Bayesian Computational Tools

This chapter surveys advances in the field of Bayesian computation over the past twenty years, from a purely personnal viewpoint, hence containing some ommissions given the spectrum of the field. Monte Carlo, MCMC and ABC themes are thus covered here, while the rapidly expanding area of particle methods is only briefly mentioned and different approximative techniques like variational Bayes and linear Bayes methods do not appear at all. This chapter also contains some novel computational entries on the double-exponential model that may be of interest per se