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。在这个框架中，通过对数据的观察，更新对感兴趣数量的先验信念，得到？后验分布,?它包含了根据我们的观测得出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最小影响。这一点很重要，因为统计数据通常是由科学家直接应用的，而客观的先验会消除结果有偏差的可能性。该项目旨在为负二项分布开发一个客观的先验，当两个参数都未知时，迄今为止还没有这种结构。本研究将在中国上海华东师范大学进行，在唐寅才博士的指导下进行，他为客观贝叶斯社区贡献了几个重要成果。由于负二项分布的参数空间的离散性，历史上可用的方法来推导客观先验不适用。Villa和Walker的2014年方法分配了？对于这个参数空间中的每个元素，通过检查当每个元素被移除时整体模型结构的变化程度，并将目标先验作为这些值的函数推导出来。在获得先验并导出后验之后，将在模拟中检查该结构的性能，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程度。美国国家科学基金会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.