Mode jumping proposals in MCMC (Q2722311)

Markov chain Monte Carlo (MCMC) algorithms allow the generation of samples from a specified target distribution. The Metropolis-Hastings setup gives a general framework for the specification of the Markov chain and each iteration consists of two parts. First, with \(x\) denoting the current state, a potential new state, \(y,\) is generated according to a specified proposal kernel, \(q(y/x),\) and, second, \(y\) is accepted with a given probability, \(\alpha(y/x).\) NEWLINENEWLINENEWLINEThe paper defines a new scheme, within the Metropolis-Hastings class, for the construction of MCMC algorithms and demonstrates how this allows local optimization be to incorporated in the MCMC procedures. Recipes for handling multimedia distributions are given and their potential are illustrated by three examples. The attention is limited to continuous distributions because mode jumping proposals are not directly applicable for discrete distributions. The continuous distributions on \(\mathbb{R}^{n}\) are considered and it is specified how an optimization for local maxima of the target distribution can be incorporated in the specification of the Markov chain. A chain with frequent jumps between modes is obtained.