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Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter

Author

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

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.

Suggested Citation

  • Mbalawata, Isambi S. & Särkkä, Simo & Vihola, Matti & Haario, Heikki, 2015. "Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 101-115.
    • Handle: RePEc:eee:csdana:v:83:y:2015:i:c:p:101-115
    DOI: 10.1016/j.csda.2014.10.006
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    References listed on IDEAS

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    1. Roberts, G. O. & Gilks, W. R., 1994. "Convergence of Adaptive Direction Sampling," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 287-298, May.
    2. Vihola, Matti, 2011. "On the stability and ergodicity of adaptive scaling Metropolis algorithms," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2839-2860.
    3. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, December.
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