Efﬁcient Sequential Monte-Carlo Samplers for Bayesian Inference
33 Pages Posted: 6 Jun 2017
Date Written: June 5, 2017
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
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