false discovery rate adjusted charting schemes for multistage process monitoring and fault identification most statistical process control research focuses on single stage processes this article considers the problem of multistage process monitoring and fault identification this problem is formulated as a multiple hypotheses testing problem however as the number of stages increases the detection power of multiple hypotheses testing methods that seek to control the type i error rate decreases dramatically to maintain the detection power we use a false discovery rate fdr control approach which is widely used in microarray research two multistage process monitoring and fault identification schemes an fdr adjusted shewhart chart and an fdr adjusted cumulative sum cusum chart are established to apply the fdr approach the distribution of the cusum statistics are obtained based on markov chain theory and brownian motion with drift models the detection and fault identification power of the new schemes are evaluated by the monte carlo method the results indicate that the novel fdr adjusted approaches

enhanced false discovery rate using gaussian mixture models for thresholding fmri statistical maps a typical fmri data analysis proceeds via the generalized linear model glm with gaussian noise using a model based on the experimental paradigm this analysis ultimately results in the production of z statistic images corresponding to the contrasts of interest thresholding such z statistic images at uncorrected thresholds suitable for testing activation at a single voxel results in the problem of multiple comparisons a number of methods which account for the problem of multiple comparisons have been proposed including gaussian random field theory mixture modeling and false discovery rate fdr the focus of this paper is on the development of a generalized version of fdr gfdr in an empirical bayesian framework specially adapted for fmri thresholding that is more robust to modeling violations as compared to traditional fdr we show theoretically as well as by simulation that for real fmri data various factors lead to a mixture of gaussians mog density for the null distribution artificial data was used to systematically study the bias of fdr and gfdr under varying intensity of modeling violations signal to noise ratios and activation fractions for a range of q values gfdr was able to handle modeling violations and produce good results when fdr failed real fmri data was also used to confirm gfdr capabilities our results indicate that it is very important to account for the form and fraction of the null hypothesis adaptively from the data in order to obtain valid inference

posterior probability of discovery and expected rate of discovery for multiple hypothesis testing and high throughput assays technologies of measuring millions of quantities at once have been rapidly developed and used in biological and biomedical research and other fields in the past decade yet a key issue remains unsettled namely how to control spurious findings for the ensuing massive number of hypothesis tests an emerging consensus is to control false discovery rate fdr with fdr defined as the expected proportion of true nulls among discoveries and a discovery the rejection of a null hypothesis however the very concept of counting true nulls implicitly or explicitly is problematic for nulls are rarely true in reality we propose an approach that is philosophically different from the fdr and other approaches taking advantage of the massive measurements we can and should directly evaluate the reproducibility of a discovery by calculating the posterior probability of discovery ppd given observed data a discovery with a great ppd is deemed to be highly reproducible that is not spurious for a subset of hypot

the false discovery rate for multiple testing in factorial experiments identifying the important factors and effects is an important goal in the analysis of two level fractional factorial experiments in moderate and large experiments the large number of potential effects presents problems of multiple statistical inference in this work we apply the false discovery rate fdr idea in multiple inference to effect identification in factorial experiments the fdr is the expected proportion of inert effects among those declared active which we believe is a more relevant quantity to control than the probability of a single erroneous declaration the criterion that has been adopted in previous studies we show how to combine the control of fdr with popular methods for estimating contrast standard error in unreplicated experiments we present simulations of unreplicated 16 and 32 run experiments that illustrate the improvements in power that can be obtained by controlling the fdr we also analyze data from an actual 128 run experiment with replication in which the fdr identifie

adapting to unknown sparsity by controlling the false discovery rate we attempt to recover an n dimensional vector observed in white noise where n is large and the vector is known to be sparse but the degree of sparsity is unknown we consider three different ways of defining sparsity of a vector using the fraction of nonzero terms imposing power law decay bounds on the ordered entries and controlling the lp norm for p small we obtain a procedure which is asymptotically minimax for l r loss simultaneously throughout a range of such sparsity classes the optimal procedure is a data adaptive thresholding scheme driven by control of the false discovery rate fdr fdr control is a relatively recent innovation in simultaneous testing ensuring that at most a certain fraction of the rejected null hypotheses will correspond to false rejections in our treatment the fdr control parameter qn also plays a determining role in asymptotic minimaxity if q lim qn 0 1 2 and also qn log n we get sharp asymptotic minimaxity simultaneously over a wide range of sparse parameter spaces and loss functions on the other hand q lim qn 1 2 1 forces the risk to exceed the minimax risk by a factor growing with q to our knowledge this relation between ideas in simultaneous inference and asymptotic decision theory is new our work provides a new perspective on a class of model selection rules which has been introduced recently by several authors these new rules impose complexity penalization of the form 2 log potential model size actual model size we exhibit a close connection with fdr controlling procedures under stringent control of the false discovery rate

