2021/07/07 by Kaspar Thommen, Thommen, Kaspar
Computer Science · Decision Sciences · Mathematics · #62E17 #62F15 #65C60 #Advanced Multi-Objective Optimization Algorithms #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #G.3 #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2107.03183
openalex publication_date 2021/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive the conjugate prior of the Dirichlet and beta distributions and\nexplore it with numerical examples to gain an intuitive understanding of the\ndistribution itself, its hyperparameters, and conditions concerning its\nconvergence. Due to the prior's intractability, we proceed to define and\nanalyze a closed-form approximation. Finally, we provide an algorithm\nimplementing this approximation that enables fully tractable Bayesian conjugate\ntreatment of Dirichlet and beta likelihoods without the need for Monte Carlo\nsimulations.\n