# Binomial sampling distribution for data
# unknown parameter is population proportion, p

# model 1

model
{
    y ~ dbin(p, n)
    p ~ dbeta( alpha, beta)
}

data
list(y = 7, n = 50, alpha = 0.5, beta = 0.5)

inits
list(p = 0.1)
list(p = 0.5)
list(p = 0.9)

The following are two versions of a model for the same data.
We assume a normal sampling distribution for the data values.

In model 2, we assume that the population precision is known, and the
mean mu is the only unknown parameter.

In model 3, we realistically assume that both population
parameters are unknown.


# Normal sampling distribution for data
# Pretending we know precision
# Population mean mu is unknown parameter
# We can also estimate the posterior predictive distribution by monitoring y[19]


# model 2
model
{
  # likelihood 
  for (i in 1:N) {
    y[i] ~ dnorm( mu, tausq ) 
  }
  # priors 
  mu ~ dnorm(0, 0.0001) 
}  


data
list(y = c(29, 27, 34, 40, 22, 28, 14, 35, 26, 35, 12, 30, 23, 17, 11, 22, 
23, 33, NA), N = 19, tausq = .02 )

inits for model 2
list(mu = 0)
list(mu = 20)
list(mu = 40)




# Normal sampling density for data
# Both mu and tausq unknown


# model 3
model
{
  # likelihood 
  for (i in 1:N) {
    y[i] ~ dnorm( mu, tausq ) 
  }
  # priors 
  mu ~ dnorm(0, 0.0001) 
  tausq ~ dgamma( 0.0001, 0.0001)  
  sigmasq <- 1/tausq
}  
  
Here is a different way to give data to WinBUGS.

data
list(N = 19 )

additional data
y[]
29
27
34
40
22
28
14
35
26
35
12
30
23
17
11 
22 
23
33
NA
END

inits for model 3
list(mu = 0, tausq = 1)
list(mu = 20, tausq = 100)
list(mu = 40, tausq = 1000)