######################
# Dugongs Nonlinear model
#  See Carlin and Louis (2008), Example 4.3
######################

model
	{
		for( i in 1 : N ) {
			Y[i] ~ dnorm(mu[i], tau)
			mu[i] <- alpha - beta * pow(gamma,x[i])			
		}

		alpha ~ dflat()
		beta ~ dflat()
		gamma ~ dunif(0.5, 1.0)
    	U3 <- logit(gamma)	

        tau <- 1/(sigma*sigma)  
        sigma ~ dunif(0.01, 100)
		
	}
	
#Data:	
	list(x = c( 1.0,  1.5,  1.5,  1.5, 2.5,   4.0,  5.0,  5.0,  7.0,
	            8.0,  8.5,  9.0,  9.5, 9.5,  10.0, 12.0, 12.0, 13.0,
	           13.0, 14.5, 15.5, 15.5, 16.5, 17.0, 22.5, 29.0, 31.5),
	     Y = c(1.80, 1.85, 1.87, 1.77, 2.02, 2.27, 2.15, 2.26, 2.47,
	           2.19, 2.26, 2.40, 2.39, 2.41, 2.50, 2.32, 2.32, 2.43,
	           2.47, 2.56, 2.65, 2.47, 2.64, 2.56, 2.70, 2.72, 2.57), N = 27)

# Inits:
list(alpha = 1, beta = 1, sigma = 1, gamma = 0.9)
list(alpha = 10, beta = 10, sigma = 10, gamma = 0.7)
list(alpha = 100, beta = 100, sigma = 100, gamma = 0.5)


#  Results:

	 node	 mean	 sd	 MC error	2.5%	median	97.5%	start	sample
	U3	1.859	0.2723	0.005911	1.305	1.863	2.39	5001	48000
	alpha	2.652	0.07341	0.001559	2.529	2.646	2.815	5001	48000
	beta	0.9741	0.07769	5.816E-4	0.826	0.973	1.131	5001	48000
	gamma	0.8621	0.03298	6.931E-4	0.7867	0.8657	0.916	5001	48000
	sigma	0.09914	0.01514	1.01E-4	0.07468	0.09736	0.1338	5001	48000
	tau	108.6	31.67	0.1976	55.86	105.5	179.3	5001	48000