On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods
| Autor: | Daniel Simpson, Anne-Marie Lyne, Yves F. Atchadé, Heiko Strathmann, Mark Girolami |
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| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
FOS: Computer and information sciences General Mathematics Posterior probability Intractable likelihood Machine Learning (stat.ML) Bayesian inference 01 natural sciences Statistics - Computation Methodology (stat.ME) 010104 statistics & probability symbols.namesake Statistics - Machine Learning 0103 physical sciences Exponential random graph models Applied mathematics Statistics::Methodology Truncation (statistics) 0101 mathematics 010306 general physics Computation (stat.CO) Statistics - Methodology stat.CO Statistical model Markov chain Monte Carlo Monte Carlo methods stat.ML Marginal likelihood Statistics::Computation pseudo-marginal MCMC stat.ME symbols Russian Roulette sampling Statistics Probability and Uncertainty Approximate Bayesian computation |
| Zdroj: | Lyne, A-M, Girolami, M, Atchadé, Y, Strathmann, H & Simpson, D 2015, ' On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods ', Statistical Science, vol. 30, no. 4, pp. 443-467 . https://doi.org/10.1214/15-STS523 Statist. Sci. 30, no. 4 (2015), 443-467 |
| DOI: | 10.1214/15-STS523 |
| Popis: | A large number of statistical models are "doubly-intractable": the likelihood normalising term, which is a function of the model parameters, is intractable, as well as the marginal likelihood (model evidence). This means that standard inference techniques to sample from the posterior, such as Markov chain Monte Carlo (MCMC), cannot be used. Examples include, but are not confined to, massive Gaussian Markov random fields, autologistic models and Exponential random graph models. A number of approximate schemes based on MCMC techniques, Approximate Bayesian computation (ABC) or analytic approximations to the posterior have been suggested, and these are reviewed here. Exact MCMC schemes, which can be applied to a subset of doubly-intractable distributions, have also been developed and are described in this paper. As yet, no general method exists which can be applied to all classes of models with doubly-intractable posteriors. In addition, taking inspiration from the Physics literature, we study an alternative method based on representing the intractable likelihood as an infinite series. Unbiased estimates of the likelihood can then be obtained by finite time stochastic truncation of the series via Russian Roulette sampling, although the estimates are not necessarily positive. Results from the Quantum Chromodynamics literature are exploited to allow the use of possibly negative estimates in a pseudo-marginal MCMC scheme such that expectations with respect to the posterior distribution are preserved. The methodology is reviewed on well-known examples such as the parameters in Ising models, the posterior for Fisher-Bingham distributions on the $d$-Sphere and a large-scale Gaussian Markov Random Field model describing the Ozone Column data. This leads to a critical assessment of the strengths and weaknesses of the methodology with pointers to ongoing research. Published at http://dx.doi.org/10.1214/15-STS523 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | OpenAIRE |
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