EAPSI:Developing an objective prior for the Negative Binomial distribution

贝叶斯统计方法涉及信息从先验知识到后验知识的自然更新。 在此框架下，先验信念的数量感兴趣的更新，通过观察数据，以获得一个？后验分布，？它包含了根据我们的观测得到的关于这些量的最新信息。 这种类型的分析可能会受到选择不当的先验结构的影响，这将对后验结果产生影响。 在客观贝叶斯方法中，数学技术被应用于观测数据的假设分布结构，因此可以计算先验，同时保持对后验分布的影响最小。 这一点很重要，因为统计学通常由科学家直接应用，客观的先验消除了有偏见结果的可能性。 这个项目旨在为负二项分布开发一个客观的先验，到目前为止，当两个参数都未知时，负二项分布还没有这种结构。 本研究将在中国上海华东师范大学进行，由唐银才博士指导。唐银才博士为客观贝叶斯社区贡献了几个重要成果。由于负二项分布参数空间的离散性，历史上用于推导客观先验的方法不适用。 维拉和步行者2014年的方法分配？值得吗通过检查当每个元素被移除时整个模型结构改变了多少，将目标先验作为这些值的函数导出。 在获得先验和推导后验之后，将在模拟下检查该结构的性能，其中生成具有已知属性的数据，以查看该方法恢复这些属性的效果如何。这个NSF EAPSI奖支持美国研究生的研究，并与中国科技部合作资助。

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.