Beta distributions are used, among other things, priors for Bernoulli and Binomial problems and range/mode/degree of certainty estimate elicitation with human experts.

Joint distributions can be obtained from Beta marginals by assuming independence (the approach I used for Greenbox,which targets parameter elicitation for Excel models), but it isn't trivially true that uncertain parameters should be considered unrelated.

This repository has a few tools for dealing with AMH/Multibeta distributions (afaik not an existing term). The Ali-Mikhail-Haq (AMH) copula is parameterized by a single dependence parameter $\theta \in [-1,1)$ and specializes to the joint-independent distribution for $\theta = 0$.

Included are:

• Rejection samplers for (generic) univariate, bivariate and multivariate distributions (there seems to be no widely-used, well-maintained Python package for this)
• Probability density functions for the bivariate and multivariate AMH/beta distributions
• Sampler (random generator) for the AMH/multibeta distributions
• A fun 2-d visualization.

This project is mostly written in Hy. It can be trivially imported to Python code once you pip install hy. It may be useful to use hy2py to examine sources if you're unsure of what's going on.