec_avg_dot_39	2000	20.2825	4.5994	12.0000	29.0000
int_dec_avg_dot_40	2000	17.6980	4.4140	9.0000	26.0000
int_dec_avg_dot_41	2000	15.5765	4.0489	7.0000	23.0000
int_dec_avg_dot_42	2000	13.5945	3.6546	6.0000	20.0000
int_dec_avg_dot_43	2000	11.7800	3.4747	5.0000	18.0000
int_dec_avg_dot_44	2000	10.4205	3.2590	4.0000	16.0000
int_dec_avg_dot_45	2000	8.9265	3.1351	2.0000	14.0000
int_dec_avg_dot_46	2000	7.7010	2.7478	2.0000	12.0000
int_dec_avg_dot_47	2000	6.6645	2.7046	2.0000	12.0000
int_dec_avg_dot_48	2000	5.8010	2.3963	1.0000	10.0000
int_dec_avg_dot_49	2000	4.9710	2.2629	1.0000	9.0000
int_dec_avg_dot_50	2000	4.3050	2.1103	1.0000	8.0000
int_dec_avg_dot_51	2000	3.7235	2.0005	0	7.0000
int_dec_avg_dot_52	2000	3.2265	1.8593	0	7.0000
int_dec_avg_dot_53	2000	2.7550	1.7121	0	6.0000
int_dec_avg_dot_54	2000	2.3310	1.5702	0	5.0000
int_dec_avg_dot_55	2000	2.0265	1.4580	0	5.0000
int_dec_avg_dot_56	2000	1.7410	1.3663	0	4.0000

MCMC analysis of regions

The MCMC Procedure

country=GER region_code=5 region_name=Nordrhein-Westfalen

MCMC analysis of regions

The MCMC Procedure

country=GER region_code=8 region_name=Baden-Württemberg

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000120
2	1	0.5783	0.0133
3	1	0.2184	0.2520
4	1	0.1782	0.5466
5	1	0.2762	0.6156
6	1	0.5142	0.5860
7	1	0.8823	0.5248
8	1	1.2965	0.4512
9	1	1.6084	0.3830

Burn-In History
Block	Scale	Acceptance Rate
1	1.6084	0.3810

Sampling History
Block	Scale	Acceptance Rate
1	1.6084	0.3818

MCMC analysis of regions

The MCMC Procedure

country=GER region_code=8 region_name=Baden-Württemberg

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.000149	9.254E-6	0.000133	0.000168
i0	2000	0.0101	0.00150	0.00697	0.0129
R0	2000	2.4625	0.3228	1.7783	3.0429
beta	2000	0.4021	0.0177	0.3722	0.4375
gamma	2000	0.1668	0.0288	0.1181	0.2244

MCMC analysis of regions

The MCMC Procedure

country=GER region_code=8 region_name=Baden-Württemberg

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	2.101E-7	9.254E-6	0.0227
i0	0.000034	0.00150	0.0229
R0	0.00734	0.3228	0.0227
beta	0.000419	0.0177	0.0236
gamma	0.000653	0.0288	0.0227

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.0156	-0.0202	0.0446	-0.0081
i0	0.0257	0.0028	-0.0076	-0.0126
R0	0.0115	-0.0248	0.0539	-0.0197
beta	0.0222	0.0127	-0.0104	-0.0025
gamma	0.0143	-0.0029	0.0373	-0.0132

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	.	.
i0	-0.2109	0.8329
R0	-0.5313	0.5952
beta	-0.3326	0.7394
gamma	0.1131	0.9100

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	.	.	Failed	.	.	.	.
i0	0.1224	0.4859	Passed	0	0.000072	0.0101	0.00716	Passed
R0	0.1780	0.3145	Passed	0	0.0153	2.4625	0.00621	Passed
beta	0.0927	0.6219	Passed	0	0.000858	0.4021	0.00213	Passed
gamma	0.1093	0.5410	Passed	0	0.00138	0.1668	0.00826	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	1939.6	1.0311	0.9698
i0	1902.4	1.0513	0.9512
R0	1934.3	1.0340	0.9672
beta	1795.4	1.1139	0.8977
gamma	1944.4	1.0286	0.9722

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	2.6990	1.6908	0	6.0000
int_dec_avg_dot_2	2000	3.3855	1.9172	0	7.0000
int_dec_avg_dot_3	2000	4.0925	2.0763	1.0000	8.0000
int_dec_avg_dot_4	2000	5.0230	2.3238	1.0000	9.0000
int_dec_avg_dot_5	2000	6.1980	2.5326	2.0000	11.0000
int_dec_avg_dot_6	2000	7.6130	2.8723	2.0000	13.0000
int_dec_avg_dot_7	2000	9.2375	3.1367	2.0000	14.0000
int_dec_avg_dot_8	2000	11.2985	3.4592	5.0000	18.0000
int_dec_avg_dot_9	2000	13.5830	3.7514	7.0000	21.0000
int_dec_avg_dot_10	2000	16.2380	4.1764	7.0000	23.0000
int_dec_avg_dot_11	2000	19.5530	4.5671	11.0000	28.0000
int_dec_avg_dot_12	2000	23.0040	5.0314	12.0000	32.0000
int_dec_avg_dot_13	2000	27.1640	5.5187	17.0000	38.0000
int_dec_avg_dot_14	2000	31.5780	5.8378	20.0000	42.0000
int_dec_avg_dot_15	2000	36.3605	6.4444	23.0000	48.0000
int_dec_avg_dot_16	2000	41.2515	6.8265	27.0000	53.0000
int_dec_avg_dot_17	2000	46.0855	7.1965	30.0000	58.0000
int_dec_avg_dot_18	2000	51.0115	7.5201	36.0000	65.0000
int_dec_avg_dot_19	2000	55.5530	7.6543	41.0000	70.0000
int_dec_avg_dot_20	2000	59.0415	8.2072	43.0000	75.0000
int_dec_avg_dot_21	2000	61.7925	8.4169	46.0000	78.0000
int_dec_avg_dot_22	2000	63.4240	8.2060	46.0000	78.0000
int_dec_avg_dot_23	2000	64.1720	8.1439	47.0000	78.0000
int_dec_avg_dot_24	2000	63.5225	8.3365	47.0000	79.0000
int_dec_avg_dot_25	2000	62.3235	8.1175	46.0000	77.0000
int_dec_avg_dot_26	2000	60.1125	8.0929	44.0000	75.0000
int_dec_avg_dot_27	2000	57.1555	7.9510	40.0000	71.0000
int_dec_avg_dot_28	2000	53.9465	7.6713	38.0000	67.0000
int_dec_avg_dot_29	2000	50.5785	7.4097	37.0000	65.0000
int_dec_avg_dot_30	2000	46.5770	7.3013	32.0000	60.0000
int_dec_avg_dot_31	2000	42.9675	6.8403	28.0000	55.0000
int_dec_avg_dot_32	2000	39.4395	6.5331	26.0000	51.0000
int_dec_avg_dot_33	2000	35.8460	6.2694	23.0000	47.0000
int_dec_avg_dot_34	2000	32.3865	5.9958	21.0000	44.0000
int_dec_avg_dot_35	2000	29.2485	5.5746	19.0000	40.0000
int_dec_avg_dot_36	2000	26.4245	5.1336	16.0000	36.0000
int_dec_avg_dot_37	2000	23.6210	4.9959	14.0000	33.0000
int_dec_avg_dot_38	2000	21.0310	4.7546	12.0000	30.0000
int_dec_avg_dot_39	2000	18.6505	4.3488	9.0000	26.0000
int_dec_avg_dot_40	2000	16.7475	4.1414	8.0000	24.0000
int_dec_avg_dot_41	2000	14.9355	3.9397	7.0000	22.0000
int_dec_avg_dot_42	2000	13.2935	3.6586	6.0000	20.0000
int_dec_avg_dot_43	2000	11.5735	3.4858	5.0000	18.0000
int_dec_avg_dot_44	2000	10.3055	3.3469	3.0000	16.0000
int_dec_avg_dot_45	2000	9.1070	3.0878	2.0000	14.0000
int_dec_avg_dot_46	2000	8.0455	2.9734	2.0000	13.0000
int_dec_avg_dot_47	2000	7.2755	2.7192	2.0000	12.0000
int_dec_avg_dot_48	2000	6.3565	2.5834	1.0000	11.0000
int_dec_avg_dot_49	2000	5.5525	2.3814	1.0000	10.0000
int_dec_avg_dot_50	2000	4.8975	2.3008	1.0000	9.0000
int_dec_avg_dot_51	2000	4.3060	2.1125	0	8.0000
int_dec_avg_dot_52	2000	3.8570	2.0051	0	7.0000
int_dec_avg_dot_53	2000	3.3100	1.8851	0	7.0000
int_dec_avg_dot_54	2000	2.9855	1.8319	0	6.0000
int_dec_avg_dot_55	2000	2.6600	1.6878	0	6.0000
int_dec_avg_dot_56	2000	2.3090	1.5400	0	5.0000

