# Histogram smoothing adapted from Example 5.9 from Congdon (2001), p 180.  
#  Illustrates a structured precision matrix for a multivariate normal prior

	Pig Weight Gain
	

	model{ 
		y[1:s] ~ dmulti(th[1 : s] , n)
		sum.g <- sum(g[])
	# smoothed frequencies
		for (i in 1 : s) {     
			Sm[i] <- n * th[i]
			g[i] <- exp(gam[i])    
			th[i]  <- g[i] / sum.g
		}
	# prior on elements of AR Precision Matrix  
		rho ~ dunif(0, 1)
		tau ~ dunif(0.5, 10)
	# MVN for logit parameters
		gam[1 : s] ~ dmnorm(mu[], T[ , ])
		for (j in 1:s) { 
			mu[j] <- -log(s)
		}
	# Define Precision Matrix
		for (j in 2 : s - 1) {
			T[j, j] <- tau * (1 + pow(rho, 2))
		}
		T[1, 1] <- tau T[s, s] <- tau
		for (j in 1 : s-1) { 
			T[j, j + 1] <- -tau * rho
			T[j + 1, j] <- T[j, j + 1]
		}
		for (i in 1 : s - 1) {
			for (j in 2 + i: s) {
				T[i, j] <- 0; T[j, i] <- 0 
			}
		}
	# Or Could do in terms of covariance, which is simpler to write but VERY slow
#		for (i in 1 :s) {
#			for (j in 1 : s) {
#				cov[i, j] <- pow(rho, abs(i - j)) / tau
#			}
#		}
#		T[1:s, 1: s] <- inverse(cov[,])
	}

Data
list(y=c(1,1,0,7,5,10,30,30,41,48,66,72,56,46,45,22,24,12,5,0,1),n=522,s=21)

Inits
list(gam=c(-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3))	

Results

	 node	 mean	 sd	 MC error	2.5%	median	97.5%	start	sample
	deviance	101.5	5.924	0.08113	91.6	100.9	114.6	1001	10000
	Sm[1]	1.445	0.8561	0.01847	0.3225	1.263	3.613	1001	10000
	Sm[2]	1.504	0.78	0.01423	0.4117	1.367	3.426	1001	10000
	Sm[3]	1.907	0.8983	0.01461	0.5813	1.769	4.058	1001	10000
	Sm[4]	4.988	1.731	0.02256	2.304	4.748	8.936	1001	10000
	Sm[5]	6.068	1.911	0.02301	2.976	5.849	10.38	1001	10000
	Sm[6]	10.88	2.775	0.03019	6.203	10.63	16.99	1001	10000
	Sm[7]	27.65	4.83	0.0428	19.26	27.28	38.02	1001	10000
	Sm[8]	30.48	4.931	0.05337	21.6	30.17	40.98	1001	10000
	Sm[9]	40.63	5.747	0.05252	30.09	40.32	52.62	1001	10000
	Sm[10]	48.26	6.207	0.06352	36.75	47.98	61.32	1001	10000
	Sm[11]	65.32	7.211	0.07429	51.98	65.21	79.97	1001	10000
	Sm[12]	71.11	7.528	0.07219	57.22	70.92	86.32	1001	10000
	Sm[13]	56.1	6.708	0.06144	43.52	55.97	69.77	1001	10000
	Sm[14]	46.31	6.084	0.06502	35.25	46.02	59.05	1001	10000
	Sm[15]	43.5	5.969	0.06257	32.59	43.22	55.94	1001	10000
	Sm[16]	23.57	4.315	0.04096	15.9	23.33	32.77	1001	10000
	Sm[17]	22.22	4.131	0.04622	14.98	21.95	31.33	1001	10000
	Sm[18]	11.45	2.837	0.03167	6.687	11.2	17.71	1001	10000
	Sm[19]	4.878	1.682	0.02169	2.187	4.669	8.783	1001	10000
	Sm[20]	1.994	0.975	0.01851	0.5311	1.837	4.297	1001	10000
	Sm[21]	1.735	0.9863	0.01857	0.3951	1.538	4.182	1001	10000

null standardized deviance: using means
	Dbar	Dhat	DIC	pD	
	
y	101.690	87.419	115.960	14.271	
total	101.690	87.419	115.960	14.271