Interacting multiple try algorithms with different proposal distributions

• DOI: 10.1007/s11222-011-9301-9
• Publication Date: 2011-12-06T15:04:44Z
• Authors: Roberto Casarin; Radu Craiu; Fabrizio Leisen
• Keywords: Population Monte Carlo; FOS: Computer and information sciences; Markov chain Monte Carlo; Interacting Monte Carlo; Estadística; 0101 mathematics; Multiple-try Metropolis; Statistics - Computation; 01 natural sciences; Computation (stat.CO); Interacting Monte Carlo, Markov chain Monte Carlo, Multiple-try Metropolis, Population Monte Carlo, Simulated annealing

We propose a new class of interacting Markov chain Monte Carlo (MCMC) algorithms designed for increasing the efficiency of a modified multiple-try Metropolis (MTM) algorithm. The extension with respect to the existing MCMC literature is twofold. The sampler proposed extends the basic MTM algorithm by allowing different proposal distributions in the multiple-try generation step. We exploit the structure of the MTM algorithm with different proposal distributions to naturally introduce an interacting MTM mechanism (IMTM) that expands the class of population Monte Carlo methods. We show the validity of the algorithm and discuss the choice of the selection weights and of the different proposals. We provide numerical studies which show that the new algorithm can perform better than the basic MTM algorithm and that the interaction mechanism allows the IMTM to efficiently explore the state space.