MCMC analysis of regions

The MCMC Procedure

country=GER region_code=8 region_name=Baden-Württemberg

MCMC analysis of regions

The MCMC Procedure

country=GER region_code=9 region_name=Bayern

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000640
2	1	0.6515	0.00216
3	1	0.1985	0.1135
4	1	0.1172	0.4668
5	1	0.1505	0.6112
6	1	0.2767	0.6230
7	1	0.5261	0.5956
8	1	0.9265	0.5446
9	1	1.4291	0.4496
10	1	1.7666	0.3938

Burn-In History
Block	Scale	Acceptance Rate
1	1.7666	0.3970

Sampling History
Block	Scale	Acceptance Rate
1	1.7666	0.3916

MCMC analysis of regions

The MCMC Procedure

country=GER region_code=9 region_name=Bayern

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.000160	4.909E-6	0.000151	0.000170
i0	2000	0.00733	0.000900	0.00558	0.00903
R0	2000	3.2071	0.3653	2.5329	3.9791
beta	2000	0.4027	0.0101	0.3845	0.4238
gamma	2000	0.1271	0.0145	0.1006	0.1549

MCMC analysis of regions

The MCMC Procedure

country=GER region_code=9 region_name=Bayern

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	1.098E-7	4.909E-6	0.0224
i0	0.000021	0.000900	0.0233
R0	0.00847	0.3653	0.0232
beta	0.000236	0.0101	0.0234
gamma	0.000324	0.0145	0.0224

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.0048	-0.0322	0.0109	-0.0146
i0	0.0413	0.0149	-0.0311	-0.0182
R0	0.0200	0.0061	0.0397	0.0108
beta	0.0256	0.0122	-0.0363	-0.0057
gamma	-0.0031	-0.0024	0.0450	-0.0000

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	.	.
i0	-0.1161	0.9075
R0	1.6882	0.0914
beta	0.4338	0.6644
gamma	-1.3056	0.1917

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	.	.	Failed	.	.	.	.
i0	0.0258	0.9879	Passed	0	0.000036	0.00733	0.00492	Passed
R0	0.3570	0.0941	Passed	0	0.0177	3.2071	0.00552	Passed
beta	0.1214	0.4898	Passed	0	0.000476	0.4027	0.00118	Passed
gamma	0.2862	0.1480	Passed	0	0.000657	0.1271	0.00517	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	2000.0	1.0000	1.0000
i0	1847.5	1.0825	0.9238
R0	1862.2	1.0740	0.9311
beta	1825.6	1.0956	0.9128
gamma	2000.0	1.0000	1.0000

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	1.9425	1.4263	0	5.0000
int_dec_avg_dot_2	2000	2.4795	1.6658	0	6.0000
int_dec_avg_dot_3	2000	3.1340	1.8592	0	6.0000
int_dec_avg_dot_4	2000	4.0170	2.1052	1.0000	8.0000
int_dec_avg_dot_5	2000	5.0255	2.3475	0	9.0000
int_dec_avg_dot_6	2000	6.4040	2.6223	1.0000	11.0000
int_dec_avg_dot_7	2000	8.0680	2.9041	2.0000	13.0000
int_dec_avg_dot_8	2000	10.0395	3.3781	3.0000	16.0000
int_dec_avg_dot_9	2000	12.6585	3.6610	5.0000	19.0000
int_dec_avg_dot_10	2000	15.8055	4.0796	7.0000	23.0000
int_dec_avg_dot_11	2000	19.5390	4.6380	10.0000	28.0000
int_dec_avg_dot_12	2000	24.1120	5.2855	15.0000	35.0000
int_dec_avg_dot_13	2000	29.7315	5.5399	19.0000	40.0000
int_dec_avg_dot_14	2000	35.7115	6.2812	24.0000	48.0000
int_dec_avg_dot_15	2000	42.6940	6.9015	29.0000	55.0000
int_dec_avg_dot_16	2000	50.0115	7.4540	36.0000	64.0000
int_dec_avg_dot_17	2000	57.8585	8.0565	41.0000	72.0000
int_dec_avg_dot_18	2000	65.8235	8.6122	49.0000	81.0000
int_dec_avg_dot_19	2000	72.5365	9.1454	55.0000	90.0000
int_dec_avg_dot_20	2000	79.2890	9.7575	59.0000	97.0000
int_dec_avg_dot_21	2000	84.2305	9.9114	65.0000	103.0
int_dec_avg_dot_22	2000	88.1620	10.0839	67.0000	106.0
int_dec_avg_dot_23	2000	89.2200	9.8595	68.0000	106.0
int_dec_avg_dot_24	2000	89.2930	9.8111	69.0000	107.0
int_dec_avg_dot_25	2000	87.9855	9.7693	68.0000	106.0
int_dec_avg_dot_26	2000	85.0980	9.3681	68.0000	105.0
int_dec_avg_dot_27	2000	81.0230	9.5514	64.0000	100.0
int_dec_avg_dot_28	2000	76.8525	9.3072	58.0000	94.0000
int_dec_avg_dot_29	2000	72.1055	8.9141	55.0000	89.0000
int_dec_avg_dot_30	2000	66.9580	8.6773	51.0000	84.0000
int_dec_avg_dot_31	2000	62.0180	8.1231	45.0000	76.0000
int_dec_avg_dot_32	2000	56.5775	7.9537	42.0000	72.0000
int_dec_avg_dot_33	2000	51.7560	7.6633	36.0000	65.0000
int_dec_avg_dot_34	2000	46.9905	7.1092	33.0000	60.0000
int_dec_avg_dot_35	2000	42.9970	6.6491	28.0000	54.0000
int_dec_avg_dot_36	2000	38.8650	6.5009	26.0000	51.0000
int_dec_avg_dot_37	2000	35.0380	6.0571	24.0000	47.0000
int_dec_avg_dot_38	2000	31.2555	5.9133	18.0000	41.0000
int_dec_avg_dot_39	2000	28.4575	5.4892	17.0000	38.0000
int_dec_avg_dot_40	2000	25.5815	5.0947	14.0000	34.0000
int_dec_avg_dot_41	2000	22.9745	4.8070	12.0000	31.0000
int_dec_avg_dot_42	2000	20.3830	4.6543	10.0000	28.0000
int_dec_avg_dot_43	2000	18.3575	4.3955	10.0000	26.0000
int_dec_avg_dot_44	2000	16.3710	4.2248	8.0000	24.0000
int_dec_avg_dot_45	2000	14.7195	3.9282	7.0000	22.0000
int_dec_avg_dot_46	2000	13.0355	3.7165	6.0000	20.0000
int_dec_avg_dot_47	2000	11.8155	3.4686	5.0000	18.0000
int_dec_avg_dot_48	2000	10.5240	3.3644	4.0000	16.0000
int_dec_avg_dot_49	2000	9.4820	3.1255	3.0000	15.0000
int_dec_avg_dot_50	2000	8.4735	2.9548	3.0000	14.0000
int_dec_avg_dot_51	2000	7.4415	2.7750	2.0000	12.0000
int_dec_avg_dot_52	2000	6.7725	2.7128	1.0000	11.0000
int_dec_avg_dot_53	2000	6.0265	2.4294	1.0000	10.0000
int_dec_avg_dot_54	2000	5.4350	2.3809	1.0000	10.0000
int_dec_avg_dot_55	2000	4.8265	2.2235	1.0000	9.0000
int_dec_avg_dot_56	2000	4.2870	2.0656	1.0000	8.0000

