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A Fast Universal Self-Tuned Sampler Within Gibbs Sampling

Authors: L. Martino, H. Yang, D. Luengo, J. Kanniainen, J. Corander

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.

Comments: Digital Signal Processing, Volume 47, Pages 68-83, 2015.

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Submission history

[v1] 2014-05-18 08:40:10
[v2] 2014-06-02 04:58:08
[v3] 2014-07-02 10:33:21
[v4] 2015-04-09 13:23:39

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