A multiple-try Metropolis–Hastings algorithm with tailored proposals

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 \(\mathcal {G}\), where one of the nodes in \(\mathcal {G}\), 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 \(\mathcal {G}\) 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.