false discovery rate control with groups in the context of large scale multiple hypothesis testing the hypotheses often possess certain group structures based on additional information such as gene ontology in gene expression data and phenotypes in genome wide association studies it is hence desirable to incorporate such information when dealing with multiplicity problems to increase statistical power in this article we demonstrate the benefit of considering group structure by presenting a p value weighting procedure which utilizes the relative importance of each group while controlling the false discovery rate under weak conditions the procedure is easy to implement and shown to be more powerful than the classical benjamini hochberg procedure in both theoretical and simulation studies by estimating the proportion of true null hypotheses the data driven procedure controls the false discovery rate asymptotically our analysis on one breast cancer dataset confirms that the procedure performs favorably compared with the classical method

non restarting cumulative sum charts and control of the false discovery rate cumulative sum or cusum charts are typically used to detect a change in the distribution of a sequence of observations e g shifts in the mean usually after signalling the chart is restarted by setting it to some value below the signalling threshold we propose a non restarting cusum chart which is able to detect periods during which the stream is out of control further we advocate an upper boundary to prevent the cusum chart rising too high which helps to detect a change back into control we present an algorithm to control the false discovery rate when considering cusum charts based on multiple streams of data we consider two definitions of a false discovery signalling out of control when the observations have been in control since the start and signalling out of control when the observations have been in control since the last time the chart was at zero we prove that the false discovery rate is controlled under both these definitions simultaneously simulations reveal the difference in false discovery rate control when using these and other desirable definitions of a false discovery copyright 2013 oxford university press

a simple finite element for elastic plastic deformations of shells abstract the quadrilateral element of this paper is especially suited to the behavior of elastoplastic shells it combines the simplicity needed in nonlinear analyses with a competitive accuracy the elemental approximation shares some common features with an earlier one applied to hookean shells 1 but incorporates an important modification which leads to further simplifications and provides a mechanism for the progressive yielding within an element the element is derived via the hu washizu functional which admits independent approximations of all basic variables the elimination of strains and stresses results in a displacement formulation with all the desired properties a positive definite matrix and convergence some properties of the elemental matrices are outlined and special considerations are given to plasticity numerical tests upon plates and shells demonstrate the efficiency of the element finally some distinctions are drawn between our model and certain mixed elements

on a generalized false discovery rate the concept of k fwer has received much attention lately as an appropriate error rate for multiple testing when one seeks to control at least k false rejections for some flxed k 1 a less conservative notion the k fdr has been introduced very recently by sarkar 19 generalizing the false discovery rate of banjamini and hochberg 1 in this article we bring newer insight to the k fdr considering a mixture model involving independent p values before motivating the developments of some new procedures that control it we prove the k fdr control of the proposed methods under a slightly weaker condition than in the mixture model we provide numerical evidence of the proposed methods superior power performance over some kfwer and k fdr methods finally we apply our methods to a real data set

an adaptive step down procedure with proven fdr control under independence 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 asymptotic optimality we are interested in its false discovery rate fdr controlling properties for a finite number of hypotheses we prove this step down procedure controls the fdr at level q for independent test statistics we then numerically compare it with two other procedures with proven fdr control under independence both in terms of power under independence and fdr control under positive dependence

edge coloring and stopping sets analysis in product codes with mds components we consider non binary product codes with mds components and their iterative row column algebraic decoding on the erasure channel both independent and block erasures are considered in this paper a compact graph representation is introduced on which we define double diversity edge colorings via the rootcheck concept an upper bound of the number of decoding iterations is given as a function of the graph size and the color palette size m then we propose a differential evolution edge coloring algorithm that produces colorings with a large population of minimal rootcheck order symbols the complexity of this algorithm per iteration is o m aleph for a given differential evolution parameter aleph where m aleph itself is small with respect to the huge cardinality of the coloring ensemble stopping sets of a product code are defined in the context of mds components and a relationship is established with the graph representation a full characterization of these stopping sets is given up to a size d 1 2 where d is the minimum hamming distance of the mds component code the performance of mds based product codes with and without double diversity coloring is analyzed in presence of both the block and the independent erasures in the latter case ml and iterative decoding are proven to coincide at small channel erasure probability furthermore numerical results show excellent performance in presence of unequal erasure probability due to double diversity colorings

