Abstract Details
Activity Number:
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401
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Type:
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Contributed
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Date/Time:
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Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistical Computing
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Abstract #312266
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View Presentation
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Title:
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Approximate Bayesian Computation for a Five-Parameter Bivariate Beta Model and Its Applications
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Author(s):
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Roberto Crackel*+ and James Flegal
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Companies:
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and University of California, Riverside
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Keywords:
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Approximate Bayesian computation ;
Bivariate beta ;
accept-reject
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Abstract:
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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 a 5 and 8 parameter model. 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 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 under various priors and tolerance levels. We make application of the 5 parameter bivariate beta in a bivariate beta binomial context. Specifically, the bivariate beta binomial distribution is used to model the probabilities and correlation of purchasing bacon and eggs on a single shopping trip, described previously by Danaher and Hardie (2005). In this model, we allow the 5 parameter model to serve as a prior distribution to correlated proportions and it serves as a competitor to the bivariate beta model prop
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Authors who are presenting talks have a * after their name.
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