Frequentist Method

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Robert Tibshirani - One of the best experts on this subject based on the ideXlab platform.

  • empirical bayes Methods and false discovery rates for microarrays
    Genetic Epidemiology, 2002
    Co-Authors: Bradley Efron, Robert Tibshirani
    Abstract:

    In a classic two-sample problem, one might use Wilcoxon's statistic to test for a difference between treatment and control subjects. The analogous microarray experiment yields thousands of Wilcoxon statistics, one for each gene on the array, and confronts the statistician with a difficult simultaneous inference situation. We will discuss two inferential approaches to this problem: an empirical Bayes Method that requires very little a priori Bayesian modeling, and the Frequentist Method of "false discovery rates" proposed by Benjamini and Hochberg in 1995. It turns out that the two Methods are closely related and can be used together to produce sensible simultaneous inferences.

  • empirical bayes Methods and false discovery rates for microarrays
    Genetic Epidemiology, 2002
    Co-Authors: Bradley Efron, Robert Tibshirani
    Abstract:

    In a classic two-sample problem, one might use Wilcoxon's statistic to test for a difference between treatment and control subjects. The analogous microarray experiment yields thousands of Wilcoxon statistics, one for each gene on the array, and confronts the statistician with a difficult simultaneous inference situation. We will discuss two inferential approaches to this problem: an empirical Bayes Method that requires very little a priori Bayesian modeling, and the Frequentist Method of “false discovery rates” proposed by Benjamini and Hochberg in 1995. It turns out that the two Methods are closely related and can be used together to produce sensible simultaneous inferences. Genet. Epidemiol. 23:70–86, 2002. © 2002 Wiley-Liss, Inc.

Bradley Efron - One of the best experts on this subject based on the ideXlab platform.

  • empirical bayes Methods and false discovery rates for microarrays
    Genetic Epidemiology, 2002
    Co-Authors: Bradley Efron, Robert Tibshirani
    Abstract:

    In a classic two-sample problem, one might use Wilcoxon's statistic to test for a difference between treatment and control subjects. The analogous microarray experiment yields thousands of Wilcoxon statistics, one for each gene on the array, and confronts the statistician with a difficult simultaneous inference situation. We will discuss two inferential approaches to this problem: an empirical Bayes Method that requires very little a priori Bayesian modeling, and the Frequentist Method of "false discovery rates" proposed by Benjamini and Hochberg in 1995. It turns out that the two Methods are closely related and can be used together to produce sensible simultaneous inferences.

  • empirical bayes Methods and false discovery rates for microarrays
    Genetic Epidemiology, 2002
    Co-Authors: Bradley Efron, Robert Tibshirani
    Abstract:

    In a classic two-sample problem, one might use Wilcoxon's statistic to test for a difference between treatment and control subjects. The analogous microarray experiment yields thousands of Wilcoxon statistics, one for each gene on the array, and confronts the statistician with a difficult simultaneous inference situation. We will discuss two inferential approaches to this problem: an empirical Bayes Method that requires very little a priori Bayesian modeling, and the Frequentist Method of “false discovery rates” proposed by Benjamini and Hochberg in 1995. It turns out that the two Methods are closely related and can be used together to produce sensible simultaneous inferences. Genet. Epidemiol. 23:70–86, 2002. © 2002 Wiley-Liss, Inc.

Mark A Beaumont - One of the best experts on this subject based on the ideXlab platform.

  • multiple approaches to detect outliers in a genome scan for selection in ocellated lizards lacerta lepida along an environmental gradient
    Molecular Ecology, 2011
    Co-Authors: Vera L Nunes, Mark A Beaumont, Roger K Butlin, Octavio S Paulo
    Abstract:

    Identification of loci with adaptive importance is a key step to understand the speciation process in natural populations, because those loci are responsible for phenotypic variation that affects fitness in different environments. We conducted an AFLP genome scan in populations of ocellated lizards (Lacerta lepida) to search for candidate loci influenced by selection along an environmental gradient in the Iberian Peninsula. This gradient is strongly influenced by climatic variables, and two subspecies can be recognized at the opposite extremes: L. lepida iberica in the northwest and L. lepida nevadensis in the southeast. Both subspecies show substantial morphological differences that may be involved in their local adaptation to the climatic extremes. To investigate how the use of a particular outlier detection Method can influence the results, a Frequentist Method, DFDIST, and a Bayesian Method, BayeScan, were used to search for outliers influenced by selection. Additionally, the spatial analysis Method was used to test for associations of AFLP marker band frequencies with 54 climatic variables by logistic regression. Results obtained with each Method highlight differences in their sensitivity. DFDIST and BayeScan detected a similar proportion of outliers (3–4%), but only a few loci were simultaneously detected by both Methods. Several loci detected as outliers were also associated with temperature, insolation or precipitation according to spatial analysis Method. These results are in accordance with reported data in the literature about morphological and life-history variation of L. lepida subspecies along the environmental gradient.

