Bayesian statistics can be hard to teach at an elementary level due to
the difficulty in deriving the posterior distribution for interesting
nonconjugate problems. One attractive method of summarizing the poste
rior distribution is to directly simulate from the probability distrib
ution of interest and then explore the simulated sample. We illustrate
the use of Rubin's Sampling-Importance-Resampling (SIR) algorithm to
simulate posterior distributions for three inference problems. In each
example, we focus on the construction of the prior distribution and t
hen use exploratory data analysis techniques to describe the posterior
samples and make inferences. The use of MINITAB macros is presented t
o illustrate the ease of performing this simulation on standard statis
tical computer programs.