In recent years, interval constraint-based solvers have shown their ability to efficiently solve complex instances of non-linear numerical CSPs. However, most of the working systems are designed to deliver point-wise solutions with an arbitrary accuracy. This works generally well for systems with isolated solutions but less well when there is a continuum of feasible points (e.g. underconstraine...

We present a novel method for controlling the k-familywise error rate (k-FWER) in the linear regression setting using the knockoffs framework first introduced by Barber and Candès. Our procedure, which we also refer to as knockoffs, can be applied with any design matrix with at least as many observations as variables, and does not require knowing the noise variance. Unlike other multiple testin...

There have been many discussions of how Type I errors should be controlled when many hypotheses are tested (e.g., all possible comparisons of means, correlations, proportions, the coefficients in hierarchical models, etc.). By and large, researchers have adopted familywise (FWER) control, though this practice certainly is not universal. Familywise control is intended to deal with the multiplici...

Frane (2015) pointed out the difference between per-family and familywise Type I error control and how different multiple comparison procedures control one method but not necessarily the other. He then went on to demonstrate in the context of a two group multivariate design containing different numbers of dependent variables and correlations between variables how the per-family rate inflates be...

In high dimensional data analysis (such as gene expression, spatial epidemiology, or brain imaging studies), we often test thousands or more hypotheses simultaneously. As the number of tests increases, the chance of observing some statistically significant tests is very high even when all null hypotheses are true. Consequently, we could reach incorrect conclusions regarding the hypotheses. Rese...

In light of the recent experimental results on decays B+ → fX(1300)K and B±(0) → J/ψK X (1430) from Belle, we study the B → P (V )S type decays, B±(0) → f0(1370)K and B±(0) → J/ψK 0 (1430), in comparison with the B → P (V )T type decays, B±(0) → f2(1270)K and B±(0) → J/ψK 2 (1430). We calculate the BRs for these decays by using the form factors obtained in the ISGW2 model [the improved version ...

The present article proposes two step-down multiple testing procedures for asymptotic control of the family-wise error rate (FWER): the first procedure is based on maxima of test statistics (step-down maxT), while the second relies on minima of unadjusted p-values (step-down minP). A key feature of our approach is the characterization and construction of a test statistics null distribution (rat...