################
#  WinBUGS code for Finite Mixture model (Carlin and Louis, 2008, Example 2.19)
#  data are "eyes" data from WinBUGS manual
################

model
{
for( i in 1 : N ) {
   y[i] ~ dnorm(mu[i], tau)
   mu[i] <- lambda[T[i]]
   T[i] ~ dcat(P[])
   }
P[1:2] ~ ddirch(alpha[])
theta ~ dnorm(0.0, 1.0E-6) I(0.0, )
lambda[2] <- lambda[1] + theta
lambda[1] ~ dnorm(0.0, 1.0E-6)

Ystar1 ~ dnorm(lambda[1], tau)
Ystar2 ~ dnorm(lambda[2], tau)
Tstar ~ dcat(P[]);  astar <- Tstar-1
Ystar <- Ystar1*(1-astar) + Ystar2*astar

sigma ~ dunif(0.01,100)   #  vague Gelman prior for sigma
tau<- 1/(sigma*sigma)
}

DATA:
list(y = c(529.0, 530.0, 532.0, 533.1, 533.4,
           533.6, 533.7, 534.1, 534.8, 535.3,
           535.4, 535.9, 536.1, 536.3, 536.4,
           536.6, 537.0, 537.4, 537.5, 538.3,
           538.5, 538.6, 539.4, 539.6, 540.4,
           540.8, 542.0, 542.8, 543.0, 543.5,
           543.8, 543.9, 545.3, 546.2, 548.8,
           548.7, 548.9, 549.0, 549.4, 549.9,
           550.6, 551.2, 551.4, 551.5, 551.6,
           552.8, 552.9,553.2), N = 48, alpha = c(1, 1),
    T = c(1, NA, NA, NA, NA, NA, NA, NA, NA, NA,
          NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
          NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
          NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
          NA, NA, NA, NA, NA, NA, NA, 2))


INITS (two sets):

list(lambda = c(535, NA), theta = 5, sigma = 1.0, P=c(0.5, 0.5))
list(lambda = c(535, NA), theta =15, sigma = 5.0, P=c(0.2, 0.8))