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307
The control of the false discovery rate in multiple testing under dependency
 Annals of Statistics
, 2001
"... Benjamini and Hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems. A simple procedure was given there as an FDR controlling procedure for independent test statistics and was shown to be much more powerful than comparab ..."
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Cited by 1058 (16 self)
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Benjamini and Hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems. A simple procedure was given there as an FDR controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate. We prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses. This condition for positive dependency is general enough to cover many problems of practical interest, including the comparisons of many treatments with a single control, multivariate normal test statistics with positive correlation matrix and multivariate t. Furthermore, the test statistics may be discrete, and the tested hypotheses composite without posing special difficulties. For all other forms of dependency, a simple conservative modification of the procedure controls the false discovery rate. Thus the range of problems for which
Nonparametric Permutation Tests for Functional Neuroimaging: A Primer with Examples. Human Brain Mapping
, 2001
"... The statistical analyses of functional mapping experiments usually proceeds at the voxel level, involving the formation and assessment of a statistic image: at each voxel a statistic indicating evidence of the experimental effect of interest, at that voxel, is computed, giving an image of statistics ..."
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Cited by 376 (10 self)
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The statistical analyses of functional mapping experiments usually proceeds at the voxel level, involving the formation and assessment of a statistic image: at each voxel a statistic indicating evidence of the experimental effect of interest, at that voxel, is computed, giving an image of statistics, a statistic
The sample average approximation method for stochastic discrete optimization
 SIAM Journal on Optimization
, 2001
"... Abstract. In this paper we study a Monte Carlo simulation based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and consequently the expected value function is approximated by the corresponding sample average function. The ob ..."
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Cited by 207 (20 self)
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Abstract. In this paper we study a Monte Carlo simulation based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and consequently the expected value function is approximated by the corresponding sample average function. The obtained sample average optimization problem is solved, and the procedure is repeated several times until a stopping criterion is satisfied. We discuss convergence rates and stopping rules of this procedure and present a numerical example of the stochastic knapsack problem. Key words. Stochastic programming, discrete optimization, Monte Carlo sampling, Law of Large Numbers, Large Deviations theory, sample average approximation, stopping rules, stochastic knapsack problem AMS subject classifications. 90C10, 90C15
Controlling the familywise error rate in functional neuroimaging: a comparative review
 Statistical Methods in Medical Research
, 2003
"... Functional neuroimaging data embodies a massive multiple testing problem, where 100 000 correlated test statistics must be assessed. The familywise error rate, the chance of any false positives is the standard measure of Type I errors in multiple testing. In this paper we review and evaluate three a ..."
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Cited by 167 (7 self)
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Functional neuroimaging data embodies a massive multiple testing problem, where 100 000 correlated test statistics must be assessed. The familywise error rate, the chance of any false positives is the standard measure of Type I errors in multiple testing. In this paper we review and evaluate three approaches to thresholding images of test statistics: Bonferroni, random �eld and the permutation test. Owing to recent developments, improved Bonferroni procedures, such as Hochberg’s methods, are now applicable to dependent data. Continuous random �eld methods use the smoothness of the image to adapt to the severity of the multiple testing problem. Also, increased computing power has made both permutation and bootstrap methods applicable to functional neuroimaging. We evaluate these approaches on t images using simulations and a collection of real datasets. We �nd that Bonferronirelated tests offer little improvement over Bonferroni, while the permutation method offers substantial improvement over the random �eld method for low smoothness and low degrees of freedom. We also show the limitations of trying to �nd an equivalent number of independent tests for an image of correlated test statistics. 1
An enhanced representation of time series which allows fast and accurate classification, clustering and relevance feedback
 In proceedings of the 4th Int'l Conference on Knowledge Discovery and Data Mining
"... We introduce an extended representation of time series that allows fast, accurate classification and clustering in addition to the ability to explore time series data in a relevance feedback framework. The representation consists of piecewise linear segments to represent shape and a weight vector th ..."
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Cited by 162 (25 self)
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We introduce an extended representation of time series that allows fast, accurate classification and clustering in addition to the ability to explore time series data in a relevance feedback framework. The representation consists of piecewise linear segments to represent shape and a weight vector that contains the relative importance of each individual linear segment. In the classification context, the weights are learned automatically as part of the training cycle. In the relevance feedback context, the weights are determined by an interactive and iterative process in which users rate various choices presented to them. Our representation allows a user to define a variety of similarity measures that can be tailored to specific domains. We demonstrate our approach on space telemetry, medical and synthetic data.
