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Adaptive Monte Carlo on Multivariate Binary Sampling Spaces

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  • Nicolas Chopin

    (Crest)

  • Christian Schafer

    (Crest)

Abstract

A Monte Carlo algorithm is said to be adaptive if it can adjust automaticallyits current proposal distribution, using past simulations. The choice of the para-metric family that defines the set of proposal distributions is critical for a goodperformance. We treat the problem of constructing such parametric families foradaptive sampling on multivariate binary spaces.A practical motivation for this problem is variable selection in a linear regres-sion context, where we need to either find the best model, with respect to somecriterion, or to sample from a Bayesian posterior distribution on the model space.In terms of adaptive algorithms, we focus on the Cross-Entropy (CE) method foroptimisation, and the Sequential Monte Carlo (SMC) methods for sampling.Raw versions of both SMC and CE algorithms are easily implemented using bi-nary vectors with independent components. However, for high-dimensional modelchoice problems, these straightforward proposals do not yields satisfactory re-sults. The key to advanced adaptive algorithms are binary parametric familieswhich take at least the linear dependencies between components into account.We review suitable multivariate binary models and make them work in thecontext of SMC and CE. Extensive computational studies on real life data with ahundred covariates seem to prove the necessity of more advanced binary families,to make adaptive Monte Carlo procedures efficient. Besides, our numerical resultsencourage the use of SMC and CE methods as alternatives to techniques basedon Markov chain exploration.

Suggested Citation

  • Nicolas Chopin & Christian Schafer, 2010. "Adaptive Monte Carlo on Multivariate Binary Sampling Spaces," Working Papers 2010-24, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2010-24
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    References listed on IDEAS

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    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. David J. Nott & Robert Kohn, 2005. "Adaptive sampling for Bayesian variable selection," Biometrika, Biometrika Trust, vol. 92(4), pages 747-763, December.
    3. D. R. Cox, 2002. "On some models for multivariate binary variables parallel in complexity with the multivariate Gaussian distribution," Biometrika, Biometrika Trust, vol. 89(2), pages 462-469, June.
    4. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    5. D. R. Cox, 1972. "The Analysis of Multivariate Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(2), pages 113-120, June.
    6. Reuven Rubinstein, 1999. "The Cross-Entropy Method for Combinatorial and Continuous Optimization," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 127-190, September.
    7. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
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