The Experts below are selected from a list of 10038 Experts worldwide ranked by ideXlab platform

Aly R Seadawy - One of the best experts on this subject based on the ideXlab platform.

Rina Foygel Barber - One of the best experts on this subject based on the ideXlab platform.

  • multiple testing with the structure adaptive Benjamini hochberg algorithm
    Journal of The Royal Statistical Society Series B-statistical Methodology, 2019
    Co-Authors: Rina Foygel Barber
    Abstract:

    In multiple‐testing problems, where a large number of hypotheses are tested simultaneously, false discovery rate (FDR) control can be achieved with the well‐known Benjamini–Hochberg procedure, which a(0,1]dapts to the amount of signal in the data, under certain distributional assumptions. Many modifications of this procedure have been proposed to improve power in scenarios where the hypotheses are organized into groups or into a hierarchy, as well as other structured settings. Here we introduce the ‘structure‐adaptive Benjamini–Hochberg algorithm’ (SABHA) as a generalization of these adaptive testing methods. The SABHA method incorporates prior information about any predetermined type of structure in the pattern of locations of the signals and nulls within the list of hypotheses, to reweight the p‐values in a data‐adaptive way. This raises the power by making more discoveries in regions where signals appear to be more common. Our main theoretical result proves that the SABHA method controls the FDR at a level that is at most slightly higher than the target FDR level, as long as the adaptive weights are constrained sufficiently so as not to overfit too much to the data—interestingly, the excess FDR can be related to the Rademacher complexity or Gaussian width of the class from which we choose our data‐adaptive weights. We apply this general framework to various structured settings, including ordered, grouped and low total variation structures, and obtain the bounds on the FDR for each specific setting. We also examine the empirical performance of the SABHA method on functional magnetic resonance imaging activity data and on gene–drug response data, as well as on simulated data.

  • multiple testing with the structure adaptive Benjamini hochberg algorithm
    arXiv: Methodology, 2016
    Co-Authors: Rina Foygel Barber
    Abstract:

    In multiple testing problems, where a large number of hypotheses are tested simultaneously, false discovery rate (FDR) control can be achieved with the well-known Benjamini-Hochberg procedure, which adapts to the amount of signal present in the data. Many modifications of this procedure have been proposed to improve power in scenarios where the hypotheses are organized into groups or into a hierarchy, as well as other structured settings. Here we introduce SABHA, the "structure-adaptive Benjamini-Hochberg algorithm", as a generalization of these adaptive testing methods. SABHA incorporates prior information about any pre-determined type of structure in the pattern of locations of the signals and nulls within the list of hypotheses, to reweight the p-values in a data-adaptive way. This raises the power by making more discoveries in regions where signals appear to be more common. Our main theoretical result proves that SABHA controls FDR at a level that is at most slightly higher than the target FDR level, as long as the adaptive weights are constrained sufficiently so as not to overfit too much to the data-interestingly, the excess FDR can be related to the Rademacher complexity or Gaussian width of the class from which we choose our data-adaptive weights. We apply this general framework to various structured settings, including ordered, grouped, and low total variation structures, and get the bounds on FDR for each specific setting. We also examine the empirical performance of SABHA on fMRI activity data and on gene/drug response data, as well as on simulated data.

Peter H Westfall - One of the best experts on this subject based on the ideXlab platform.

  • the Benjamini hochberg method with infinitely many contrasts in linear models
    Biometrika, 2008
    Co-Authors: Peter H Westfall
    Abstract:

