Abstract
Several Monte Carlo methods have been proposed for computing marginal likelihoods in Bayesian analyses. Some of these involve sampling from a sequence of intermediate distributions between the prior and posterior. A difficulty arises if the support in the posterior distribution is a proper subset of that in the prior distribution. This can happen in problems involving latent variables whose support depends upon the data and can make some methods inefficient and others invalid. The correction required for models of this type is derived and its use is illustrated by finding the marginal likelihoods in two examples. One concerns a model for competing risks. The other involves a zero-inflated over-dispersed Poisson model for counts of centipedes, using latent Gaussian variables to capture spatial dependence.
Highlights
The marginal likelihood, known as the integrated likelihood or the evidence, plays an important role in Bayesian inference, in model selection and model averaging, where it is used in the computation of Bayes factors and posterior model probabilities.Consider data y and a statistical model p(y|θ) which depends on unknowns θ
Sometimes the posterior support of the latent variables depends on the data and is a proper subset of the prior support
Sampling from a sequence of intermediate distributions which connect the prior to the posterior is the basis for several Monte Carlo methods for approximating marginal likelihoods
Summary
The marginal likelihood, known as the integrated likelihood or the evidence, plays an important role in Bayesian inference, in model selection and model averaging, where it is used in the computation of Bayes factors and posterior model probabilities. Data-dependent support can present problems for Chib’s method if the likelihood ordinate (typically the observed data likelihood) is difficult to evaluate This paper addresses the former of these issues and describes a general two-stage procedure to correct, or improve the efficiency of, intermediate-density-methods in problems involving datadependent support, whilst highlighting the situations in which implementation of the proposed approach is likely to be simpler than Chib’s method. In this model, latent Gaussian variables capture the spatial dependences between the presence and the abundance of centipedes and we compare three variants of the model which use different parametric forms for the covariance matrix.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
