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Activity Number: 433
Type: Contributed
Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #309090
Title: Approximate Bayesian Computation for a Flexible Class of Bivariate Beta Distributions
Author(s): Roberto Crackel*+ and James M. Flegal
Companies: UC Riverside and University of California, Riverside
Keywords: approximate Bayesian computation ; MH algorithm ; bivariate beta ; accept-reject
Abstract:

Several bivariate beta distributions have been proposed in the literature. In particular, Olkin and Liu (2003) proposed a 3 parameter bivariate beta model, while Arnold and Ng (2011) proposed a 5 parameter model. The 3 parameter model allows for only positive correlation, while the latter can accommodate both positive and negative correlation; however it comes at the expense of a density that is mathematically intractable. Arnold and Ng discuss an extension to an 8 parameter case.

The focus of this research is on Bayesian estimation for the 5 and 8 parameter model. Since the likelihood does not exist in closed form, we apply approximate Bayesian computation (ABC), a likelihood free based approach. We consider two particular algorithms encompassed within the ABC framework: the accept-reject method and the ABC-Metropolis Hastings algorithm. Simulation studies have been carried out for the 5 and 8 parameter cases under various priors and tolerance levels. Results and comparisons are discussed between the two proposed algorithms.


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