Expectation propagation for estimating the parameters of the beta distribution

Parameter estimation for the beta distribution is analytically intractable due to the integration expression in the normalization constant. For maximum likelihood estimation, numerical methods can be used to calculate the parameters. For Bayesian estimation, we can utilize different approximations to the posterior parameter distribution. A method based on the variational inference (VI) framework reported the posterior mean of the parameters analytically but the approximating distribution violated the correlation between the parameters. We now propose a method via the expectation propagation (EP) framework to approximate the posterior distribution analytically and capture the correlation between the parameters. Compared to the method based on VI, the EP based algorithm performs better with small amounts of data and is more stable.