  Using Markov chain Monte Carlo to sample from posterior distributions was the
key innovation which made Bayesian data analysis practical. Notoriously,
however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This
pedagogical note explores variants on a universal {\em non}-Markov-chain Monte
Carlo scheme for sampling from posterior distributions. The basic idea is to
draw parameter values from the prior distributions, evaluate the likelihood of
each draw, and then copy that draw a number of times proportional to its
likelihood. The distribution after copying is an approximation to the posterior
which becomes exact as the number of initial samples goes to infinity; the
convergence of the approximation is easily analyzed, and is uniform over
Glivenko-Cantelli classes. While not {\em entirely} practical, the schemes are
straightforward to implement (a few lines of R), easily parallelized, and
require no rejection, burn-in, convergence diagnostics, or tuning of any
control settings. I provide references to the prior art which deals with some
of the practical obstacles, at some cost in computational and analytical
simplicity.

Computation