## Learning about a correlation — part III

In Chapter 5, we discuss the SIR method of simulating from a posterior density . Like rejection sampling, we find a proposal density that is easy to simulate from and covers the posterior density of interest. Here’s the algorithm:

1. We simulate a sample from the proposal density .

2. We compute weights .

3. We resample from the with replacement with weights proportional to .

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)