Efficient Sequential Monte-Carlo Samplers for Bayesian Inference

33 Pages Posted: 6 Jun 2017

See all articles by Thi Nguyen

Thi Nguyen

Institut Mines-Télécom Business School

Francois Septier

Institut Mines-Télécom Business School

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Yves Delignon

Institut Mines-Télécom Business School

Date Written: June 5, 2017

Abstract

In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such inference problems. However, in the presence of a high-dimensional and/or multi-modal posterior distribution, it is widely documented that standard Monte-Carlo techniques could lead to poor performance. In this paper, the study is focused on a Sequential Monte-Carlo (SMC) sampler framework, a more robust and efficient Monte Carlo algorithm. Although this approach presents many advantages over traditional Monte-Carlo methods, the potential of this emergent technique is however largely under-exploited in signal processing. In this work, we aim at proposing some novel strategies that will improve the efficiency and facilitate practical implementation of the SMC sampler specifically for signal processing applications.

Firstly, we propose an automatic and adaptive strategy that selects the sequence of distributions within the SMC sampler that minimizes the asymptotic variance of the estimator of the posterior normalization constant. This is critical for performing model selection in modelling applications in Bayesian signal processing. The second original contribution we present improves the global efficiency of the SMC sampler by introducing a novel correction mechanism that allows the use of the particles generated through all the iterations of the algorithm (instead of only particles from the last iteration). This is a significant contribution as it removes the need to discard a large portion of the samples obtained, as is standard in standard SMC methods. This will improve estimation performance in practical settings where computational budget is important to consider.

Keywords: Bayesian inference, Sequential Monte Carlo sampler, complex models

Suggested Citation

Nguyen, Thi and Septier, Francois and Peters, Gareth and Delignon, Yves, Efficient Sequential Monte-Carlo Samplers for Bayesian Inference (June 5, 2017). Available at SSRN: https://ssrn.com/abstract=2980602 or http://dx.doi.org/10.2139/ssrn.2980602

Thi Nguyen

Institut Mines-Télécom Business School

9 rue Charles Fourier
Evry, 91011
France

Francois Septier

Institut Mines-Télécom Business School ( email )

9 rue Charles Fourier
Evry, 91011
France

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Yves Delignon

Institut Mines-Télécom Business School

9 rue Charles Fourier
Evry, 91011
France

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