MCMC analysis of regions

The MCMC Procedure

country=GER region_code=9 region_name=Bayern

MCMC analysis of regions

The MCMC Procedure

country=ITA region_code=01 region_name=Piemonte

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000220
2	1	0.6020	0.00632
3	1	0.2060	0.2159
4	1	0.1556	0.4977
5	1	0.2145	0.5687
6	1	0.3517	0.5378
7	1	0.5335	0.4448
8	1	0.6525	0.3953

Burn-In History
Block	Scale	Acceptance Rate
1	0.6525	0.3832

Sampling History
Block	Scale	Acceptance Rate
1	0.6525	0.4090

MCMC analysis of regions

The MCMC Procedure

country=ITA region_code=01 region_name=Piemonte

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.00105	0.000163	0.000895	0.00134
i0	2000	0.0254	0.00923	0.00795	0.0428
R0	2000	2.2933	0.5579	1.2858	3.3286
beta	2000	0.2305	0.0422	0.1824	0.3072
gamma	2000	0.1102	0.0498	0.0476	0.2054

MCMC analysis of regions

The MCMC Procedure

country=ITA region_code=01 region_name=Piemonte

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	0.000011	0.000163	0.0675
i0	0.000263	0.00923	0.0285
R0	0.0145	0.5579	0.0260
beta	0.00269	0.0422	0.0638
gamma	0.00299	0.0498	0.0602

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.5647	0.3166	0.1992	-0.0448
i0	0.1399	-0.0007	0.0290	-0.0434
R0	0.0810	-0.0160	0.0257	-0.0285
beta	0.5256	0.2776	0.1736	-0.0506
gamma	0.4619	0.2279	0.1534	-0.0509

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	-1.2201	0.2224
i0	1.2730	0.2030
R0	0.9671	0.3335
beta	-1.3111	0.1898
gamma	-1.2678	0.2049

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	0.0650	0.7824	Passed	0	0.000026	0.00105	0.0248	Passed
i0	0.1392	0.4243	Passed	0	0.000630	0.0254	0.0249	Passed
R0	0.1852	0.2981	Passed	0	0.0349	2.2933	0.0152	Passed
beta	0.0683	0.7621	Passed	0	0.00643	0.2305	0.0279	Passed
gamma	0.0740	0.7270	Passed	0	0.00703	0.1102	0.0638	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	219.2	9.1222	0.1096
i0	1231.0	1.6247	0.6155
R0	1477.1	1.3540	0.7386
beta	245.4	8.1491	0.1227
gamma	276.3	7.2385	0.1382

