An Example That Illustrates the NORMALCAR Prior
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/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: MCMCSPA */
/* TITLE: An Example That Illustrates the NORMALCAR Prior */
/* PRODUCT: STAT */
/* SYSTEM: ALL */
/* KEYS: */
/* PROCS: MCMC */
/* DATA: */
/* */
/* SUPPORT: Fang Chen */
/* REF: PROC MCMC */
/* MISC: */
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title 'Spatial Analysis';
data London;
input ID N1-N9 NumNei O E Depriv;
datalines;
1 4 8 9 12 17 . . . . 5 4 7.2090 1.233
2 7 10 13 14 . . . . . 4 8 7.8144 8.162
3 6 8 11 15 17 32 . . . 6 3 3.4669 0.919
4 1 12 14 16 17 32 33 . . 7 6 7.0439 -0.780
5 6 15 19 21 . . . . . 4 2 7.3741 -1.182
6 3 5 11 15 19 . . . . 5 7 4.4575 3.647
7 2 10 13 14 16 43 . . . 6 7 6.3285 6.470
8 1 3 9 15 17 18 . . . 6 2 4.4575 0.948
9 1 8 18 . . . . . . 3 10 6.3285 4.479
10 2 7 13 20 38 43 . . . 6 13 6.7688 11.739
11 3 6 19 24 32 . . . . 5 5 9.3002 -0.125
12 1 4 14 16 . . . . . 4 7 6.6037 0.063
13 2 7 10 20 . . . . . 4 9 3.1729 4.392
14 2 4 7 12 16 . . . . 5 3 1.6871 -1.021
15 3 5 6 8 18 21 . . . 6 3 4.4386 -0.609
16 4 7 12 14 23 33 43 . . 7 1 6.6037 1.896
17 1 3 4 8 32 . . . . 5 2 7.2641 -0.053
18 8 9 15 . . . . . . 3 3 6.2185 1.043
19 5 6 11 24 27 . . . . 5 19 7.3191 -0.899
20 10 13 38 . . . . . . 3 7 6.2185 8.441
21 5 15 . . . . . . . 2 5 7.0439 5.810
22 25 26 39 44 . . . . . 4 4 5.2934 3.575
23 16 31 33 43 . . . . . 4 9 10.3705 5.780
24 11 19 27 32 40 41 44 . . 7 2 6.5899 -0.375
25 22 28 31 34 39 44 . . . 6 4 6.1574 4.828
26 22 39 44 . . . . . . 3 6 7.6702 1.668
27 19 24 40 . . . . . . 3 14 13.9360 4.970
28 25 29 31 34 35 39 . . . 6 13 12.7473 10.210
29 28 34 35 36 . . . . . 4 6 6.2658 -0.234
30 34 36 38 43 . . . . . 4 7 10.9649 7.804
31 23 25 28 32 33 34 43 44 . 8 9 8.5342 5.544
32 3 4 11 17 24 31 33 41 44 9 3 6.1035 -1.699
33 4 16 23 31 32 . . . . 5 4 6.6978 7.029
34 25 28 29 30 31 36 43 . . 7 10 8.9662 2.581
35 28 29 39 . . . . . . 3 10 8.8044 0.958
36 29 30 34 . . . . . . 3 8 8.3724 2.811
37 40 42 . . . . . . . 2 23 15.3166 6.376
38 10 20 30 43 . . . . . 4 24 15.7486 8.627
39 22 25 26 28 35 . . . . 5 18 17.6934 1.139
40 24 27 37 41 42 . . . . 5 10 8.6426 3.169
41 24 32 40 42 44 . . . . 5 6 4.9693 3.332
42 37 40 41 . . . . . . 3 4 6.3737 2.754
43 7 10 16 23 30 31 34 38 . 8 17 11.2890 7.550
44 22 24 25 26 31 32 41 . . 7 7 6.3737 3.961
run;
ods select none;
proc mcmc data=london seed=615926 nbi=10000 nmc=50000 thin=10
plots=none outpost=londonpost;
parms tau_b 0.5 tau_h 0.2;
parms alpha 0 beta 0;
prior tau: ~ gamma(0.5, is=0.0005);
prior alpha ~ general(0);
prior beta ~ n(0, prec=1e-5);
random h ~ n(0, prec=tau_h) s=id;
random b ~ normalcar(neighbors=n,num=numnei,prec=tau_b*numnei) s=id;
mu=e*exp(alpha + beta*depriv + b + h);
model o ~ poisson(mu);
run;