Higher criticism for detecting sparse heterogeneous mixtures
 Ann. Statist
, 2004
"... Higher Criticism, or secondlevel significance testing, is a multiple comparisons concept mentioned in passing by Tukey (1976). It concerns a situation where there are many independent tests of significance and one is interested in rejecting the joint null hypothesis. Tukey suggested to compare the ..."
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Cited by 160 (23 self)
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Higher Criticism, or secondlevel significance testing, is a multiple comparisons concept mentioned in passing by Tukey (1976). It concerns a situation where there are many independent tests of significance and one is interested in rejecting the joint null hypothesis. Tukey suggested to compare the fraction of observed significances at a given αlevel to the expected fraction under the joint null, in fact he suggested to standardize the difference of the two quantities and form a zscore; the resulting zscore tests the significance of the body of significance tests. We consider a generalization, where we maximize this zscore over a range of significance levels 0 < α ≤ α0. We are able to show that the resulting Higher Criticism statistic is effective at resolving a very subtle testing problem: testing whether n normal means are all zero versus the alternative that a small fraction is nonzero. The subtlety of this ‘sparse normal means ’ testing problem can be seen from work of Ingster (1999) and Jin (2002), who studied such problems in great detail. In their studies, they identified an interesting range of cases where the small fraction of nonzero means is so
Detecting group differences: Mining contrast sets
 Data Mining and Knowledge Discovery
, 2001
"... A fundamental task in data analysis is understanding the differences between several contrasting groups. These groups can represent different classes of objects, such as male or female students, or the same group over time, e.g. freshman students in 1993 through 1998. We present the problem of mini ..."
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Cited by 108 (3 self)
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A fundamental task in data analysis is understanding the differences between several contrasting groups. These groups can represent different classes of objects, such as male or female students, or the same group over time, e.g. freshman students in 1993 through 1998. We present the problem of mining contrast sets: conjunctions of attributes and values that differ meaningfully in their distribution across groups. We provide a search algorithm for mining contrast sets with pruning rules that drastically reduce the computational complexity. Once the contrast sets are found, we postprocess the results to present a subset that are surprising to the user given what we have already shown. We explicitly control the probability of Type I error (false positives) and guarantee a maximum error rate for the entire analysis by using Bonferroni corrections.
A linear nongaussian acyclic model for causal discovery
 J. Machine Learning Research
, 2006
"... In recent years, several methods have been proposed for the discovery of causal structure from nonexperimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to ..."
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Cited by 101 (28 self)
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In recent years, several methods have been proposed for the discovery of causal structure from nonexperimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to discover the complete causal structure of continuousvalued data, under the assumptions that (a) the data generating process is linear, (b) there are no unobserved confounders, and (c) disturbance variables have nonGaussian distributions of nonzero variances. The solution relies on the use of the statistical method known as independent component analysis, and does not require any prespecified timeordering of the variables. We provide a complete Matlab package for performing this LiNGAM analysis (short for Linear NonGaussian Acyclic Model), and demonstrate the effectiveness of the method using artificially generated data and realworld data.
Statistical selection of the best system
, 2005
"... This tutorial discusses some statistical procedures for selecting the best of a number of competing systems. The term “best” may refer to that simulated system having, say, the largest expected value or the greatest likelihood of yielding a large observation. We describe various procedures for findi ..."
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Cited by 81 (8 self)
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This tutorial discusses some statistical procedures for selecting the best of a number of competing systems. The term “best” may refer to that simulated system having, say, the largest expected value or the greatest likelihood of yielding a large observation. We describe various procedures for finding the best, some of which assume that the underlying observations arise from competing normal distributions, and some of which are essentially nonparametric in nature. In each case, we comment on how to apply the above procedures for use in simulations.
Generalizations of the familywise error rate
 Ann. Statist
, 2005
"... Consider the problem of simultaneously testing null hypotheses H1,...,Hs. The usual approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. In many applications, particularly ..."
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Cited by 70 (7 self)
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Consider the problem of simultaneously testing null hypotheses H1,...,Hs. The usual approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. In many applications, particularly if s is large, one might be willing to tolerate more than one false rejection provided the number of such cases is controlled, thereby increasing the ability of the procedure to detect false null hypotheses. This suggests replacing control of the FWER by controlling the probability of k or more false rejections, which we call the kFWER. We derive both singlestep and stepdown procedures that control the kFWER, without making any assumptions concerning the dependence structure of the pvalues of the individual tests. In particular, we derive a stepdown procedure that is quite simple to apply, and prove that it cannot be improved without violation of control of the kFWER. We also consider the false discovery proportion (FDP) defined by the number of false rejections divided by the total number of rejections (defined to be 0 if there are no rejections). The false discovery rate proposed by Benjamini