# Bayesian Inference for Gamma Models

@inproceedings{He2021BayesianIF, title={Bayesian Inference for Gamma Models}, author={Jingyu He and Nicholas G. Polson and Jianeng Xu}, year={2021} }

We use the theory of normal variance-mean 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 Multinomial-Dirichlet distributions, Negative binomial regression, Poisson-Gamma 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…

## One Citation

### On Data Augmentation for Models Involving Reciprocal Gamma Functions

- Mathematics, Computer ScienceJournal of Computational and Graphical Statistics
- 2022

This paper introduces a new and eﬃcient data augmentation approach to the posterior inference of the models with shape parameters when the reciprocal gamma function appears in full conditional densities by using Gauss's multiplication formula and Stirling’s formula for the gamma function.

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