Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter
Copyright policy )Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter
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.
Research paper: 30 pages, 10 figures
- University of Oxford United Kingdom
- University of Jyväskylä Finland
- Lappeenranta-Lahti University of Technology LUT Finland
- University of Jyväskylä Finland
- Aalto University Finland
variational Bayes, ta113, adaptive Metropolis algorithm, ta114, ta1182, Monte Carlo methods, Mathematics - Statistics Theory, Statistics Theory (math.ST), adaptive Kalman filter, ta3112, Markov chain Monte Carlo, Computational methods in Markov chains, FOS: Mathematics, Numerical analysis or methods applied to Markov chains, Computational methods for problems pertaining to statistics, ta515, ta217
variational Bayes, ta113, adaptive Metropolis algorithm, ta114, ta1182, Monte Carlo methods, Mathematics - Statistics Theory, Statistics Theory (math.ST), adaptive Kalman filter, ta3112, Markov chain Monte Carlo, Computational methods in Markov chains, FOS: Mathematics, Numerical analysis or methods applied to Markov chains, Computational methods for problems pertaining to statistics, ta515, ta217
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