A multiple-try Metropolis-Hastings algorithm with tailored proposals

摘要

We present a new multiple-try Metropolis-Hastings algorithm designed to be especially beneficial when a tailored proposal distribution is available. The algorithm is based on a given acyclic graph G, where one of the nodes in G, k say, contains the current state of the Markov chain and the remaining nodes contain proposed states generated by applying the tailored proposal distribution. The Metropolis-Hastings algorithm alternates between two types of updates. The first type of update is using the tailored proposal distribution to generate new states for all nodes in G except node k. The second type of update is generating a new value for k, thereby changing the value of the current state. We evaluate the effectiveness of the proposed scheme in two examples with previously defined target and proposal distributions.