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	10.9710	3.4840	4.0000	17.0000
int_dec_avg_dot_2	2000	12.0770	3.5997	4.0000	18.0000
int_dec_avg_dot_3	2000	13.6365	3.8608	6.0000	21.0000
int_dec_avg_dot_4	2000	15.1460	3.9509	7.0000	22.0000
int_dec_avg_dot_5	2000	16.5295	4.1936	8.0000	24.0000
int_dec_avg_dot_6	2000	18.2115	4.3924	9.0000	26.0000
int_dec_avg_dot_7	2000	20.2940	4.7590	11.0000	29.0000
int_dec_avg_dot_8	2000	22.3545	4.9873	12.0000	31.0000
int_dec_avg_dot_9	2000	24.8490	5.1394	14.0000	34.0000
int_dec_avg_dot_10	2000	27.2840	5.2641	17.0000	37.0000
int_dec_avg_dot_11	2000	29.8795	5.6950	18.0000	40.0000
int_dec_avg_dot_12	2000	32.5535	5.7449	21.0000	43.0000
int_dec_avg_dot_13	2000	35.8650	6.1771	23.0000	47.0000
int_dec_avg_dot_14	2000	38.7330	6.2376	26.0000	50.0000
int_dec_avg_dot_15	2000	42.3820	6.6828	29.0000	55.0000
int_dec_avg_dot_16	2000	45.7705	7.0524	30.0000	58.0000
int_dec_avg_dot_17	2000	49.2715	7.2851	36.0000	64.0000
int_dec_avg_dot_18	2000	53.3550	7.5318	38.0000	67.0000
int_dec_avg_dot_19	2000	56.7270	7.7411	41.0000	71.0000
int_dec_avg_dot_20	2000	60.1040	8.0228	44.0000	75.0000
int_dec_avg_dot_21	2000	63.8640	8.3828	47.0000	80.0000
int_dec_avg_dot_22	2000	67.3700	8.2956	51.0000	83.0000
int_dec_avg_dot_23	2000	70.8605	8.6319	54.0000	87.0000
int_dec_avg_dot_24	2000	73.8560	8.8429	54.0000	89.0000
int_dec_avg_dot_25	2000	76.7925	9.0927	58.0000	93.0000
int_dec_avg_dot_26	2000	79.7400	9.2605	62.0000	96.0000
int_dec_avg_dot_27	2000	81.9245	9.2556	62.0000	99.0000
int_dec_avg_dot_28	2000	83.8915	9.2994	65.0000	101.0
int_dec_avg_dot_29	2000	85.3385	9.4663	66.0000	102.0
int_dec_avg_dot_30	2000	86.6155	9.3949	68.0000	104.0
int_dec_avg_dot_31	2000	87.4150	9.2403	69.0000	104.0
int_dec_avg_dot_32	2000	87.9310	9.6281	69.0000	106.0
int_dec_avg_dot_33	2000	87.7170	9.7187	69.0000	106.0
int_dec_avg_dot_34	2000	87.7790	9.7858	69.0000	106.0
int_dec_avg_dot_35	2000	86.7505	9.5056	68.0000	105.0
int_dec_avg_dot_36	2000	85.4715	9.5884	66.0000	103.0
int_dec_avg_dot_37	2000	84.1285	9.6359	66.0000	103.0
int_dec_avg_dot_38	2000	82.5705	9.3525	64.0000	100.0
int_dec_avg_dot_39	2000	80.5960	9.3383	63.0000	99.0000
int_dec_avg_dot_40	2000	78.7170	9.2434	58.0000	95.0000
int_dec_avg_dot_41	2000	76.0440	8.8328	58.0000	92.0000
int_dec_avg_dot_42	2000	73.6435	8.6199	56.0000	89.0000
int_dec_avg_dot_43	2000	71.1610	8.8545	55.0000	88.0000
int_dec_avg_dot_44	2000	68.1170	8.6347	53.0000	85.0000
int_dec_avg_dot_45	2000	65.6800	8.4256	51.0000	83.0000
int_dec_avg_dot_46	2000	62.7175	8.0810	45.0000	76.0000
int_dec_avg_dot_47	2000	60.0500	8.0792	43.0000	74.0000
int_dec_avg_dot_48	2000	57.0710	7.8157	41.0000	71.0000
int_dec_avg_dot_49	2000	54.9000	7.6881	39.0000	69.0000
int_dec_avg_dot_50	2000	51.9565	7.5427	37.0000	66.0000
int_dec_avg_dot_51	2000	49.5235	7.3634	36.0000	64.0000
int_dec_avg_dot_52	2000	46.9045	7.0428	33.0000	60.0000
int_dec_avg_dot_53	2000	44.6715	7.0014	30.0000	57.0000
int_dec_avg_dot_54	2000	42.1750	6.9133	30.0000	56.0000
int_dec_avg_dot_55	2000	39.5905	6.7495	26.0000	52.0000
int_dec_avg_dot_56	2000	37.3645	6.3786	24.0000	49.0000
int_dec_avg_dot_57	2000	35.2905	6.5332	23.0000	48.0000

MCMC analysis of regions

The MCMC Procedure

country=ITA region_code=01 region_name=Piemonte

MCMC analysis of regions

The MCMC Procedure

country=ITA region_code=03 region_name=Lombardia

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000380
2	1	0.6259	0.000620
3	1	0.1709	0.1013
4	1	0.0975	0.4923
5	1	0.1327	0.6215
6	1	0.2511	0.6254
7	1	0.4807	0.6104
8	1	0.8818	0.5531
9	1	1.3896	0.4755
10	1	1.8201	0.3997

Burn-In History
Block	Scale	Acceptance Rate
1	1.8201	0.3999

Sampling History
Block	Scale	Acceptance Rate
1	1.8201	0.3999

MCMC analysis of regions

The MCMC Procedure

country=ITA region_code=03 region_name=Lombardia

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.00167	0.000019	0.00164	0.00171
i0	2000	0.1281	0.00556	0.1167	0.1382
R0	2000	6.7552	0.3832	5.9764	7.4867
beta	2000	0.2812	0.00853	0.2637	0.2973
gamma	2000	0.0417	0.00141	0.0392	0.0447

MCMC analysis of regions

The MCMC Procedure

country=ITA region_code=03 region_name=Lombardia

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	4.269E-7	0.000019	0.0224
i0	0.000130	0.00556	0.0233
R0	0.00857	0.3832	0.0224
beta	0.000191	0.00853	0.0224
gamma	0.000031	0.00141	0.0224

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.0009	0.0220	0.0319	-0.0158
i0	0.0101	-0.0139	0.0176	0.0277
R0	-0.0008	0.0010	0.0435	-0.0011
beta	-0.0004	-0.0135	0.0342	0.0078
gamma	-0.0098	0.0175	0.0243	-0.0051

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	0.7764	0.4375
i0	0.4395	0.6603
R0	0.5115	0.6090
beta	0.3333	0.7389
gamma	-0.5967	0.5507

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	.	.	Failed	.	.	.	.
i0	0.0599	0.8149	Passed	0	0.000250	0.1281	0.00195	Passed
R0	0.0829	0.6751	Passed	0	0.0184	6.7552	0.00272	Passed
beta	0.0956	0.6071	Passed	0	0.000422	0.2812	0.00150	Passed
gamma	0.0613	0.8059	Passed	0	0.000065	0.0417	0.00156	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	2000.0	1.0000	1.0000
i0	1840.5	1.0867	0.9202
R0	2000.0	1.0000	1.0000
beta	2000.0	1.0000	1.0000
gamma	2000.0	1.0000	1.0000