  • identifying adaptive genetic divergence among populations from genome scans
    Molecular Ecology, 2004
    Co-Authors: Mark A Beaumont, David J Balding
    Abstract:

    The identification of signatures of natural selection in genomic surveys has become an area of intense research, stimulated by the increasing ease with which genetic markers can be typed. Loci identified as subject to selection may be functionally important, and hence (weak) candidates for involvement in disease causation. They can also be useful in determining the adaptive differentiation of populations, and exploring hypotheses about speciation. Adaptive differentiation has traditionally been identified from differences in allele frequencies among different populations, summarised by an estimate of F-ST. Low outliers relative to an appropriate neutral population-genetics model indicate loci subject to balancing selection, whereas high outliers suggest adaptive (directional) selection. However, the problem of identifying statistically significant departures from neutrality is complicated by confounding effects on the distribution of F-ST estimates, and current Methods have not yet been tested in large-scale simulation experiments. Here, we simulate data from a structured population at many unlinked, diallelic loci that are predominantly neutral but with some loci subject to adaptive or balancing selection. We develop a hierarchical-Bayesian Method, implemented via Markov chain Monte Carlo (MCMC), and assess its performance in distinguishing the loci simulated under selection from the neutral loci. We also compare this performance with that of a Frequentist Method, based on moment-based estimates of F-ST. We find that both Methods can identify loci subject to adaptive selection when the selection coefficient is at least five times the migration rate. Neither Method could reliably distinguish loci under balancing selection in our simulations, even when the selection coefficient is twenty times the migration rate.

Michele Calvello - One of the best experts on this subject based on the ideXlab platform.

  • definition and performance of a threshold based regional early warning model for rainfall induced landslides
    Landslides, 2017
    Co-Authors: Luca Piciullo, M T Brunetti, Silvia Peruccacci, Fausto Guzzetti, Stefano Luigi Gariano, Massimo Melillo, Michele Calvello
    Abstract:

    A process chain for the definition and the performance assessment of an operational regional warning model for rainfall-induced landslides, based on rainfall thresholds, is proposed and tested in a landslide-prone area in the Campania region, southern Italy. A database of 96 shallow landslides triggered by rainfall in the period 2003–2010 and rainfall data gathered from 58 rain gauges are used. First, a set of rainfall threshold equations are defined applying a well-known Frequentist Method to all the reconstructed rainfall conditions responsible for the documented landslides in the area of analysis. Several thresholds at different exceedance probabilities (percentiles) are evaluated, and nine different percentile combinations are selected for the activation of three warning levels. Subsequently, for each combination, the issuing of warning levels is computed by comparing, over time, the measured rainfall with the pre-defined warning level thresholds. Finally, the optimal percentile combination to be employed in the regional early warning system, i.e. the one providing the best model performance in terms of success and error indicators, is selected employing the “event, duration matrix, performance” (EDuMaP) Method.

David J Balding - One of the best experts on this subject based on the ideXlab platform.

  • identifying adaptive genetic divergence among populations from genome scans
    Molecular Ecology, 2004
    Co-Authors: Mark A Beaumont, David J Balding
    Abstract:

    The identification of signatures of natural selection in genomic surveys has become an area of intense research, stimulated by the increasing ease with which genetic markers can be typed. Loci identified as subject to selection may be functionally important, and hence (weak) candidates for involvement in disease causation. They can also be useful in determining the adaptive differentiation of populations, and exploring hypotheses about speciation. Adaptive differentiation has traditionally been identified from differences in allele frequencies among different populations, summarised by an estimate of F-ST. Low outliers relative to an appropriate neutral population-genetics model indicate loci subject to balancing selection, whereas high outliers suggest adaptive (directional) selection. However, the problem of identifying statistically significant departures from neutrality is complicated by confounding effects on the distribution of F-ST estimates, and current Methods have not yet been tested in large-scale simulation experiments. Here, we simulate data from a structured population at many unlinked, diallelic loci that are predominantly neutral but with some loci subject to adaptive or balancing selection. We develop a hierarchical-Bayesian Method, implemented via Markov chain Monte Carlo (MCMC), and assess its performance in distinguishing the loci simulated under selection from the neutral loci. We also compare this performance with that of a Frequentist Method, based on moment-based estimates of F-ST. We find that both Methods can identify loci subject to adaptive selection when the selection coefficient is at least five times the migration rate. Neither Method could reliably distinguish loci under balancing selection in our simulations, even when the selection coefficient is twenty times the migration rate.