A colleague of mine was using the functions
sim() from the
R to fit a Bayesian logistic regression model. I found little information on the two functions in the documentation. However, there is a short paper covering the
bayesglm-function where it is stated:
bayesglmfunction represents a kind of short cut of the Bayesian approach to inference. Typically, the posterior is not used directly for making inferences. Instead, an empirical distribution is constructed based on draws from the posterior and that empirical distribution is what informs the inference(s). With the
bayesglmwe get a distribution of ’simulates’ which are used in place of an actual empirical distribution.
I have not seen this usage of the term "empirical distribution" in this context before. I guess it has to do with the approximate EM-algorithm, which is used in
bayesglm instead of MCMC methods, but I am not sure what it precisely means.
Also, I have troubles to make sense out of the statement "typically, the posterior is not used directly for making inferences". Does it refer to the fact that one typically uses either samples from the posterior or an approximation, when no closed form solution for the posterior exists?
A similar question is bayesglm (arm) versus MCMCpack, but the only answer there does not contain information to answer this new question.