Eye Tracking 
adapted from Congdon (2001), example 6.27, page 263, 
to allow learning of baseline distribution.

	model{	
		for( i in 1 : N ) {
			S[i] ~ dcat(pi[])
			mu[i] <- theta[S[i]]
			x[i] ~ dpois(mu[i])	
			for (j in 1 : C) {
				SC[i, j] <- equals(j, S[i])
			}
		}
	# Precision Parameter 		
#		alpha <- 1
                   alpha~ dgamma(0.1,0.1)
	# Constructive DPP
		p[1] <- r[1]
		for (j in 2 : C) {
			p[j] <- r[j] * (1 - r[j - 1]) * p[j -1 ] / r[j - 1]
		}
		p.sum <- sum(p[])		
		for (j in 1:C){     
			theta[j] ~ dgamma(A, B)
			r[j] ~ dbeta(1, alpha)			
	# scaling to ensure sum to 1 
			pi[j] <- p[j] / p.sum 
		}
	# hierarchical prior on theta[i] or preset parameters
		A ~ dexp(0.1)     B ~dgamma(0.1, 0.1)
	#	A <- 1 B <- 1
	# total clusters			
		K <- sum(cl[])
		for (j in 1 : C) {
			sumSC[j] <- sum(SC[ , j])
			cl[j] <- step(sumSC[j] -1)
		}
	}

Data

list(x=c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,
2,3, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6,7,7,7,8,9,9,10, 10,
11, 11, 12,  12,  14,  15,  15,  17,  17,  22,  24,  34), N=101, C=19)

Generate Inits
list(alpha=1)
Results

a)    fixed A and B, fixed alpha=1, C=10 (max catgeories)

	 node	 mean	 sd	 MC error	2.5%	median	97.5%	start	sample
	Deviance	301.3	15.86	0.4314	269.3	301.7	332.2	1001	10000
	K	6.764	1.494	0.07225	4.0	7.0	10.0	1001	10000
	mu[92]	13.34	3.113	0.04068	5.656	14.11	17.5	1001	10000


prior and data conflict


for variable A and B, fixed alpha=1, C=10 (max catgeories)

	 node	 mean	 sd	 MC error	2.5%	median	97.5%	start	sample
	A	0.679	0.4227	0.01953	0.1564	0.5794	1.771	1001	10000
	B	0.08799	0.06615	0.002155	0.00683	0.07225	0.2592	1001	10000
	deviance	279.6	16.54	0.5693	247.1	279.5	311.7	1001	10000
	K	7.358	1.412	0.07133	5.0	7.0	10.0	1001	10000
	mu[92]	11.12	3.063	0.05199	6.251	10.7	18.15	1001	10000

	
	
	
	for variable A and B, variable alpha, C=19 (max catgeories)

	
	Node statistics
	 node	 mean	 sd	 MC error	2.5%	median	97.5%	start	sample
	A	0.485	0.2813	0.01951	0.1448	0.4216	1.215	1001	5000
	B	0.08348	0.05173	0.002143	0.01334	0.07347	0.2077	1001	5000
	K	14.13	2.889	0.256	7.0	15.0	18.0	1001	5000
	alpha	7.973	6.609	0.5684	0.7644	6.14	24.07	1001	5000
	deviance	270.5	15.8	0.6138	241.0	270.3	303.0	1001	5000
	mu[92]	11.23	3.004	0.0517	6.393	10.84	18.18	1001	5000

Kernel density