Final-model.txt

# SDS 384.7 Bayesian Statistical Methods Fall 2016 FINAL Exam (Take-Home) Fall 2016 
# Building a Bayesian Model in OPENBUGS
# Bayesian Inferences for Comparing three normal populations
# Data Source: Simulate in R Data from the 3
# populations and export them to OpenBUGS

model{

for( i in 1 : n[1]) { y1[i] ~ dnorm(mu1,tau)} 
for( i in 1 : n[2]) { y2[i] ~ dnorm(mu2,tau)}
for( i in 1 : n[3]) { y3[i] ~ dnorm(mu3,tau)}

# A Priori, mu1, mu2, mu3 and tau are mutually independent
# Marginal proper diffuse priors

mu1 ~ dnorm( 0.0,1.0E-6)
mu2 ~ dnorm( 0.0,1.0E-6)
mu3 ~ dnorm( 0.0,1.0E-6)
tau ~ dgamma(0.01,0.001)

# delta 
delta <- mu1-mu2

# W|theta
W~ dnorm(mu.W, tau.W) 
mu.W<- mu1-mu2+mu3
tau.W<- tau/3.0

# test H_0: 2 mu_1<mu_2<mu_3 vs H_1: H_0 is not true
delta1 <- mu2-(2*mu1)
delta2 <- mu3-mu2 
post.prob.h0 <- step(delta1)*step(delta2)

# predictive probability that y1.26 is at most 9.5
y1.26 ~ dnorm(mu1,tau)
pred.prob.y1.26 <- step(9.5-y1.26)

# gamma=Prob(y1.26<=9.5|mu1,tau)
gamma <- phi((9.5-mu1)*sqrt(tau))

# Monitor DIC separately from Inference > DIC menu
}