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An Overview of Stochastic Approximation Monte Carlo

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During the past few decades, Markov chain Monte Carlo (MCMC) has been widely used in Bayesian statistical inference and scientific computing. Its successes have proven it to be a very powerful and typically unique computational tool for analyzing data of complex structures. However, conventional MCMC algorithms often suffer from the local trap problem which renders the simulation ineffective. This paper provides an overview of the theory, variants, and applications for stochastic approximation Monte Carlo (SAMC), an advanced MCMC algorithm that is essentially immune to the local trap problem. WIREs Comput Stat 2014, 6:240–254. doi: 10.1002/wics.1305 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)
(a) Contour of U(x). (b) Sample path of SAMC. (c) Sample path of MH at the temperature τ = 5.
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Mean square errors (MSEs) produced by population‐SAMC and SAMC at different iterations for a multimodal example. The left plot is produced with at = t0/max(t0, t), and the right plot is produced with at = t0/max(t0, t0.6).
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Average progression curves of the best function values (over 20 runs) and their 95% confidence regions (shaded area) produced by SAA, annealing evolutionary SAMC, space annealing SAMC, simulated annealing, and the genetic algorithm for minimizing the rational‐expectations model.
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Progressive curves of the highest test statistic values sampled by SAMC (‘+’) and the permutation method (‘o’) for a two‐sample t‐test example. The x‐axis plots the logarithm (based 10) of iterations.
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Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)

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