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Start Over Region hastings (england) Database Academic Search Index Publisher elsevier b.v.
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1. Optimal scaling of random-walk metropolis algorithms on general target distributions.

Author

Yang, Jun, Roberts, Gareth O., and Rosenthal, Jeffrey S.

Subjects
*METROPOLIS, *ALGORITHMS, *MARKOV chain Monte Carlo, *STATISTICS, *DIFFUSION, *TRACKING algorithms, *RANDOM walks
Abstract

One main limitation of the existing optimal scaling results for Metropolis–Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis algorithms on general target distributions in high dimensions arising from practical MCMC models from Bayesian statistics. For optimal scaling by maximizing expected squared jumping distance (ESJD), we show the asymptotically optimal acceptance rate 0.234 can be obtained under general realistic sufficient conditions on the target distribution. The new sufficient conditions are easy to be verified and may hold for some general classes of MCMC models arising from Bayesian statistics applications, which substantially generalize the product i.i.d. condition required in most existing literature of optimal scaling. Furthermore, we show one-dimensional diffusion limits can be obtained under slightly stronger conditions, which still allow dependent coordinates of the target distribution. We also connect the new diffusion limit results to complexity bounds of Metropolis algorithms in high dimensions. [ABSTRACT FROM AUTHOR]

Published
2020
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2. Weak convergence and optimal tuning of the reversible jump algorithm.

Author

Gagnon, Philippe, Bédard, Mylène, and Desgagné, Alain

Subjects
*STOCHASTIC convergence, *GIBBS sampling, *MARKOV chain Monte Carlo
Abstract

Abstract The reversible jump algorithm is a useful Markov chain Monte Carlo method introduced by Green (1995) that allows switches between subspaces of differing dimensionality, and therefore, model selection. Although this method is now increasingly used in key areas (e.g. biology and finance), it remains a challenge to implement it. In this paper, we focus on a simple sampling context in order to obtain theoretical results that lead to an optimal tuning procedure for the considered reversible jump algorithm, and consequently, to easy implementation. The key result is the weak convergence of the sequence of stochastic processes engendered by the algorithm. It represents the main contribution of this paper as it is, to our knowledge, the first weak convergence result for the reversible jump algorithm. The sampler updating the parameters according to a random walk, this result allows to retrieve the well-known 0.234 rule for finding the optimal scaling. It also leads to an answer to the question: "with what probability should a parameter update be proposed comparatively to a model switch at each iteration?" [ABSTRACT FROM AUTHOR]

Published
2019
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