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	87.5655	10.2640	65.0000	105.0
int_dec_avg_dot_2	2000	104.9	11.1033	83.0000	126.0
int_dec_avg_dot_3	2000	125.5	12.0788	101.0	148.0
int_dec_avg_dot_4	2000	148.3	13.0467	121.0	172.0
int_dec_avg_dot_5	2000	174.5	13.9657	150.0	204.0
int_dec_avg_dot_6	2000	202.0	15.1097	173.0	231.0
int_dec_avg_dot_7	2000	231.0	15.8236	200.0	260.0
int_dec_avg_dot_8	2000	260.2	16.9815	225.0	291.0
int_dec_avg_dot_9	2000	290.7	18.0894	256.0	325.0
int_dec_avg_dot_10	2000	317.8	18.7823	280.0	353.0
int_dec_avg_dot_11	2000	343.6	19.3637	305.0	379.0
int_dec_avg_dot_12	2000	365.2	19.8738	328.0	407.0
int_dec_avg_dot_13	2000	382.8	20.2958	342.0	420.0
int_dec_avg_dot_14	2000	396.0	19.8220	354.0	431.0
int_dec_avg_dot_15	2000	405.5	21.1388	360.0	443.0
int_dec_avg_dot_16	2000	410.6	20.8994	369.0	450.0
int_dec_avg_dot_17	2000	412.4	20.8948	372.0	454.0
int_dec_avg_dot_18	2000	410.7	21.0833	369.0	452.0
int_dec_avg_dot_19	2000	405.7	20.6141	367.0	447.0
int_dec_avg_dot_20	2000	399.5	20.6752	357.0	437.0
int_dec_avg_dot_21	2000	391.5	20.5514	352.0	430.0
int_dec_avg_dot_22	2000	382.0	20.2759	340.0	419.0
int_dec_avg_dot_23	2000	372.0	19.5844	331.0	407.0
int_dec_avg_dot_24	2000	361.0	19.4648	322.0	398.0
int_dec_avg_dot_25	2000	350.2	19.0457	313.0	387.0
int_dec_avg_dot_26	2000	338.6	18.5222	304.0	374.0
int_dec_avg_dot_27	2000	327.5	18.6880	287.0	360.0
int_dec_avg_dot_28	2000	316.4	17.9954	278.0	350.0
int_dec_avg_dot_29	2000	305.3	17.9703	272.0	340.0
int_dec_avg_dot_30	2000	293.8	17.6884	255.0	325.0
int_dec_avg_dot_31	2000	283.0	16.6464	251.0	315.0
int_dec_avg_dot_32	2000	272.1	16.7591	238.0	304.0
int_dec_avg_dot_33	2000	261.6	16.6000	229.0	294.0
int_dec_avg_dot_34	2000	252.0	16.0275	220.0	282.0
int_dec_avg_dot_35	2000	241.8	15.3847	212.0	272.0
int_dec_avg_dot_36	2000	232.7	15.9737	202.0	263.0
int_dec_avg_dot_37	2000	222.6	15.1468	194.0	252.0
int_dec_avg_dot_38	2000	214.4	15.2802	184.0	243.0
int_dec_avg_dot_39	2000	205.4	14.3299	175.0	231.0
int_dec_avg_dot_40	2000	196.8	14.7748	165.0	222.0
int_dec_avg_dot_41	2000	189.6	13.8207	162.0	216.0
int_dec_avg_dot_42	2000	181.9	13.8115	153.0	207.0
int_dec_avg_dot_43	2000	174.3	13.2933	146.0	197.0
int_dec_avg_dot_44	2000	167.4	13.1725	141.0	192.0
int_dec_avg_dot_45	2000	160.7	13.0766	135.0	185.0
int_dec_avg_dot_46	2000	154.0	12.8816	130.0	179.0
int_dec_avg_dot_47	2000	147.6	12.6385	123.0	172.0
int_dec_avg_dot_48	2000	141.8	12.0246	118.0	164.0
int_dec_avg_dot_49	2000	135.6	11.8210	111.0	157.0
int_dec_avg_dot_50	2000	130.7	11.6751	107.0	152.0
int_dec_avg_dot_51	2000	125.0	11.4003	102.0	146.0
int_dec_avg_dot_52	2000	120.5	11.1535	99.0000	142.0
int_dec_avg_dot_53	2000	114.6	10.9413	93.0000	135.0
int_dec_avg_dot_54	2000	110.3	10.8847	88.0000	130.0
int_dec_avg_dot_55	2000	105.9	10.8707	85.0000	127.0
int_dec_avg_dot_56	2000	101.7	10.3110	80.0000	120.0
int_dec_avg_dot_57	2000	97.2085	10.2101	76.0000	116.0

MCMC analysis of regions

The MCMC Procedure

country=ITA region_code=03 region_name=Lombardia

MCMC analysis of regions

The MCMC Procedure

country=ITA region_code=08 region_name=Emilia-Romagna

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000240
2	1	0.6056	0.0152
3	1	0.2332	0.3317

Burn-In History
Block	Scale	Acceptance Rate
1	0.2332	0.3287

Sampling History
Block	Scale	Acceptance Rate
1	0.2332	0.3313

MCMC analysis of regions

The MCMC Procedure

country=ITA region_code=08 region_name=Emilia-Romagna

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.00104	0.000037	0.000965	0.00111
i0	2000	0.1603	0.0150	0.1330	0.1918
R0	2000	7.7059	1.3599	5.3132	10.5080
beta	2000	0.2454	0.0220	0.2017	0.2861
gamma	2000	0.0324	0.00335	0.0263	0.0391

MCMC analysis of regions

The MCMC Procedure

country=ITA region_code=08 region_name=Emilia-Romagna

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	8.06E-7	0.000037	0.0215
i0	0.000340	0.0150	0.0227
R0	0.0306	1.3599	0.0225
beta	0.000490	0.0220	0.0223
gamma	0.000077	0.00335	0.0230

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.0395	-0.0427	0.0099	-0.0040
i0	0.0151	0.0210	0.0267	-0.0069
R0	0.0439	-0.0023	-0.0297	0.0335
beta	0.0420	0.0181	-0.0146	0.0495
gamma	0.0307	-0.0228	-0.0152	0.0015

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	-0.2692	0.7878
i0	0.0603	0.9519
R0	0.1255	0.9001
beta	0.0161	0.9872
gamma	-0.1865	0.8521

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	0.4068	0.0693	Passed	600	1.893E-6	0.00104	0.00182	Passed
i0	0.0589	0.8207	Passed	0	0.000739	0.1603	0.00461	Passed
R0	0.0915	0.6279	Passed	0	0.0568	7.7059	0.00738	Passed
beta	0.0888	0.6426	Passed	0	0.000945	0.2454	0.00385	Passed
gamma	0.0716	0.7418	Passed	0	0.000133	0.0324	0.00411	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	2163.4	0.9245	1.0817
i0	1941.2	1.0303	0.9706
R0	1971.0	1.0147	0.9855
beta	2010.1	0.9950	1.0051
gamma	1884.1	1.0615	0.9421