coded modulation in the block fading channel coding theorems and code construction we consider coded modulation schemes for the block fading channel in the setting where a codeword spans a finite number n of fading degrees of freedom we show that coded modulations of rate r bit per complex dimension over a finite signal set spl chi spl sube spl copf of size 2 sup m achieve the optimal rate diversity tradeoff given by the singleton bound spl delta n m r 1 spl lfloor n 1 r m spl rfloor for r spl isin 0 m spl rfloor furthermore we show also that the popular bit interleaved coded modulation achieves the same optimal rate diversity tradeoff we present a novel coded modulation construction based on blockwise concatenation that systematically yields singleton bound achieving turbo like codes defined over an arbitrary signal set spl chi spl sub spl copf the proposed blockwise concatenation significantly outperforms conventional serial and parallel turbo codes in the block fading channel we analyze the ensemble average performance under maximum likelihood ml decoding of the proposed codes by means of upper bounds and tight approximations we show that differently from the additive white gaussian noise awgn and fully interleaved fading cases belief propagation iterative decoding performs very close to ml on the block fading channel for any signal to noise ratio snr and even for relatively short block lengths we also show that at constant decoding complexity per information bit the proposed codes perform close to the information outage probability for any block length while standard block codes e g obtained by trellis termination of convolutional codes have a gap from outage that increases with the block length this is a different and more subtle manifestation of the so called interleaving gain of turbo codes

comparing connectomes across subjects and populations at different scales brain connectivity can be represented by a network that enables the comparison of the different patterns of structural and functional connectivity among individuals in the literature two levels of statistical analysis have been considered in comparing brain connectivity across groups and subjects 1 the global comparison where a single measure that summarizes the information of each brain is used in a statistical test 2 the local analysis where a single test is performed either for each node connection which implies a multiplicity correction or for each group of nodes connections where each subset is summarized by one single test in order to reduce the number of tests to avoid a penalizing multiplicity correction we comment on the different levels of analysis and present some methods that have been proposed at each scale we highlight as well the possible factors that could influence the statistical results and the questions that have to be addressed in such an analysis

strong control conservative point estimation and simultaneous conservative consistency of false discovery rates a unified approach summary the false discovery rate fdr is a multiple hypothesis testing quantity that describes the expected proportion of false positive results among all rejected null hypotheses benjamini and hochberg introduced this quantity and proved that a particular step up p value method controls the fdr storey introduced a point estimate of the fdr for fixed significance regions the former approach conservatively controls the fdr at a fixed predetermined level and the latter provides a conservatively biased estimate of the fdr for a fixed predetermined significance region in this work we show in both finite sample and asymptotic settings that the goals of the two approaches are essentially equivalent in particular the fdr point estimates can be used to define valid fdr controlling procedures in the asymptotic setting we also show that the point estimates can be used to estimate the fdr conservatively over all significance regions simultaneously which is equivalent to controlling the fdr at all levels simultaneously the main tool that we use is to translate existing fdr methods into procedures involving empirical processes this simplifies finite sample proofs provides a framework for asymptotic results and proves that these procedures are valid even under certain forms of dependence

an inequality for correlations in unidimensional monotone latent variable models for binary variables it is shown that a unidimensional monotone latent variable model for binary items implies a restriction on the relative sizes of item correlations the negative logarithm of the correlations satisfies the triangle inequality this inequality is not implied by the condition that the correlations are nonnegative the criterion that coefficient h exceeds 0 30 or manifest monotonicity the inequality implies both a lower bound and an upper bound for each correlation between two items based on the correlations of those two items with every possible third item it is discussed how this can be used in mokken s a theory and procedure of scale analysis mouton the hague 1971 scale analysis

