Monte Carlo methods

R. Bardenet 1, 2
1 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
2 Appstat
LAL - Laboratoire de l'Accélérateur Linéaire, LRI - Laboratoire de Recherche en Informatique, Department of Statistics [Oxford]
Abstract : Bayesian inference often requires integrating some function with respect to a posterior distribution. Monte Carlo methods are sampling algorithms that allow to compute these integrals numerically when they are not analytically tractable. We review here the basic principles and the most common Monte Carlo algorithms, among which rejection sampling, importance sampling and Monte Carlo Markov chain (MCMC) methods. We give intuition on the theoretical justification of the algorithms as well as practical advice, trying to relate both. We discuss the application of Monte Carlo in experimental physics, and point to landmarks in the literature for the curious reader.
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Last modification on : Thursday, April 5, 2018 - 12:30:24 PM
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R. Bardenet. Monte Carlo methods. IN2P3 School of Statistics (SOS2012), May 2012, Autrans, France. pp.022002, ⟨10.1051/epjconf/20135502002⟩. ⟨in2p3-00846142⟩

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