The Inuence of Misspecified Covariance on False Discovery Control when Using Posterior Probabilities

This paper focuses on the influence of a misspecified covariance structure on false discovery rate for the large scale multiple testing problem. Specifically, we evaluate the influence on the marginal distribution of local fdr statistics, which are used in many multiple testing procedures and related to Bayesian posterior probabilities. Explicit forms of the marginal distributions under both correctly specified and incorrectly specified models are derived. The Kullback-Leibler divergence is used to quantify the influence caused by a misspecification. Several numerical examples are provided to illustrate the influence. A real spatio-temporal data on soil humidity is discussed.Comment: 22 pages, 5 figure

Power-enhanced multiple decision functions controlling family-wise error and false discovery rates

Improved procedures, in terms of smaller missed discovery rates (MDR), for performing multiple hypotheses testing with weak and strong control of the family-wise error rate (FWER) or the false discovery rate (FDR) are developed and studied. The improvement over existing procedures such as the \v{S}id\'ak procedure for FWER control and the Benjamini--Hochberg (BH) procedure for FDR control is achieved by exploiting possible differences in the powers of the individual tests. Results signal the need to take into account the powers of the individual tests and to have multiple hypotheses decision functions which are not limited to simply using the individual $p$-values, as is the case, for example, with the \v{S}id\'ak, Bonferroni, or BH procedures. They also enhance understanding of the role of the powers of individual tests, or more precisely the receiver operating characteristic (ROC) functions of decision processes, in the search for better multiple hypotheses testing procedures. A decision-theoretic framework is utilized, and through auxiliary randomizers the procedures could be used with discrete or mixed-type data or with rank-based nonparametric tests. This is in contrast to existing $p$-value based procedures whose theoretical validity is contingent on each of these $p$-value statistics being stochastically equal to or greater than a standard uniform variable under the null hypothesis. Proposed procedures are relevant in the analysis of high-dimensional "large $M$, small $n$" data sets arising in the natural, physical, medical, economic and social sciences, whose generation and creation is accelerated by advances in high-throughput technology, notably, but not limited to, microarray technology.Comment: Published in at http://dx.doi.org/10.1214/10-AOS844 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Classes of Multiple Decision Functions Strongly Controlling FWER and FDR

This paper provides two general classes of multiple decision functions where each member of the first class strongly controls the family-wise error rate (FWER), while each member of the second class strongly controls the false discovery rate (FDR). These classes offer the possibility that an optimal multiple decision function with respect to a pre-specified criterion, such as the missed discovery rate (MDR), could be found within these classes. Such multiple decision functions can be utilized in multiple testing, specifically, but not limited to, the analysis of high-dimensional microarray data sets.Comment: 19 page

Quality control in resting-state fMRI: the benefits of visual inspection

Background: A variety of quality control (QC) approaches are employed in resting-state functional magnetic resonance imaging (rs-fMRI) to determine data quality and ultimately inclusion or exclusion of a fMRI data set in group analysis. Reliability of rs-fMRI data can be improved by censoring or “scrubbing” volumes affected by motion. While censoring preserves the integrity of participant-level data, including excessively censored data sets in group analyses may add noise. Quantitative motion-related metrics are frequently reported in the literature; however, qualitative visual inspection can sometimes catch errors or other issues that may be missed by quantitative metrics alone. In this paper, we describe our methods for performing QC of rs-fMRI data using software-generated quantitative and qualitative output and trained visual inspection. Results: The data provided for this QC paper had relatively low motion-censoring, thus quantitative QC resulted in no exclusions. Qualitative checks of the data resulted in limited exclusions due to potential incidental findings and failed pre-processing scripts. Conclusion: Visual inspection in addition to the review of quantitative QC metrics is an important component to ensure high quality and accuracy in rs-fMRI data analysis

Optimal Rejection Curves for Exact False Discovery Rate Control

Finner et al. (2012) provided multiple hypothesis testing procedures based on a nonlinear rejection curve for exact false discovery rate control. This paper constructs classes of such procedures and compares the most powerful procedure in each class to competing procedures