EAPSI:Developing an objective prior for the Negative Binomial distribution

EAPSI：为负二项式分布制定目标先验

• 批准号: 1515156
• 负责人: John Snyder
• 金额: $ 0.51万
• 依托单位: Snyder John C
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-01 至 2016-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1515156&HistoricalAwards=false
• 关键词: EAPSI; Developing; objective; prior; Negative

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.

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，通过观察数据来更新有关感兴趣数量的先验信念以获得“后验分布”。其中包含根据我们的观察得出的有关这些数量的最新信息。 这种类型的分析可能会受到先验结构选择不当的影响，这会对后验结果产生影响。 在客观贝叶斯方法中，数学技术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。 这很重要，因为统计数据通常由科学家直接应用，而客观的先验消除了出现有偏见结果的可能性。 该项目旨在为负二项式分布开发一个目标先验，迄今为止，当两个参数未知时，负二项式分布不具有这种结构。 这项研究将在中国上海华东师范大学进行，在唐银才博士的指导下进行，唐银才博士为客观贝叶斯界贡献了多项重要成果。由于负二项分布参数空间的离散性，历史上可用的推导客观先验的方法并不适用。 维拉和沃克的2014年方法分配“价值”通过检查当每个元素被删除时整体模型结构发生了多少变化，并根据这些值导出目标先验，从而对该参数空间中的每个元素进行分析。 获得先验并导出后验后，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。该 NSF EAPSI 奖项支持美国研究生的研究，并由与中国科学技术部合作资助。