Topics in multiple hypotheses testing

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Title: Topics in multiple hypotheses testing
Author: Qian, Yi
Abstract: It is common to test many hypotheses simultaneously in the application of statistics . The probability of making a false discovery grows with the number of statistical tests performed . When all the null hypotheses are true , and the test statistics are indepen - dent and continuous , the error rates from the family wise error rate (FWER ) - and the false discovery rate (FDR ) -controlling procedures are equal to the nominal level . When some of the null hypotheses are not true , both procedures are conservative . In the first part of this study , we review the background of the problem and propose methods to estimate the number of true null hypotheses . The estimates can be used in FWER - and FDR -controlling procedures with a consequent increase in power . We conduct simulation studies and apply the estimation methods to data sets with bio - logical or clinical significance . In the second part of the study , we propose a mixture model approach for the analysis of ChIP -chip high density oligonucleotide array data to study the interac - tions between proteins and DNA . If we could identify the specific locations where proteins interact with DNA , we could increase our understanding of many important cellular events . Most experiments to date are performed in culture on cell lines , bac - teria , or yeast , and future experiments will include those in developing tissues , organs , or cancer biopsies , and they are critical in understanding the function of genes and proteins . Here we investigate the ChIP -chip data structure and use a beta -mixture model to help identify the binding sites . To determine the appropriate number of components in the mixture model , we suggest the Anderson -Darling testing . Our study indicates that it is a reasonable means of choosing the number of components in a beta -mixture model . The mixture model procedure has broad applications in biology and is illustrated with several data sets from bioinformatics experiments .
URI: http : / /hdl .handle .net /1969 .1 /4754
Date: 2007-04-25

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Topics in multiple hypotheses testing. Available electronically from http : / /hdl .handle .net /1969 .1 /4754 .

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