Affiliation:
1. CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris, Cedex 16, France
Abstract
Summary
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are, however, sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this dimension grows. To tackle this difficulty we explore a Gibbs version of the approximate Bayesian computation approach that runs component-wise approximate Bayesian computation steps aimed at the corresponding conditional posterior distributions, and based on summary statistics of reduced dimensions. While lacking the standard justifications for the Gibbs sampler, the resulting Markov chain is shown to converge in distribution under some partial independence conditions. The associated stationary distribution can further be shown to be close to the true posterior distribution, and some hierarchical versions of the proposed mechanism enjoy a closed-form limiting distribution. Experiments also demonstrate the gain in efficiency brought by the Gibbs version over the standard solution.
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Statistics, Probability and Uncertainty,General Agricultural and Biological Sciences,Agricultural and Biological Sciences (miscellaneous),General Mathematics,Statistics and Probability
Cited by
10 articles.
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