A Closed-Form Approximation to the Conjugate Prior of the Dirichlet and Beta Distributions
Machine Learning
2021-07-08 v1 Machine Learning
Statistics Theory
Statistics Theory
Abstract
We derive the conjugate prior of the Dirichlet and beta distributions and explore it with numerical examples to gain an intuitive understanding of the distribution itself, its hyperparameters, and conditions concerning its convergence. Due to the prior's intractability, we proceed to define and analyze a closed-form approximation. Finally, we provide an algorithm implementing this approximation that enables fully tractable Bayesian conjugate treatment of Dirichlet and beta likelihoods without the need for Monte Carlo simulations.
Keywords
Cite
@article{arxiv.2107.03183,
title = {A Closed-Form Approximation to the Conjugate Prior of the Dirichlet and Beta Distributions},
author = {Kaspar Thommen},
journal= {arXiv preprint arXiv:2107.03183},
year = {2021}
}