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Abstract We propose a Bayesian model selection approach for generalized linear mixed models (GLMMs). We consider covariance structures for the random effects that are widely used in areas such as longitudinal studies, genome-wide association studies, and spatial statistics. Since the random effects cannot be integrated out of GLMMs analytically, we approximate the integrated likelihood function using a pseudo-likelihood approach. Our Bayesian approach assumes a flat prior for the fixed effects and includes both approximate reference prior and half-Cauchy prior choices for the variances of random effects. Since the flat prior on the fixed effects is improper, we develop a fractional Bayes factor approach to obtain posterior probabilities of the several competing models. Simulation studies with Poisson GLMMs with spatial random effects and overdispersion random effects show that our approach performs favorably when compared to widely used competing Bayesian methods including deviance information criterion and Watanabe–Akaike information criterion. We illustrate the usefulness and flexibility of our approach with three case studies including a Poisson longitudinal model, a Poisson spatial model, and a logistic mixed model. Our proposed approach is implemented in the R package GLMMselect that is available on CRAN.
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Pseudo-Bayesian Learning via Direct Loss Minimization with Applications to Sparse Gaussian Process Models
We propose that approximate Bayesian algorithms should optimize a new criterion, directly derived from the loss, to calculate their approximate posterior which we refer to as pseudo-posterior. Unlike standard variational inference which optimizes a lower bound on the log marginal likelihood, the new algorithms can be analyzed to provide loss guarantees on the predictions with the pseudo-posterior. Our criterion can be used to derive new sparse Gaussian process algorithms that have error guarantees applicable to various likelihoods.
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- PAR ID:
- 10146126
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- ISSN:
- 2640-3498
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
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