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Free Energy Sequential Monte Carlo Application to Mixture Modelling

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  • Nicolas Chopin

    (Crest)

  • Pierre Jacob

    (Crest)

Abstract

We introduce a new class of Sequential Monte Carlo (SMC) methods, whichwe call free energy SMC. This class is inspired by free energy methods, whichoriginate from Physics, and where one samples from a biased distribution suchthat a given function !(") of the state " is forced to be uniformly distributedover a given interval. From an initial sequence of distributions (#t) of interest,and a particular choice of !("), a free energy SMC sampler computes sequentiallya sequence of biased distributions (˜#t) with the following properties: (a)the marginal distribution of !(") with respect to ˜#t is approximatively uniformover a specified interval, and (b) ˜#t and #t have the same conditional distributionwith respect to !. We apply our methodology to mixture posteriordistributions, which are highly multimodal. In the mixture context, forcingcertain hyper-parameters to higher values greatly faciliates mode swapping,and makes it possible to recover a symetric output. We illustrate our approachwith univariate and bivariate Gaussian mixtures and two real-world datasets.

Suggested Citation

  • Nicolas Chopin & Pierre Jacob, 2010. "Free Energy Sequential Monte Carlo Application to Mixture Modelling," Working Papers 2010-34, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2010-34
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    Cited by:

    1. Drovandi, Christopher C. & Pettitt, Anthony N. & Henderson, Robert D. & McCombe, Pamela A., 2014. "Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 128-146.
    2. Garland Durham & John Geweke, 2013. "Adaptive Sequential Posterior Simulators for Massively Parallel Computing Environments," Working Paper Series 9, Economics Discipline Group, UTS Business School, University of Technology, Sydney.

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