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Malakoff, France

Statistics and Computing | Year: 2011

We consider the problem of simulating a Gaussian vector X, conditional on the fact that each component of X belongs to a finite interval [ai,bi], or a semi-finite interval [ai,+∞). In the one-dimensional case, we design a table-based algorithm that is computationally faster than alternative algorithms. In the two-dimensional case, we design an accept-reject algorithm. According to our calculations and numerical studies, the acceptance rate of this algorithm is bounded from below by 0.5 for semi-finite truncation intervals, and by 0.47 for finite intervals. Extension to three or more dimensions is discussed. © 2010 Springer Science+Business Media, LLC. Source

Barthelme S.,TU Berlin | Chopin N.,ENSAE CREST
Proceedings of the 28th International Conference on Machine Learning, ICML 2011 | Year: 2011

Many statistical models of interest to the natural and social sciences have no tractable likelihood function. Until recently, Bayesian inference for such models was thought infeasible. Pritchard et al. (1999) introduced an algorithm known as ABC, for Approximate Bayesian Computation, that enables Bayesian computation in such models. Despite steady progress since this first breakthrough, such as the adaptation of MCMC and Sequential Monte Carlo techniques to likelihood-free inference, state-of-the art methods remain hard to use and require enormous computation times. Among other issues, one faces the difficult task of finding appropriate summary statistics for the model, and tuning the algorithm can be time-consuming when little prior information is available. We show that Expectation Propagation, a widely successful approximate inference technique, can be adapted to the likelihood-free context. The resulting algorithm does not require summary statistics, is an order of magnitude faster than existing techniques, and remains usable when prior information is vague. Copyright 2011 by the author(s)/owner(s). Source

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