Distribution of Error Rates in Multiple Testing

• Activity Number: 189
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Wen Zhong* and Donald Martin
• Companies: and North Carolina State University
• Keywords: false discovery rate ; graphical models ; multiple testing

Abstract

We give a framework to compute distributions of errors rates in multiple testing with dependence. A hidden binary random field is used to model the truth of the hypotheses, and the distribution of each observed test statistic is then assumed to depend on the truth of the corresponding underlying hypothesis. Inference for the hidden variables conditional on observed test statistics is carried out using the sum-product algorithm in the case of trees, and an approximate inference algorithm for graphs with loops. Distributions of error rates such as the false discovery proportion and false negative proportion will then be obtained using an algorithm to compute distributions of statistics of hidden state sequences. We then show how to use the derived distributions to develop testing procedures, for example one controlling the false discovery rate or false discovery exceedance.