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	24.1065	5.6353	13.0000	35.0000
int_dec_avg_dot_2	2000	28.0305	5.7640	16.0000	38.0000
int_dec_avg_dot_3	2000	32.7830	6.2791	20.0000	44.0000
int_dec_avg_dot_4	2000	37.7775	6.6537	24.0000	50.0000
int_dec_avg_dot_5	2000	43.1935	6.9852	29.0000	56.0000
int_dec_avg_dot_6	2000	49.1475	7.3337	35.0000	63.0000
int_dec_avg_dot_7	2000	54.9070	7.6435	39.0000	68.0000
int_dec_avg_dot_8	2000	61.1205	8.3737	43.0000	76.0000
int_dec_avg_dot_9	2000	66.7595	8.5318	50.0000	82.0000
int_dec_avg_dot_10	2000	72.9210	8.7365	55.0000	89.0000
int_dec_avg_dot_11	2000	77.7940	9.5383	59.0000	95.0000
int_dec_avg_dot_12	2000	82.4750	9.4824	61.0000	98.0000
int_dec_avg_dot_13	2000	86.0800	10.0364	68.0000	106.0
int_dec_avg_dot_14	2000	89.3735	9.6810	68.0000	106.0
int_dec_avg_dot_15	2000	91.6215	10.0673	72.0000	110.0
int_dec_avg_dot_16	2000	93.3330	10.0730	74.0000	112.0
int_dec_avg_dot_17	2000	94.0965	9.8888	75.0000	112.0
int_dec_avg_dot_18	2000	94.0730	9.9468	75.0000	113.0
int_dec_avg_dot_19	2000	93.8585	9.8732	74.0000	112.0
int_dec_avg_dot_20	2000	93.8980	9.8951	73.0000	112.0
int_dec_avg_dot_21	2000	92.5075	9.7687	73.0000	111.0
int_dec_avg_dot_22	2000	91.3245	9.9501	72.0000	110.0
int_dec_avg_dot_23	2000	90.1455	9.7908	70.0000	108.0
int_dec_avg_dot_24	2000	88.6615	9.5827	70.0000	106.0
int_dec_avg_dot_25	2000	86.5610	9.5903	69.0000	106.0
int_dec_avg_dot_26	2000	84.6800	9.7907	66.0000	103.0
int_dec_avg_dot_27	2000	82.5210	9.3809	63.0000	99.0000
int_dec_avg_dot_28	2000	80.7050	9.0838	63.0000	98.0000
int_dec_avg_dot_29	2000	78.5315	9.3100	60.0000	96.0000
int_dec_avg_dot_30	2000	76.4870	8.9149	59.0000	93.0000
int_dec_avg_dot_31	2000	74.5625	8.9188	57.0000	91.0000
int_dec_avg_dot_32	2000	72.1790	8.5941	55.0000	87.0000
int_dec_avg_dot_33	2000	70.0150	8.6306	51.0000	85.0000
int_dec_avg_dot_34	2000	68.2880	8.1163	53.0000	84.0000
int_dec_avg_dot_35	2000	66.0150	8.2610	49.0000	81.0000
int_dec_avg_dot_36	2000	64.2695	8.1268	48.0000	80.0000
int_dec_avg_dot_37	2000	62.4605	8.1874	45.0000	77.0000
int_dec_avg_dot_38	2000	60.4580	8.0183	45.0000	76.0000
int_dec_avg_dot_39	2000	58.4130	7.8442	44.0000	74.0000
int_dec_avg_dot_40	2000	56.5455	7.5871	41.0000	70.0000
int_dec_avg_dot_41	2000	54.9280	7.6438	40.0000	69.0000
int_dec_avg_dot_42	2000	53.4930	7.5649	38.0000	67.0000
int_dec_avg_dot_43	2000	51.6115	7.3294	37.0000	65.0000
int_dec_avg_dot_44	2000	50.2705	7.0183	36.0000	63.0000
int_dec_avg_dot_45	2000	48.7720	7.1551	34.0000	62.0000
int_dec_avg_dot_46	2000	46.8530	6.9893	33.0000	60.0000
int_dec_avg_dot_47	2000	45.7755	6.9743	31.0000	58.0000
int_dec_avg_dot_48	2000	44.0675	6.9215	29.0000	56.0000
int_dec_avg_dot_49	2000	42.7360	6.6949	29.0000	55.0000
int_dec_avg_dot_50	2000	41.5635	6.6396	27.0000	53.0000
int_dec_avg_dot_51	2000	40.2255	6.5803	26.0000	52.0000
int_dec_avg_dot_52	2000	38.9095	6.3239	26.0000	50.0000
int_dec_avg_dot_53	2000	37.7080	6.3706	26.0000	50.0000
int_dec_avg_dot_54	2000	36.6170	6.3251	23.0000	47.0000
int_dec_avg_dot_55	2000	35.6420	6.2438	23.0000	47.0000
int_dec_avg_dot_56	2000	34.0820	6.0304	23.0000	46.0000
int_dec_avg_dot_57	2000	33.2555	5.9329	21.0000	44.0000

MCMC analysis of regions

The MCMC Procedure

country=ITA region_code=08 region_name=Emilia-Romagna

MCMC analysis of regions

The MCMC Procedure

country=US region_code=MA region_name=Massachusetts

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000440
2	1	0.6328	0.00516
3	1	0.2115	0.1616
4	1	0.1412	0.4710
5	1	0.1831	0.5639
6	1	0.2964	0.5471
7	1	0.4602	0.4396
8	1	0.5564	0.3710

Burn-In History
Block	Scale	Acceptance Rate
1	0.5564	0.3826

Sampling History
Block	Scale	Acceptance Rate
1	0.5564	0.3836

MCMC analysis of regions

The MCMC Procedure

country=US region_code=MA region_name=Massachusetts

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.000988	0.000077	0.000890	0.00113
i0	2000	0.00881	0.00297	0.00249	0.0142
R0	2000	2.7025	0.7358	1.4578	4.0579
beta	2000	0.2915	0.0474	0.2256	0.3859
gamma	2000	0.1199	0.0535	0.0405	0.2250

MCMC analysis of regions

The MCMC Procedure

country=US region_code=MA region_name=Massachusetts

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	3.174E-6	0.000077	0.0413
i0	0.000085	0.00297	0.0287
R0	0.0206	0.7358	0.0280
beta	0.00184	0.0474	0.0388
gamma	0.00203	0.0535	0.0380

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.4493	0.1012	-0.0212	0.0351
i0	0.2052	0.0407	-0.0010	0.0142
R0	0.1909	0.0276	0.0022	0.0176
beta	0.4083	0.0658	-0.0054	0.0511
gamma	0.3915	0.0624	-0.0024	0.0468

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	0.9888	0.3228
i0	-0.4503	0.6525
R0	-0.2425	0.8084
beta	0.8593	0.3902
gamma	0.7908	0.4291

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	0.2213	0.2297	Passed	0	5.837E-6	0.000988	0.00591	Passed
i0	0.0721	0.7389	Passed	0	0.000162	0.00881	0.0184	Passed
R0	0.0801	0.6912	Passed	0	0.0401	2.7025	0.0149	Passed
beta	0.1594	0.3620	Passed	0	0.00332	0.2915	0.0114	Passed
gamma	0.1378	0.4289	Passed	0	0.00367	0.1199	0.0306	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	586.8	3.4081	0.2934
i0	1212.8	1.6490	0.6064
R0	1278.1	1.5648	0.6391
beta	665.2	3.0064	0.3326
gamma	691.3	2.8929	0.3457

