Fitting distributions the Bayesian way

In this next example, we are going to be fitting a normal distribution to the precipitation dataset that we worked with in the previous chapter. We will wrap up with Bayesian analogue to the one sample t-test.

The results we want from this analysis are credible values of the true population mean of the precipitation data. Refer back to the previous chapter to recall that the sample mean was 34.89. In addition, we will also be determining credible values of the standard deviation of the precipitation data. Since we are interested in the credible values of two parameters, our posterior distribution is a joint distribution.

Our model will look a little differently now:

the.model <- " 
model { 
  mu ~ dunif(0, 60)        # prior 
  stddev ~ dunif(0, 30)    # prior 
  tau <- pow(stddev, -2)   
 
  for(i in 1:theLength){ 
    samp[i] ~ dnorm(mu, tau)   # likelihood function 
  } 
}" 

This time, we have to set two priors, one for the mean of the Gaussian...