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

比克尔博士发表了一种综合概率分布的一般方法，而无需主观设定权重，就像许多以先验分布形式综合专家意见的方法所做的那样。这一通用方法被用来结合以前的统计方法，即使它们分别对同一组测量给出了相互矛盾的解释。 这项建议将这项工作扩展到测量统计分析中所面临的具体问题。此外，该分布组合方法的可靠性将与其他组合概率分布的方法以及不涉及组合概率分布的常用统计方法进行比较。这种可靠性将在可能的情况下根据数学理论确定，否则将根据模拟测量确定。 拟议研究的应用包括分析对数千个基因活性水平的测量，以及其他大规模测量。在解释这些新数据类型的结果方面的改进可以带来新的生物学发现，例如，西红柿中的哪些基因具有活动水平取决于品种或水果发育阶段。这一知识可能会在加拿大国内及其贸易伙伴内部导致更高效的食品生产，使加拿大人更容易获得更高质量的食品。 拟议研究的应用还包括在当前的数据分析方法报告不同的解释时，从较小规模的测量集合中学习。这种情况不仅在基础科学中很常见，在农业中也很常见。 除了上述研究对科学知识增长的长期好处和提高粮食生产效率的可能性外，这一建议还可以通过培训高素质人员而产生短期经济效益。在拟议项目过程中接受培训的学生将为基础科学和农业应用生物统计学方面的数据分析做出贡献，这两个领域共同为很大一部分加拿大统计学家提供就业机会。

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.