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

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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.