    SUMMARY Benjamini and Hochberg's method for controlling the false discovery rate is applied to the problem of testing infinitely many contrasts in linear models. Exact, easily calculated critical values are derived, defining a new multiple comparisons method for testing contrasts in linear models. The method is adaptive, depending on the data through the F-statistic, like the Waller Duncan Bayesian multiple comparisons method. Comparisons with Scheffes method are given, and the method is extended to the simultaneous confidence intervals of Benjamini and Yekutieli. Testing contrasts of a variety of types is a standard practice in the analysis of variance, leading to the problem of multiple comparisons and multiple tests. This issue is also controversial, with much literature that is not completely reviewed here. Hochberg and Tamhane (1987) is a good general reference for multiple comparisons methods that control the familywise error rate. Benjamini and Hochberg (1995) introduced a method to control the false discovery rate, and an extension of this method to confidence intervals for selected significant parameters is given by Benjamini and Yekutieli (2005). A common modem thread in the literature is the 'small n, large k' case, in which the number of tests k is large and the sample size n is small. We provide an exact characterization of the problem of testing infinitely many contrasts, k = oo, in linear models using the Benjamini Hochberg method, for fixed, possibly small n. The characterization is completely nonparametric, without distributional assumptions concerning the data-generating process; instead we assume that the contrasts tested are a random sample from contrast space. The resulting infinite-contrasts characterization of the Benjamini-Hochberg method is shown, surprisingly, to depend on the data

  • using the false discovery rate approach in the genetic dissection of complex traits a response to weller et al
    Genetics, 2000
    Co-Authors: Peter H Westfall, Dmitri V Zaykin, Stanley S Young
    Abstract:

    WELLER et al. ([1998][1]) proposed controlling the “false discovery rate” (FDR) or the expected proportion of false rejections within the class of rejected null hypotheses when performing preliminary genome scans, adopting the method of Benjamini and Hochberg ([1995][2]; hereafter BH). The BH

Asaf Nachmias - One of the best experts on this subject based on the ideXlab platform.

  • indistinguishability of trees in uniform spanning forests
    Probability Theory and Related Fields, 2017
    Co-Authors: Tom Hutchcroft, Asaf Nachmias
    Abstract:

    We prove that in both the free and the wired uniform spanning forest (FUSF and WUSF) of any unimodular random rooted network (in particular, of any Cayley graph), it is impossible to distinguish the connected components of the forest from each other by invariantly defined graph properties almost surely. This confirms a conjecture of Benjamini et al. (Ann Probab 29(1):1–65, 2001). We also answer positively two additional questions of Benjamini et al. (Ann Probab 29(1):1–65, 2001) under the assumption of unimodularity. We prove that on any unimodular random rooted network, the FUSF is either connected or has infinitely many connected components almost surely, and, if the FUSF and WUSF are distinct, then every component of the FUSF is transient and infinitely-ended almost surely. All of these results are new even for Cayley graphs.

  • indistinguishability of trees in uniform spanning forests
    arXiv: Probability, 2015
    Co-Authors: Tom Hutchcroft, Asaf Nachmias
    Abstract:

    We prove that in both the free and the wired uniform spanning forest (FUSF and WUSF) of any unimodular random rooted network (in particular, of any Cayley graph), it is impossible to distinguish the connected components of the forest from each other by invariantly defined graph properties almost surely. This confirms a conjecture of Benjamini, Lyons, Peres and Schramm. We use this to answer positively two additional questions of Benjamini, Lyons, Peres and Schramm under the assumption of unimodularity. We prove that on any unimodular random rooted network, the FUSF is either connected or has infinitely many connected components almost surely, and, if the FUSF and WUSF are distinct, then every component of the FUSF is transient and infinitely-ended almost surely. All of these results are new even for Cayley graphs.

  • recurrence of planar graph limits
    Annals of Mathematics, 2013
    Co-Authors: Ori Gurelgurevich, Asaf Nachmias
    Abstract:

    We prove that any distributional limit of nite planar graphs in which the degree of the root has an exponential tail is almost surely recurrent. As a corollary, we obtain that the uniform innite planar triangulation and quadrangulation (UIPT and UIPQ) are almost surely recurrent, resolving a conjecture of Angel, Benjamini and Schramm. We also settle another related problem of Benjamini and Schramm. We show that in any bounded degree, nite planar graph the probability that the simple random walk started at a uniform random vertex avoids its initial location for T steps is at most C logT .

Kalim U Tariq - One of the best experts on this subject based on the ideXlab platform.