• Importance sampling;
  • Markov chain Monte Carlo methods;
  • Ratio of normalizing constants;
  • Resampling;
  • Sequential Monte Carlo methods;
  • Simulated annealing

Summary.  We propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space, each distribution being known up to a normalizing constant. These probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential Monte Carlo methods. This methodology allows us to derive simple algorithms to make parallel Markov chain Monte Carlo algorithms interact to perform global optimization and sequential Bayesian estimation and to compute ratios of normalizing constants. We illustrate these algorithms for various integration tasks arising in the context of Bayesian inference.