Beta-Binomial

data
list(X = 621, n = 1000)	# frequentist estimate 0.621

inits
list(p = 0.25)				# starting values for p
list(p = 0.50)
list(p = 0.75)

model;
{
   X ~ dbin(p,n)
   p ~ dbeta(225,185)	# prior mode = 0.55, 95% prior interval (0.51, 0.59)
}

-----

Normal-Normal 

# Example 2, Problem 3.2

data

list(X = c(198.14, 198.45, 196.59, 197.64, 198.12), n = 5, sigma = 1)	# frequentist estimate, mean = 197.79

inits
list(mu = 198)

model;
{
   for( i in 1 : n ) {
      X[i] ~ dnorm(mu,tau)
   }
   mu ~ dnorm( 200.0,0.01)	# prior mode = 200, 95% prior interval (180,220), Normal(200,10) prec = 1/10 = 0.01
   tau <- 1 / pow(sigma,2)
}

-----

Gamma-Poisson

# Example 3

data
list(T = 256, n = 50)

inits
list(lambda = 10)

model;
{
   T ~ dpois(lambda0)
   lambda ~ dgamma(4,3)
   lambda0 <- n*lambda
}