Markov Chain Monte Carlo (MCMC) algorithms and Sequential Monte Carlo (SMC) methods (a.k.a., particle filters) are well-known Monte Carlo methodologies, widely used in different fields for Bayesian inference and stochastic optimization. The Multiple Try Metropolis (MTM) algorithm is an extension of the standard Metropolis- Hastings (MH) algorithm in which the next state of the chain is chosen among a set of candidates, according to certain weights. The Particle MH (PMH) algorithm is another advanced MCMC technique specifically designed for scenarios where the multidimensional target density can be easily factorized as multiplication of conditional densities. PMH combines jointly SMC and MCMC approaches. Both, MTM and PMH, have been widely studied and applied in literature. PMH variants have been often applied for the joint purpose of tracking dynamic variables and tuning constant parameters in a state space model. Furthermore, PMH can be also considered as an alternative particle smoothing method. In this work, we investigate connections, similarities and differences among MTM schemes and PMH methods. This study allows the design of novel efficient schemes for filtering and smoothing purposes in state space models. More specially, one of them, called Particle Multiple Try Metropolis (P-MTM), obtains very promising results in different numerical simulations.
Comments: 21 Pages.
[v1] 2014-09-08 03:03:33
[v2] 2014-09-23 02:30:02 (removed)
[v3] 2016-01-04 12:40:57 (removed)
[v4] 2016-01-05 08:47:18 (removed)
[v5] 2016-01-14 12:54:49 (removed)
[v6] 2016-02-17 13:27:24 (removed)
[v7] 2016-03-17 14:39:23
[v8] 2016-05-25 09:33:48
[v9] 2016-05-27 09:29:29
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