On the flexibility of the design of multiple try Metropolis schemes
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The multiple try Metropolis (MTM) method is a generalization of the classical Metropolis–Hastings algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In the literature, several extensions have been proposed. In this work, we show and remark upon the flexibility of the design of MTM-type methods, fulfilling the detailed balance condition. We discuss several possibilities, show different numerical simulations and discuss the implications of the results.
KeywordsMetropolis–Hasting method Multiple try Metropolis algorithm Multi-point Metropolis algorithm MCMC techniques
We would like to thank the Reviewers for their comments which have helped us to improve the first version of manuscript. Moreover, this work has been partially supported by Ministerio de Ciencia e Innovacin and by the Ministerio de Economía of Spain (project MONIN, ref. TEC-2006-13514-C02- 01/TCM, project COMONSENS, id. CSD2008-00010, project DEIPRO ref. TEC2009-14504-C02-01, project ALCIT, id. TEC2012-38800-C03-01 and project COMPREHENSION, id. TEC2012-38883-C02-01) and Comunidad Autonoma de Madrid (project PROMULTIDIS-CM, ref. S-0505/TIC/0233).
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