# Bayesian inference for a flexible class of bivariate beta distributions

arXiv: https://arxiv.org/abs/1402.1782 · HTML: https://mlsanity.com/paper/1402.1782/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2014.

## Built on by (most cited first, 1 of 1)

- [Adapting Rule Representation With Four-Parameter Beta Distribution for Learning Classifier Systems](https://mlsanity.com/paper/2506.03602/) (2025)

## Abstract (arXiv)

Several bivariate beta distributions have been proposed in the literature. In particular, Olkin and Liu (2003) proposed a 3 parameter bivariate beta model, which Arnold and Ng (2011) extend to 5 and 8 parameter models. The 3 parameter model allows for only positive correlation, while the latter models can accommodate both positive and negative correlation. However, these come at the expense of a density that is mathematically intractable. The focus of this research is on Bayesian estimation for the 5 and 8 parameter models. Since the likelihood does not exist in closed form, we apply approximate Bayesian computation, a likelihood free approach. Simulation studies have been carried out for the 5 and 8 parameter cases under various priors and tolerance levels. We apply the 5 parameter model to a real data set by allowing the model to serve as a prior to correlated proportions of a bivariate beta binomial model. Results and comparisons are then discussed.