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	6.2730	2.5309	2.0000	11.0000
int_dec_avg_dot_2	2000	7.2680	2.7550	2.0000	12.0000
int_dec_avg_dot_3	2000	8.4765	2.9545	3.0000	14.0000
int_dec_avg_dot_4	2000	9.8670	3.2736	4.0000	16.0000
int_dec_avg_dot_5	2000	11.5680	3.5431	5.0000	18.0000
int_dec_avg_dot_6	2000	13.4975	3.9087	6.0000	21.0000
int_dec_avg_dot_7	2000	15.6185	4.1656	7.0000	23.0000
int_dec_avg_dot_8	2000	18.2395	4.4150	9.0000	26.0000
int_dec_avg_dot_9	2000	21.2730	4.7677	11.0000	30.0000
int_dec_avg_dot_10	2000	24.6845	5.0554	14.0000	33.0000
int_dec_avg_dot_11	2000	28.3505	5.4143	17.0000	38.0000
int_dec_avg_dot_12	2000	32.6500	5.8356	20.0000	43.0000
int_dec_avg_dot_13	2000	37.7005	6.3200	25.0000	49.0000
int_dec_avg_dot_14	2000	43.2390	6.8884	28.0000	55.0000
int_dec_avg_dot_15	2000	49.4500	7.2360	34.0000	62.0000
int_dec_avg_dot_16	2000	56.1785	7.6985	42.0000	71.0000
int_dec_avg_dot_17	2000	63.9185	8.4804	48.0000	80.0000
int_dec_avg_dot_18	2000	72.7570	8.8241	54.0000	88.0000
int_dec_avg_dot_19	2000	81.3190	9.3825	61.0000	97.0000
int_dec_avg_dot_20	2000	90.5560	9.9185	69.0000	108.0
int_dec_avg_dot_21	2000	100.6	10.4777	80.0000	120.0
int_dec_avg_dot_22	2000	111.3	10.9632	89.0000	132.0
int_dec_avg_dot_23	2000	121.8	11.2621	101.0	144.0
int_dec_avg_dot_24	2000	131.5	12.0480	107.0	153.0
int_dec_avg_dot_25	2000	141.3	12.5487	118.0	166.0
int_dec_avg_dot_26	2000	150.8	12.5832	128.0	176.0
int_dec_avg_dot_27	2000	159.6	13.0580	133.0	183.0
int_dec_avg_dot_28	2000	166.4	13.2120	140.0	192.0
int_dec_avg_dot_29	2000	171.9	13.6568	143.0	196.0
int_dec_avg_dot_30	2000	177.3	13.9323	145.0	201.0
int_dec_avg_dot_31	2000	182.4	13.9579	154.0	208.0
int_dec_avg_dot_32	2000	181.8	14.3315	156.0	211.0
int_dec_avg_dot_33	2000	181.3	14.5160	153.0	209.0
int_dec_avg_dot_34	2000	178.3	14.3843	149.0	205.0
int_dec_avg_dot_35	2000	174.7	14.0618	146.0	201.0
int_dec_avg_dot_36	2000	169.6	13.3792	144.0	195.0
int_dec_avg_dot_37	2000	163.8	13.2905	137.0	188.0
int_dec_avg_dot_38	2000	157.9	13.2220	130.0	182.0
int_dec_avg_dot_39	2000	151.1	12.9412	124.0	174.0
int_dec_avg_dot_40	2000	143.7	12.8153	120.0	168.0
int_dec_avg_dot_41	2000	136.8	12.7000	109.0	160.0
int_dec_avg_dot_42	2000	129.9	13.1982	104.0	155.0

MCMC analysis of regions

The MCMC Procedure

country=US region_code=MA region_name=Massachusetts

MCMC analysis of regions

The MCMC Procedure

country=US region_code=NJ region_name=New Jersey

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000360
2	1	0.6234	0.00494
3	1	0.2073	0.1923
4	1	0.1486	0.5369
5	1	0.2249	0.6217
6	1	0.4260	0.6049
7	1	0.7695	0.5623
8	1	1.2412	0.4778
9	1	1.6342	0.4138

Burn-In History
Block	Scale	Acceptance Rate
1	1.6342	0.4096

Sampling History
Block	Scale	Acceptance Rate
1	1.6342	0.4133

MCMC analysis of regions

The MCMC Procedure

country=US region_code=NJ region_name=New Jersey

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.00291	0.000502	0.00210	0.00390
i0	2000	0.0340	0.00289	0.0282	0.0393
R0	2000	22.3195	5.5975	13.6574	33.6495
beta	2000	0.2814	0.0115	0.2603	0.3049
gamma	2000	0.0133	0.00275	0.00827	0.0189

MCMC analysis of regions

The MCMC Procedure

country=US region_code=NJ region_name=New Jersey

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	0.000013	0.000502	0.0250
i0	0.000067	0.00289	0.0230
R0	0.1416	5.5975	0.0253
beta	0.000262	0.0115	0.0229
gamma	0.000065	0.00275	0.0237

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.0243	0.0258	0.0123	0.0157
i0	0.0306	-0.0104	0.0098	-0.0258
R0	0.0196	0.0302	0.0252	0.0142
beta	0.0224	0.0264	0.0444	-0.0183
gamma	0.0184	0.0217	0.0112	0.0121

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	-0.5401	0.5892
i0	-1.4603	0.1442
R0	-0.3568	0.7212
beta	0.5742	0.5659
gamma	0.3576	0.7207

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	0.0736	0.7299	Passed	0	0.000026	0.00291	0.00908	Passed
i0	0.1573	0.3681	Passed	0	0.000119	0.0340	0.00351	Passed
R0	0.0658	0.7775	Passed	0	0.2956	22.3195	0.0132	Passed
beta	0.0906	0.6332	Passed	0	0.000493	0.2814	0.00175	Passed
gamma	0.0675	0.7668	Passed	0	0.000141	0.0133	0.0106	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	1605.6	1.2456	0.8028
i0	1884.8	1.0611	0.9424
R0	1562.3	1.2801	0.7812
beta	1914.1	1.0449	0.9571
gamma	1782.1	1.1223	0.8911

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	11.2525	3.5199	5.0000	18.0000
int_dec_avg_dot_2	2000	14.1935	3.8836	7.0000	21.0000
int_dec_avg_dot_3	2000	17.7125	4.5397	8.0000	25.0000
int_dec_avg_dot_4	2000	22.2490	4.9574	12.0000	31.0000
int_dec_avg_dot_5	2000	27.9665	5.6288	17.0000	38.0000
int_dec_avg_dot_6	2000	34.4940	6.2502	22.0000	46.0000
int_dec_avg_dot_7	2000	42.6665	6.6306	29.0000	54.0000
int_dec_avg_dot_8	2000	52.6330	7.5897	36.0000	66.0000
int_dec_avg_dot_9	2000	63.7270	8.2978	45.0000	78.0000
int_dec_avg_dot_10	2000	77.6925	9.1597	61.0000	96.0000
int_dec_avg_dot_11	2000	93.1065	10.0439	73.0000	112.0
int_dec_avg_dot_12	2000	110.4	10.7504	90.0000	131.0
int_dec_avg_dot_13	2000	129.3	11.7303	107.0	152.0
int_dec_avg_dot_14	2000	149.0	13.1936	122.0	174.0
int_dec_avg_dot_15	2000	168.2	13.8530	140.0	194.0
int_dec_avg_dot_16	2000	187.4	14.6993	158.0	214.0
int_dec_avg_dot_17	2000	206.6	15.2836	174.0	234.0
int_dec_avg_dot_18	2000	222.9	15.7686	190.0	252.0
int_dec_avg_dot_19	2000	236.2	15.7238	207.0	267.0
int_dec_avg_dot_20	2000	247.8	16.4647	216.0	280.0
int_dec_avg_dot_21	2000	256.8	16.7105	221.0	286.0
int_dec_avg_dot_22	2000	263.0	16.8572	230.0	294.0
int_dec_avg_dot_23	2000	268.5	17.4207	235.0	303.0
int_dec_avg_dot_24	2000	270.9	16.8131	236.0	301.0
int_dec_avg_dot_25	2000	272.3	17.2291	238.0	306.0
int_dec_avg_dot_26	2000	272.2	16.9429	239.0	304.0
int_dec_avg_dot_27	2000	272.0	16.9976	237.0	303.0
int_dec_avg_dot_28	2000	270.7	17.0415	235.0	303.0
int_dec_avg_dot_29	2000	268.8	17.1411	232.0	299.0
int_dec_avg_dot_30	2000	266.6	16.4735	233.0	298.0
int_dec_avg_dot_31	2000	264.1	16.6696	232.0	296.0
int_dec_avg_dot_32	2000	258.4	16.5014	226.0	291.0
int_dec_avg_dot_33	2000	255.4	16.4794	225.0	288.0
int_dec_avg_dot_34	2000	252.9	16.2435	221.0	283.0
int_dec_avg_dot_35	2000	250.1	16.0980	217.0	279.0
int_dec_avg_dot_36	2000	246.4	15.4709	215.0	274.0
int_dec_avg_dot_37	2000	242.9	15.8255	211.0	272.0
int_dec_avg_dot_38	2000	240.0	16.4826	209.0	272.0
int_dec_avg_dot_39	2000	236.6	16.1939	202.0	266.0
int_dec_avg_dot_40	2000	233.7	16.2702	198.0	262.0
int_dec_avg_dot_41	2000	230.8	16.1554	197.0	260.0
int_dec_avg_dot_42	2000	227.6	16.2452	196.0	258.0
int_dec_avg_dot_43	2000	224.7	16.2736	193.0	256.0

