A fast universal self-tuned sampler within Gibbs sampling

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• 作者：L. Martino^a ; ^{lukatotal@gmail.com" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; H. Yang^bAuthor Vitae ; D. Luengo^cAuthor Vitae ; J. Kanniainen^bAuthor Vitae ; J. Corander^aAuthor Vitae
• 关键词：Markov Chain Monte Carlo (MCMC) ; Gibbs sampling ; Bayesian inference ; Metropolis within Gibbs ; Adaptive rejection Metropolis sampling
• 刊名：Digital Signal Processing
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：47
• 期：Complete
• 页码：68-83
• 全文大小：979 K

文摘

Bayesian inference often requires efficient numerical approximation algorithms, such as sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) methods. The Gibbs sampler is a well-known MCMC technique, widely applied in many signal processing problems. Drawing samples from univariate full-conditional distributions efficiently is essential for the practical application of the Gibbs sampler. In this work, we present a simple, self-tuned and extremely efficient MCMC algorithm which produces virtually independent samples from these univariate target densities. The proposal density used is self-tuned and tailored to the specific target, but it is not adaptive. Instead, the proposal is adjusted during an initial optimization stage, following a simple and extremely effective procedure. Hence, we have named the newly proposed approach as FUSS (Fast Universal Self-tuned Sampler), as it can be used to sample from any bounded univariate distribution and also from any bounded multi-variate distribution, either directly or by embedding it within a Gibbs sampler. Numerical experiments, on several synthetic data sets (including a challenging parameter estimation problem in a chaotic system) and a high-dimensional financial signal processing problem, show its good performance in terms of speed and estimation accuracy.