controlling the familywise error rate with plug in estimator for the proportion of true null hypotheses summary estimation of the number or proportion of true null hypotheses in multiple testing problems has become an interesting area of research the first important work in this field was performed by schweder and spjotvoll among others they proposed to use plug in estimates for the proportion of true null hypotheses in multiple test procedures to improve the power we investigate the problem of controlling the familywise error rate fwer when such estimators are used as plug in estimators in single step or step down multiple test procedures first we investigate the case of independent p values under the null hypotheses and show that a suitable choice of plug in estimates leads to control of fwer in single step procedures we also investigate the power and study the asymptotic behaviour of the number of false rejections although step down procedures are more difficult to handle we briefly consider a possible solution to this problem anyhow plug in step down procedures are not recommended here for dependent p values we derive a condition for asymptotic control of fwer and provide some simulations with respect to fwer and power for various models and hypotheses

operating characteristics and extensions of the false discovery rate procedure summary we investigate the operating characteristics of the benjamini hochberg false discovery rate procedure for multiple testing this is a distribution free method that controls the expected fraction of falsely rejected null hypotheses among those rejected the paper provides a framework for understanding more about this procedure we first study the asymptotic properties of the deciding point d that determines the critical p value from this we obtain explicit asymptotic expressions for a particular risk function we introduce the dual notion of false non rejections and we consider a risk function that combines the false discovery rate and false non rejections we also consider the optimal procedure with respect to a measure of conditional risk

discovering findings that replicate from a primary study of high dimension to a follow up study we consider the problem of identifying whether findings replicate from one study of high dimension to another when the primary study guides the selection of hypotheses to be examined in the follow up study as well as when there is no division of roles into the primary and the follow up study we show that existing meta analysis methods are not appropriate for this problem and suggest novel methods instead we prove that our multiple testing procedures control for appropriate error rates the suggested family wise error rate controlling procedure is valid for arbitrary dependence among the test statistics within each study a more powerful procedure is suggested for false discovery rate fdr control we prove that this procedure controls the fdr if the test statistics are independent within the primary study and independent or have positive dependence in the follow up study for arbitrary dependence within the primary study and either arbitrary dependence or positive dependence in the follow up study

plots of p values to evaluate many tests simultaneously summary when a large number of tests are made possibly on the same data it is proposed to base a simultaneous evaluation of all the tests on a plot of cumulative p values using the observed significance probabilities the points corresponding to true null hypotheses should form a straight line while those for false null hypotheses should deviate from this line the line may be used to estimate the number of true hypotheses the properties of the method are studied in some detail for the problems of comparing all pairs of means in a one way layout testing all correlation coefficients in a large correlation matrix and the evaluation of all 2 x 2 subtables in a contingency table the plot is illustrated on real data

multiple testing in a two stage adaptive design with combination tests controlling fdr testing multiple null hypotheses in two stages to decide which of these can be rejected or accepted at the first stage and which should be followed up for further testing having had additional observations is of importance in many scientific studies we develop two procedures each with two different combination functions fisher s and simes to combine p values from two stages given prespecified boundaries on the first stage p values in terms of the false discovery rate fdr and controlling the overall fdr at a desired level the fdr control is proved when the pairs of first and second stage p values are independent and those corresponding to the null hypotheses are identically distributed as a pair p 1 p 2 satisfying the p clud property we did simulations to show that 1 our two stage procedures can have significant power improvements over the first stage benjamini hochberg bh procedure compared to the improvement offered by the ideal bh procedure that one would have used had the second stage

empirical bayes analysis of a microarray experiment microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels a typical microarray experiment can produce millions of data points raising serious problems of data reduction and simultaneous inference we consider one such experiment in which oligonucleotide arrays were employed to assess the genetic effects of ionizing radiation on seven thousand human genes a simple nonparametric empirical bayes model is introduced which is used to guide the efficient reduction of the data to a single summary statistic per gene and also to make simultaneous inferences concerning which genes were affected by the radiation although our focus is on one specific experiment the proposed methods can be applied quite generally the empirical bayes inferences are closely related to the frequentist false discovery rate fdr criterion

proportion of non zero normal means universal oracle equivalences and uniformly consistent estimators d0 we propose a general approach to construct the universal oracle equivalence of the proportion the construction is based on the underlying characteristic function the oracle equivalence reduces the problem of estimating the proportion to the problem of estimating the oracle which is relatively easier to handle in fact the oracle equivalence naturally yields a family of estimators for the proportion which are consistent under mild conditions uniformly across a wide class of parameters the approach compares favourably with recent works by meinshausen and rice and genovese and wasserman in particular the consistency is proved for an unprecedentedly broad class of situations the class is almost the largest that can be hoped for without further constraints on the model we also discuss various extensions of the approach report results on simulation experiments and make connections between the approach and several recent procedures in large scale multiple testing including the false discovery rate approach and the local false discovery rate approach

