First model in JAGS

y <- c(23,17,25,28,38,18,32,51,
       32,41,51,33,21,52,11,19)
N <- length(y)

my.data <- list(y=y, N=N)
my.data

$y
 [1] 23 17 25 28 38 18 32 51 32 41 51 33 21 52 11 19

$N
[1] 16

\[ p(\theta|y) = \frac {p(\theta) \times p(y|\theta)}{p(y)} \]

where \( \theta \) are model parameters, and \( y \) are the data

\( p(y|\theta) \) … likelihood

\( p(\theta) \) … prior

\( p(\theta|y) \) … posterior

\( p(y) \) … the horrible thing

This is the model that we will fit: \( y_i \sim Poisson(\lambda) \)

model
{
  # p(lambda) 

  # p(y|lambda)

}

This is the model that we will fit: \( y_i \sim Poisson(\lambda) \)

model
{
  # p(lambda) ... prior

  # p(y|lambda) ... likelihood

}

This is the model that we will fit: \( y_i \sim Poisson(\lambda) \)

model
{
  # prior
    lambda ~ dunif(0, 100)

  # likelihood
    for(i in 1:N)
    {
      y[i] ~ dpois(lambda)    
    }
}

We will dump the model to a file using cat("", file="")

cat("
model
{
  # prior
    lambda ~ dunif(0, 100)

  # likelihood
    for(i in 1:N)
    {
      y[i] ~ dpois(lambda)    
    }
}
", file="my_model.txt")

library(R2jags)

fitted.model <- jags(data=my.data,  model.file="my_model.txt", parameters.to.save="lambda", n.chains=3, n.iter=2000, n.burnin=1000)

Compiling model graph
   Resolving undeclared variables
   Allocating nodes
Graph information:
   Observed stochastic nodes: 16
   Unobserved stochastic nodes: 1
   Total graph size: 20

Initializing model

  fitted.model

Inference for Bugs model at "my_model.txt", fit using jags,
 3 chains, each with 2000 iterations (first 1000 discarded)
 n.sims = 3000 iterations saved
         mu.vect sd.vect    2.5%     25%     50%     75%   97.5%  Rhat
lambda    30.772   1.347  28.265  29.822  30.734  31.679  33.451 1.001
deviance 165.818   1.301 164.877 164.969 165.327 166.172 169.363 1.012
         n.eff
lambda    3000
deviance   650

For each parameter, n.eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor (at convergence, Rhat=1).

DIC info (using the rule, pD = var(deviance)/2)
pD = 0.8 and DIC = 166.7
DIC is an estimate of expected predictive error (lower deviance is better).