Combining probability distributions for statistical inference on the basis of complementary methods

基于互补方法组合概率分布进行统计推断

• 批准号: RGPIN-2014-06495
• 负责人: Bickel, David
• 金额: $ 1.02万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635803
• 关键词: Combining; probability; distributions; statistical; inference

Dr. Bickel published a general method of combining probability distributions without setting weights subjectively, as is done with many methods of combining expert opinions in the form of prior distributions. That general method was used to combine previous statistical methods even when they individually give conflicting interpretations of the same set of measurements. This proposal extends that work to concrete problems faced in statistical analyses of measurements. In addition, the reliability of that method of distribution combination will be compared to other methods of combining probability distributions and to the usual statistical methods, which do not involve combining probability distributions. That reliability will be determined on the basis of mathematical theory when possible and on the basis of simulated measurements otherwise.Applications of the proposed research include the analysis of measurements of the activity levels of thousands of genes and other large-scale measurements. Improvements in interpreting the results of these new data types can lead to new biological discoveries, for example, of which genes in tomatoes have activity levels depending on the breed or on the stage of fruit development. This knowledge may potentially result in more efficient food production within Canada and within its trading partners, making higher-quality food more readily available to Canadians. Applications of the proposed research also include learning from smaller-scale sets of measurements whenever current methods of data analysis report different interpretations. Such situations are common not only in basic science but also in agriculture. In addition to the above long-term benefits of the research to the growth of scientific knowledge and the possibility of more efficient food production, this proposal can have short-term economic benefits via the training of highly qualified personnel. The students trained in the course of the proposed projects will be equipped to contribute to data analyses in basic sciences and in biostatistics for agricultural applications, fields that together provide employment opportunities to a large proportion of Canadian statisticians.

Bickel博士发表了一种将概率分布相结合而不主观设置的概率分布的通用方法，就像以先验分布形式结合专家意见的许多方法一样。即使对以前的统计方法对同一组测量值进行了矛盾的解释，该方法也被用来结合以前的统计方法。该建议将这项工作扩展到了测量统计分析中面临的具体问题。另外，将这种分布组合方法的可靠性与其他概率分布和通常的统计方法的方法进行比较，而概率分布不涉及组合概率分布。可靠性将在可能的情况下基于数学理论确定，并基于模拟测量，否则将确定。拟议的研究的应用包括分析数千基因和其他大规模测量的活性水平的测量。解释这些新数据类型的结果的改进可能会导致新的生物学发现，例如，西红柿中的基因具有活性水平，具体取决于品种或水果发展阶段。这些知识可能会导致加拿大及其贸易伙伴内部更有效的粮食生产，从而使加拿大人更容易获得更高质量的食物。拟议研究的应用还包括从较小规模的测量集中学习，只要当前的数据分析方法报告不同的解释。这种情况不仅在基础科学中很常见，而且在农业中也很常见。除了研究对科学知识增长和更有效粮食生产的可能性的上述长期益处外，该提案还可以通过培训高素质的人员来获得短期经济利益。在拟议项目过程中接受培训的学生将有能力为基础科学和农业应用生物统计学的数据分析做出贡献，这些领域共同为加拿大统计学家提供了很大比例的就业机会。