BibTeX
@MISC{Paquet08bayesianinference,
author = {Ulrich Paquet},
title = {Bayesian inference for},
year = {2008}
}
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Abstract
ISSN 1476-2986Abstract 3 Bayes ’ theorem is the cornerstone of statistical inference. It provides the tools for dealing with knowledge in an uncertain world, allowing us to explain observed phenomena through the refinement of belief in model parameters. At the heart of this elegant framework lie intractable integrals, whether in computing an average over some posterior distribution, or in determining the normalizing constant of a distribution. This thesis examines both deterministic and stochastic methods in which these integrals can be treated. Of particular interest shall be parametric models where the parameter space can be extended with additional latent variables to get distributions that are easier to handle algorithmically. Deterministic methods approximate the posterior distribution with a simpler distribution over which the required integrals become tractable. We derive and examine a new generic α-divergence message passing scheme for a multivariate mixture of Gaussians, a particular modeling problem requiring latent variables. This algorithm minimizes local α-divergences over a chosen posterior factorization, and includes variational Bayes and expectation propagation as
Keyphrases
bayesian inference posterior distribution stochastic method expectation propagation particular modeling problem multivariate mixture variational bayes local divergence deterministic method parametric model observed phenomenon chosen posterior factorization model parameter elegant framework latent variable uncertain world intractable integral simpler distribution parameter space particular interest bayes theorem new generic divergence message normalizing constant statistical inference required integral additional latent variable
