Extended likelihood approach to multiple testing with directional error control under a hidden Markov random field model

Current multiple testing procedures are often based on assumptions of independence of observations. However, the observations in genomics and neuroimaging are correlated and ignoring such a correlation can severely distort the conclusions of a test. Moreover, most tests investigate two-sided alternatives only as a two-action problem and do not worry about directional errors. Misspecifications in signs of effects should not be regarded as power. In this study, we derive an optimal multiple testing procedure to incorporate dependence among tests, controlling directional false discovery rates. Real data examples for gene expression and neuroimaging using hidden Markov random field models show that an appropriate model is crucial for the efficiency of tests. Proper modeling of the correlation structure and model selection tools in the likelihood approach enhance the performance of a test. Reporting the estimates of various error rates is useful for the test's validity.