2014/02/07 by Roberto C. Crackel, James M. Flegal, Crackel, Roberto C. +1 · 1 citation
Computer Science · Mathematics · #62F15 #62H12 #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #msc:62F15 #msc:62H12 #stat.CO #stat.ME
paper · pdf · doi:10.48550/arxiv.1402.1782
22 pages, 3 figures
openalex publication_date 2014/02/07 · arxiv created 2015/08/20 · arxiv updated 2015/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several bivariate beta distributions have been proposed in the literature. In particular, Olkin and Liu (2003) proposed a 3 parameter bivariate beta model, which Arnold and Ng (2011) extend to 5 and 8 parameter models. The 3 parameter model allows for only positive correlation, while the latter models can accommodate both positive and negative correlation. However, these come at the expense of a density that is mathematically intractable. The focus of this research is on Bayesian estimation for the 5 and 8 parameter models. Since the likelihood does not exist in closed form, we apply approximate Bayesian computation, a likelihood free approach. Simulation studies have been carried out for the 5 and 8 parameter cases under various priors and tolerance levels. We apply the 5 parameter model to a real data set by allowing the model to serve as a prior to correlated proportions of a bivariate beta binomial model. Results and comparisons are then discussed.