Interacting multiple -- Try algorithms with different proposal distributions
AbstractWe 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 multipletry 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 and builds connections with the rapidly expanding world of adaptive MCMC. 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.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws110402.
Date of creation: Mar 2011
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Interacting Monte Carlo; Markov chain Monte Carlo; Multiple-try Metropolis; Population Monte Carlo;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-04-16 (All new papers)
- NEP-CMP-2011-04-16 (Computational Economics)
- NEP-ECM-2011-04-16 (Econometrics)
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- Monica Billio & Roberto Casarin & Anthony Osuntuyi, 2012. "Efficient Gibbs Sampling for Markov Switching GARCH Models," Working Papers 2012:35, Department of Economics, University of Venice "Ca' Foscari".
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