In Chapter 5, we discuss the SIR method of simulating from a posterior density

1. We simulate a sample

2. We compute weights

3. We resample from the

The resampled values are approximately from the distribution of interest

The function sir in the LearnBayes package implements this algorithm when the proposal density is a t density with arbitrary mean, variance and degrees of freedom.

For this example, we showed that a Normal(0.50, 0.009) density was a reasonable approximation to the posterior. So we use a t proposal density with location 0.50, variance 0.009 and 4 degrees of freedom. We decide to simulate 10,000 values.

The sir function’s arguments are similar to those for rejectsampling — function that defines the log posterior, parameters of the t proposal, number of simulated draws, and the data used in the log posterior function.

R=sir(cor.sampling,list(m=.5,var=.009,df=4),10000,dz)

plot(density(R),col=”blue”,lwd=3)