adaptive and dynamic adaptive procedures for false discovery rate control and estimation summary many methods for estimation or control of the false discovery rate fdr can be improved by incorporating information about 0 the proportion of all tested null hypotheses that are true estimates of 0 are often based on the number of p values that exceed a threshold we first give a finite sample proof for conservative point estimation of the fdr when the parameter is fixed then we establish a condition under which a dynamic adaptive procedure whose parameter is determined by data will lead to conservative 0 and fdr estimators we also present asymptotic results on simultaneous conservative fdr estimation and control for a class of dynamic adaptive procedures simulation results show that a novel dynamic adaptive procedure achieves more power through smaller estimation errors for 0 under independence and mild dependence conditions we conclude by discussing the connection between estimation and control of the fdr and show that several recently developed fdr control procedures can be cast in a unifying framework where the strength of the procedures can be easily evaluated

selective inference on multiple families of hypotheses summary in many complex multiple testing problems the hypotheses are divided into families given the data families with evidence for true discoveries are selected and hypotheses within them are tested neither controlling the error rate in each family separately nor controlling the error rate over all hypotheses together can assure some level of confidence about the filtration of errors within the selected families we formulate this concern about selective inference in its generality for a very wide class of error rates and for any selection criterion and present an adjustment of the testing level inside the selected families that retains control of the expected average error over the selected families

an equivalent measure of partial correlation coefficients for high dimensional gaussian graphical models gaussian graphical models ggms are frequently used to explore networks such as gene regulatory networks among a set of variables under the classical theory of ggms the construction of gaussian graphical networks amounts to finding the pairs of variables with nonzero partial correlation coefficients however this is infeasible for high dimensional problems for which the number of variables is larger than the sample size in this article we propose a new measure of partial correlation coefficient which is evaluated with a reduced conditional set and thus feasible for high dimensional problems under the markov property and adjacency faithfulness conditions the new measure of partial correlation coefficient is equivalent to the true partial correlation coefficient in construction of gaussian graphical networks based on the new measure of partial correlation coefficient we propose a multiple hypothesis test based method for the construction of gaussian graphical networks furthermore we establish

asymptotic optimality of the westfall young permutation procedure for multiple testing under dependence test statistics are often strongly dependent in large scale multiple testing applications most corrections for multiplicity are unduly conservative for correlated test statistics resulting in a loss of power to detect true positives we show that the westfallyoung permutation method has asymptotically optimal power for a broad class of testing problems with a block dependence and sparsity structure among the tests when the number of tests tends to infinity

reduction of excessive energy in the four noded membrane quadrilateral element part ii near incompressibility and j2 plasticity abstract the elemental formulation presented in part i of this study e paraskevopoulos d talaslidis reduction of excessive energy in the four noded membrane quadrilateral element part i linear theory compressible materials comput methods appl mech engrg 194 2005 3771 3796 is extended in a straightforward manner to problems with nearly incompressible materials and to j 2 plastic flow problems sources of excessive energy resulting from the incompressibility constraint as well as the coupling between the deviatoric components of strain are examined and conclusions are drawn concerning the selection of appropriate approximations for the field variables a modified version of the hu washizu principle is employed that utilizes the orthogonality between deviatoric and volumetric terms and incorporates part of the plane strain conditions furthermore satisfaction of the patch test is analytically verified in deriving the weak form of the equations governing the j 2 plasticity problem attention is focused on a straightforward extension of the linear problem without reference to additional postulates in case of j 2 plasticity the current formulation incorporates an important modification that leads to further simplifications the continuous linear functions employed for the approximations are replaced by the heaviside function finally results of numerical examples and comparisons with other formulations are presented

false discovery rate adjusted multiple confidence intervals for selected parameters often in applied research confidence intervals cis are constructed or reported only for parameters selected after viewing the data we show that such selected intervals fail to provide the assumed coverage probability by generalizing the false discovery rate fdr approach from multiple testing to selected multiple cis we suggest the false coverage statement rate fcr as a measure of interval coverage following selection a general procedure is then introduced offering fcr control at level q under any selection rule the procedure constructs a marginal ci for each selected parameter but instead of the confidence level 1 q being used marginally q is divided by the number of parameters considered and multiplied by the number selected if we further use the fdr controlling testing procedure of benjamini and hochberg for selecting the parameters the newly suggested procedure offers cis that are dual to the testing procedure and are shown to be optimal in the independent case under the positive re

