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.

翻译：我们用数字实例来探索Drichlet 和 beta 分布之前的相似点, 以便获得对分布本身、 其超参数及其趋同条件的直觉理解。 由于先前的可吸引性, 我们着手定义和分析一个封闭式近似值。 最后, 我们提供一种算法来实施这一近似值, 使Drichlet 和 beta 可能性的完全可移动的 Bayesian 共解处理, 而无需蒙特卡洛模拟。