MCMC analysis of regions

The MCMC Procedure

country=US region_code=NJ region_name=New Jersey

MCMC analysis of regions

The MCMC Procedure

country=US region_code=NY region_name=New York

Number of Observations Read

Number of Observations Used

Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	log_mort	N-Metropolis	-4.6052	normal(-4.605170186, sd= 2.302585093)
	log_i0		-4.6052	normal(-4.605170186, sd=3.4538776395)
	log_R0		1.0986	normal(1.0986122887, sd=0.9210340372)
	log_gamma		-2.9957	normal(-2.995732274, sd=1.1512925465)

Tuning History
Phase	Block	Scale	Acceptance Rate
1	1	2.3800	0.000160
2	1	0.5892	0.00582
3	1	0.1997	0.1649
4	1	0.1344	0.4832
5	1	0.1791	0.5891
6	1	0.3099	0.5457
7	1	0.4794	0.5033
8	1	0.6694	0.4781
9	1	0.8820	0.4344
10	1	1.0545	0.3833

Burn-In History
Block	Scale	Acceptance Rate
1	1.0545	0.3695

Sampling History
Block	Scale	Acceptance Rate
1	1.0545	0.3743

MCMC analysis of regions

The MCMC Procedure

country=US region_code=NY region_name=New York

Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
mortality	2000	0.00220	0.000962	0.000960	0.00397
i0	2000	0.0442	0.00481	0.0343	0.0530
R0	2000	15.2264	8.1769	4.4892	30.8782
beta	2000	0.3540	0.0118	0.3319	0.3768
gamma	2000	0.0290	0.0137	0.00733	0.0565

MCMC analysis of regions

The MCMC Procedure

country=US region_code=NY region_name=New York

Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
mortality	0.000022	0.000962	0.0224
i0	0.000114	0.00481	0.0237
R0	0.1828	8.1769	0.0224
beta	0.000271	0.0118	0.0229
gamma	0.000318	0.0137	0.0233

Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
mortality	0.0095	0.0082	-0.0081	-0.0279
i0	0.0600	-0.0024	-0.0239	-0.0172
R0	0.0098	0.0107	-0.0059	-0.0261
beta	0.0243	-0.0304	-0.0287	-0.0274
gamma	0.0870	-0.0089	-0.0177	-0.0224

Geweke Diagnostics
Parameter	z	Pr > \|z\|
mortality	-0.7126	0.4761
i0	-1.3281	0.1842
R0	-0.7895	0.4298
beta	0.1730	0.8627
gamma	1.6071	0.1080

Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
mortality	.	.	3746	.
i0	.	.	3746	.
R0	.	.	3746	.
beta	.	.	3746	.
gamma	.	.	3746	.
NOTE: The minimum required sample size of 3746 is larger than the available chain length of 2000.

Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
mortality	0.0434	0.9151	Passed	0	0.000038	0.00220	0.0172	Passed
i0	0.1070	0.5517	Passed	0	0.000190	0.0442	0.00430	Passed
R0	0.0503	0.8746	Passed	0	0.3265	15.2264	0.0214	Passed
beta	0.0261	0.9872	Passed	0	0.000435	0.3540	0.00123	Passed
gamma	0.2487	0.1901	Passed	0	0.000557	0.0290	0.0192	Passed

Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
mortality	2000.0	1.0000	1.0000
i0	1785.9	1.1199	0.8929
R0	2000.0	1.0000	1.0000
beta	1907.2	1.0487	0.9536
gamma	1847.0	1.0828	0.9235

Posterior Summaries and Intervals for Prediction
Parameter	N	Mean	Standard Deviation	95% HPD Interval
int_dec_avg_dot_1	2000	45.4910	7.4043	31.0000	59.0000
int_dec_avg_dot_2	2000	59.6665	8.3763	44.0000	75.0000
int_dec_avg_dot_3	2000	77.7210	9.5252	58.0000	95.0000
int_dec_avg_dot_4	2000	100.7	10.7515	80.0000	121.0
int_dec_avg_dot_5	2000	130.1	12.5906	104.0	153.0
int_dec_avg_dot_6	2000	166.1	13.5826	140.0	192.0
int_dec_avg_dot_7	2000	210.3	15.5702	181.0	241.0
int_dec_avg_dot_8	2000	262.4	16.5278	232.0	295.0
int_dec_avg_dot_9	2000	321.4	18.8291	284.0	356.0
int_dec_avg_dot_10	2000	387.5	21.4496	344.0	429.0
int_dec_avg_dot_11	2000	456.2	22.6808	413.0	501.0
int_dec_avg_dot_12	2000	525.6	25.1288	476.0	572.0
int_dec_avg_dot_13	2000	590.3	26.4393	535.0	637.0
int_dec_avg_dot_14	2000	646.2	27.0348	590.0	696.0
int_dec_avg_dot_15	2000	693.0	28.1182	641.0	750.0
int_dec_avg_dot_16	2000	727.2	29.2865	666.0	781.0
int_dec_avg_dot_17	2000	750.5	29.4738	690.0	806.0
int_dec_avg_dot_18	2000	762.4	30.5351	700.0	819.0
int_dec_avg_dot_19	2000	765.7	30.2257	710.0	827.0
int_dec_avg_dot_20	2000	762.5	30.7080	702.0	818.0
int_dec_avg_dot_21	2000	755.5	32.5203	690.0	817.0

MCMC analysis of regions

The MCMC Procedure

country=US region_code=NY region_name=New York