Bayesian Inference for Gamma Models
Abstract
We use the theory of normal variancemean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including MultinomialDirichlet distributions, Negative binomial regression, PoissonGamma hierarchical models, Extreme value models, to name but a few. All of those models include a gamma function which does not admit a natural conjugate prior distribution providing a significant challenge to inference and prediction. To provide a data augmentation strategy, we construct and develop the theory of the class of Exponential Reciprocal Gamma distributions. This allows scalable EM and MCMC algorithms to be developed. We illustrate our methodology on a number of examples, including gamma shape inference, negative binomial regression and Dirichlet allocation. Finally, we conclude with directions for future research.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.01906
 Bibcode:
 2021arXiv210601906H
 Keywords:

 Statistics  Methodology;
 Statistics  Computation;
 Statistics  Machine Learning
 EPrint:
 Duplicate submission of arXiv:1905.12141 Please check arXiv:1905.12141 for future update