Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter

Isambi S. Mbalawata, Simo Särkkä, Matti Vihola and Heikki Haario

Computational Statistics & Data Analysis, 2015, vol. 83, issue C, 101-115

Abstract: Markov chain Monte Carlo (MCMC) methods are powerful computational tools for analysis of complex statistical problems. However, their computational efficiency is highly dependent on the chosen proposal distribution, which is generally difficult to find. One way to solve this problem is to use adaptive MCMC algorithms which automatically tune the statistics of a proposal distribution during the MCMC run. A new adaptive MCMC algorithm, called the variational Bayesian adaptive Metropolis (VBAM) algorithm, is developed. The VBAM algorithm updates the proposal covariance matrix using the variational Bayesian adaptive Kalman filter (VB-AKF). A strong law of large numbers for the VBAM algorithm is proven. The empirical convergence results for three simulated examples and for two real data examples are also provided.

Keywords: Markov chain Monte Carlo; Adaptive Metropolis algorithm; Adaptive Kalman filter; Variational Bayes (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:83:y:2015:i:c:p:101-115

DOI: 10.1016/j.csda.2014.10.006

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