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Statistics and Computing

, Volume 23, Issue 2, pp 163–184 | Cite as

Sequential Monte Carlo on large binary sampling spaces

  • Christian SchäferEmail author
  • Nicolas Chopin
Article

Abstract

A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for good performance. In this paper, we present such a parametric family for adaptive sampling on high dimensional binary spaces.

A practical motivation for this problem is variable selection in a linear regression context. We want to sample from a Bayesian posterior distribution on the model space using an appropriate version of Sequential Monte Carlo.

Raw versions of Sequential Monte Carlo are easily implemented using binary vectors with independent components. For high dimensional problems, however, these simple proposals do not yield satisfactory results. The key to an efficient adaptive algorithm are binary parametric families which take correlations into account, analogously to the multivariate normal distribution on continuous spaces.

We provide a review of models for binary data and make one of them work in the context of Sequential Monte Carlo sampling. Computational studies on real life data with about a hundred covariates suggest that, on difficult instances, our Sequential Monte Carlo approach clearly outperforms standard techniques based on Markov chain exploration.

Keywords

Adaptive Monte Carlo Multivariate binary data Sequential Monte Carlo Linear regression Variable selection 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Centre de Recherche en Économie et StatistiqueMalakoffFrance
  2. 2.CEntre de REcherches en MAthématiques de la DEcisionUniversité Paris-DauphineParisFrance
  3. 3.Ecole Nationale de la Statistique et de l’AdministrationMalakoffFrance

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