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In a multiple testing problem where one is willing to tolerate a few false rejections, procedure controlling the familywise error rate (FWER) can potentially be improved in terms of its ability to detect false null hypotheses by generalizing it to control the k-FWER, the probability of falsely rejecting at least k null hypotheses, for some fixed k > 1.(More)
Results on the false discovery rate (FDR) and the false nondiscov-ery rate (FNR) are developed for single-step multiple testing procedures. In addition to verifying desirable properties of FDR and FNR as measures of error rates, these results extend previously known results , providing further insights, particularly under dependence, into the notions of FDR(More)
In this work we study an adaptive step-down procedure for testing m hypotheses. It stems from the repeated use of the false discovery rate controlling the linear step-up procedure (sometimes called BH), and makes use of the critical constants iq/[(m + 1 − i(1 − q)], i = 1,. .. , m. Motivated by its success as a model selection procedure, as well as by its(More)
Spread Spectrum (SS) modulation principle has been widely used in digital watermarking due to its distinguishing characteristics viz. excellent security and robustness in performance. The use of wide spectrum of the host signal in message hiding process puts a limit on the data rate subject to a given embedding distortion. In SS communication the use of M–(More)
Mixing of a conserved scalar representing the mixture fraction, of primary importance in modelling non-premixed turbulent combustion, is studied by direct numerical simulation (DNS) in strongly turbulent planar shear layers both with and without heat release at a reaction sheet. For high heat release, typical of hydrocarbon combustion, the mixing is found(More)
The original definitions of false discovery rate (FDR) and false non-discovery rate (FNR) can be understood as the frequentist risks of false rejections and false non-rejections, respectively, conditional on the unknown parameter, while the Bayesian posterior FDR and posterior FNR are conditioned on the data. From a Bayesian point of view, it seems natural(More)
Microarray gene expression studies over ordered categories are routinely conducted to gain insights into biological functions of genes and the underlying biological processes. Some common experiments are time-course/dose-response experiments where a tissue or cell line is exposed to different doses and/or durations of time to a chemical. A goal of such(More)
Among the visual illusions there is a class, which is known as low-level brightness contrast illusions. These illusions are processed probably at the retinal ganglion cell without necessitating any intervention from higher order cortical processing. The concept of classical receptive field of the ganglion cell, derived from early physiological studies,(More)
In many applications of multiple hypothesis testing where more than one false rejection can be tolerated, procedures controlling error rates measuring at least k false rejections, instead of at least one, for some fixed k ≥ 1 can potentially increase the ability of a procedure to detect false null hypotheses. The k-FWER, a generalized version of the usual(More)
A linear combination of Gaussian functions at various scales is being suggested as a suitable model for the human visual system. It reduces to the DOG (difference of Gaussian) model at the most primitive level of processing. The model is actually equivalent to the experimentally observed receptive field profiles that can be fitted by various even order(More)