EAPSI:Developing an objective prior for the Negative Binomial distribution

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Bayesian statistical methodology involves the natural updating of information from a priori knowledge to a posteriori knowledge. In this framework, the prior belief about quantities of interest is updated through the observation of data to obtain a ?posterior distribution,? which contains the updated information about these quantities in light of our observations. This type of analysis can suffer from a poorly chosen prior structure which will have an impact on the posterior results. In objective Bayesian methodology, mathematical techniques are applied to the assumed distributional structure of the observed data so a prior can be computed while maintaining minimal impact on the posterior distribution. This is important because statistics is commonly being applied by scientists directly, and an objective prior takes away the potential for biased results. This project seeks to develop an objective prior for the negative binomial distribution, which to date does not have this structure when both parameters are unknown. This research will be conducted at East China Normal University in Shanghai, China, under the guidance of Dr. Yincai Tang, who has contributed several important results to the objective Bayesian community.Because of the discrete nature of the parameter space of the negative binomial distribution, historically available methods for deriving objective priors do not apply. The 2014 method of Villa and Walker assigns ?worth? to every element in this parameter space by examining how much the overall model structure changes when each element is removed and the objective prior is derived as a function of these values. After the prior is obtained and the posterior is derived, the performance of this structure will be examined under simulation where data with known properties is generated to see how well the method recovers these properties. This NSF EAPSI award supports reserach by a U.S. graduate student and is funded in collaboratin with the Chinese Ministry of Science and Technology.