91 research outputs found
Calibration of conditional composite likelihood for Bayesian inference on Gibbs random fields
Gibbs random fields play an important role in statistics, however, the
resulting likelihood is typically unavailable due to an intractable normalizing
constant. Composite likelihoods offer a principled means to construct useful
approximations. This paper provides a mean to calibrate the posterior
distribution resulting from using a composite likelihood and illustrate its
performance in several examples.Comment: JMLR Workshop and Conference Proceedings, 18th International
Conference on Artificial Intelligence and Statistics (AISTATS), San Diego,
California, USA, 9-12 May 2015 (Vol. 38, pp. 921-929). arXiv admin note:
substantial text overlap with arXiv:1207.575
Bayesian inference for Gibbs random fields using composite likelihoods
Gibbs random fields play an important role in statistics, for example the
autologistic model is commonly used to model the spatial distribution of binary
variables defined on a lattice. However they are complicated to work with due
to an intractability of the likelihood function. It is therefore natural to
consider tractable approximations to the likelihood function. Composite
likelihoods offer a principled approach to constructing such approximation. The
contribution of this paper is to examine the performance of a collection of
composite likelihood approximations in the context of Bayesian inference.Comment: To appear in the proceedings of the 2012 Winter Simulation Conferenc
Bayesian model selection for exponential random graph models via adjusted pseudolikelihoods
Models with intractable likelihood functions arise in areas including network
analysis and spatial statistics, especially those involving Gibbs random
fields. Posterior parameter es timation in these settings is termed a
doubly-intractable problem because both the likelihood function and the
posterior distribution are intractable. The comparison of Bayesian models is
often based on the statistical evidence, the integral of the un-normalised
posterior distribution over the model parameters which is rarely available in
closed form. For doubly-intractable models, estimating the evidence adds
another layer of difficulty. Consequently, the selection of the model that best
describes an observed network among a collection of exponential random graph
models for network analysis is a daunting task. Pseudolikelihoods offer a
tractable approximation to the likelihood but should be treated with caution
because they can lead to an unreasonable inference. This paper specifies a
method to adjust pseudolikelihoods in order to obtain a reasonable, yet
tractable, approximation to the likelihood. This allows implementation of
widely used computational methods for evidence estimation and pursuit of
Bayesian model selection of exponential random graph models for the analysis of
social networks. Empirical comparisons to existing methods show that our
procedure yields similar evidence estimates, but at a lower computational cost.Comment: Supplementary material attached. To view attachments, please download
and extract the gzzipped source file listed under "Other formats
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