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.