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Monte Carlo methods for sampling high-dimensional binary vectors


  • Chopin, Nicolas


  • Schäfer, Christian


This thesis is concerned with Monte Carlo methods for sampling high-dimensional binary vectors from complex distributions of interest. If the state space is too large for exhaustive enumeration, these methods provide a mean of estimating the expected value with respect to some function of interest. Standard approaches are mostly based on random walk type Markov chain Monte Carlo, where the equilibrium distribution of the chain is the distribution of interest and its ergodic mean converges to the expected value. We propose a novel sampling algorithm based on sequential Monte Carlo methodology which copes well with multi-modal problems by virtue of an annealing schedule. The performance of the proposed sequential Monte Carlo sampler depends on the ability to sample proposals from auxiliary distributions which are, in a certain sense, close to the current distribution of interest. The core work of this thesis discusses strategies to construct parametric families for sampling binary vectors with dependencies. The usefulness of this approach is demonstrated in the context of Bayesian variable selection and combinatorial optimization of pseudo-Boolean objective functions.

Suggested Citation

  • Schäfer, Christian, 2012. "Monte Carlo methods for sampling high-dimensional binary vectors," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/10860 edited by Chopin, Nicolas, June.
  • Handle: RePEc:dau:thesis:123456789/10860
    Note: dissertation

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    References listed on IDEAS

    1. repec:dau:papers:123456789/5671 is not listed on IDEAS
    2. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320.
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    More about this item


    Optimisation binaire; Familles paramétriques binaires; Sélection bayésienne de variable; Monte Carlo sequentiel;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General


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