This article surveys advances in the field of Bayesian computation over the past 20 years from a purely personal viewpoint, hence containing some ommissions given the spectrum of the field. Monte Carlo, MCMC, and ABC themes are covered here, whereas the rapidly expanding area of particle methods...

We analyze the general (multiallelic) Hardy-Weinberg equilibrium problem from an objective Bayesian testing standpoint. We argue that for small or moderate sample sizes the answer is rather sensitive to the prior chosen, and this suggests to carry out a sensitivity analysis with respect to the...