Investigations particulaires pour l'inférence statistique et l'optimisation de plan d'expériences

Parent, Éric; Amzal, Billy; Girard, Philippe

Journal de la Société française de statistique & Revue de statistique appliquée, Tome 149 (2008) no. 1, pp. 27-51.

Les algorithmes particulaires sont des techniques de Monte-Carlo qui associent des étapes d'échantillonnage pondéré, de rééchantillonnage bootstrap, de régénérescence markovienne et de recuit simulé. Grâce à trois exemples de complexité croissante, nous décrivons leurs implémentations pour l'estimation du maximum de vraisemblance, l'évaluation de la distribution a posteriori pour un modèle à variables latentes et la recherche du plan d'expérience optimal. Les solutions de ces exemples pédagogiques illustrent les performances et les limites de ces algorithmes, promis à une place de choix dans la trousse à outils du statisticien.

Particle algorithms are Monte Carlo techniques that put together steps of importance sampling, bootstrap resampling, markovian rejuvenating and simulated annealing. We develop three examples of increasing complexity and explain how to implement such algorithms for maximum likelihood search, for inference of a model with latent variables and for optimal design. Since we believe that particle algorithms will soon become tools of choice for statistical practitioners, their results are compared with the known solutions of these rather common examples so as to test the algorithms' performances and to show their limits.

Mot clés : algorithmes particulaires, simulation de Monte-Carlo, plan d'expérience optimal, inférence bayésienne
Mots clés : particle algorithms, Monte Carlo simulation, optimal experimental design, bayesian inference

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