A Closed-Type Approximation to the Conjugate Prior of the Dirichlet and Beta Distributions
Authors: Kaspar Thommen
Summary: We derive the conjugate prior of the Dirichlet and beta distributions and discover it with numerical examples to achieve an intuitive understanding of the distribution itself, its hyperparameters, and circumstances regarding its convergence. As a result of prior’s intractability, we proceed to outline and analyze a closed-form approximation. Lastly, we offer an algorithm implementing this approximation that allows absolutely tractable Bayesian conjugate therapy of Dirichlet and beta likelihoods with out the necessity for Monte Carlo simulations.
