Population Monte Carlo algorithms

We give a cross-disciplinary survey on “population” Monte Carlo algorithms.In these algorithms, a set of “walkers” or “particles” is used as a representation of a high-dimensional vector. The computation is carried out by a random walk and split/deletion of these objects. The algorithms are developed in various fields in physics and statistical sciences and called by lots of different terms — “quantum Monte Carlo”, “transfer-matrix Monte Carlo”, “Monte Carlo filter (particle filter)”, “sequential Monte Carlo” and “PERM” etc. Here we discuss them in a coherent framework. We also touch on related algorithms —genetic algorithms and annealed importance sampling.