adaptive linear step up procedures that control the false discovery rate we provide a new two stage procedure in which the linear step up procedure is used in stage one to estimate mo providing a new level q which is used in the linear step up procedure in the second stage we prove that a general form of the two stage procedure controls the false discovery rate at the desired level q this framework enables us to study analytically the properties of other procedures that exist in the literature a simulation study is presented that shows that two stage adaptive procedures improve in power over the original procedure mainly because they provide tighter control of the false discovery rate we further study the performance of the current suggestions some variations of the procedures and previous suggestions in the case where the test statistics are positively dependent a case for which the original procedure controls the false discovery rate in the setting studied here the newly proposed two stage procedure is the only one that controls the false discovery rate the procedures are illustrated with two examples of biological importance

single index modulated multiple testing in the context of large scale multiple testing hypotheses are often accompanied with certain prior information in this paper we present a single index modulated sim multiple testing procedure which maintains control of the false discovery rate while incorporating prior information by assuming the availability of a bivariate p value p 1 p 2 for each hypothesis where p 1 is a preliminary p value from prior information and p 2 is the primary p value for the ultimate analysis to find the optimal rejection region for the bivariate p value we propose a criteria based on the ratio of probability density functions of p 1 p 2 under the true null and nonnull this criteria in the bivariate normal setting further motivates us to project the bivariate p value to a single index p theta for a wide range of directions theta the true null distribution of p theta is estimated via parametric and nonparametric approaches leading to two procedures for estimating and controlling the false discovery rate to derive the optimal projection direction theta we propose a new approach based on power comparison which is further shown to be consistent under some mild conditions simulation evaluations indicate that the sim multiple testing procedure improves the detection power significantly while controlling the false discovery rate analysis of a real dataset will be illustrated

discovering the false discovery rate summary i describe the background for the paper controlling the false discovery rate a new and powerful approach to multiple comparisons by benjamini and hochberg that was published in the journal of the royal statistical society series b in 1995 i review the progress since made on the false discovery rate as well as the major conceptual developments that followed

some results on false discovery rate in stepwise multiple testing procedures the concept of false discovery rate fdr has been receiving increasing attention by researchers in multiple hypotheses testing this paper produces some theoretical results on the fdr in the context of stepwise multiple testing procedures with dependent test statistics it was recently shown by benjamini and yekutieli that the benjamini hochberg step up procedure controls the fdr when the test statistics are positively dependent in a certain sense this paper strengthens their work by showing that the critical values of that procedure can be used in a much more general stepwise procedure under similar positive dependency it is also shown that the fdr controlling benjamini liu step down procedure originally developed for independent test statistics works even when the test statistics are positively dependent in some sense an explicit expression for the fdr of a generalized stepwise procedure and an upper bound to the fdr of a step down procedure are obtained in terms of probability distributions of ordered components of dependent random variables before establishing the main results 1 introduction the main purpose of this paper is to present some formulas and inequalities providing theoretical insight into when and what stepwise procedures control the false discovery rate fdr at a prespecified level in multiple hypotheses testing the fdr first introduced in multiple testing by benjamini and hochberg 1995 is the expected proportion of erroneously rejected null hypotheses with v and r representing respectively the number of true null hypotheses rejected and the total number of null hypotheses rejected in a multiple testing procedure let q v r if r 0a nd 0i fr 0 then e q is the fdr of that procedure as they have argued it is an appropriate error rate to control in many practical situations particularly where a large number of null hypotheses are involved they also put forward an fdr controlling stepup procedure that is more powerful than comparable procedures controlling the traditional familywise error fwe rate when the underlying test statistics are independent benjamini and liu 1999 recently introduced a step down procedure with the same property the concept of fdr is now being used in a wide variety of applications abramovich and benjamini 1996 basford and tukey 1997 drigalenko

false discovery rates for spatial signals the problem of multiple testing for the presence of signal in spatial data can involve numerous locations traditionally each location is tested separately for signal presence but then the findings are reported in terms of clusters of nearby locations this is an indication that the units of interest for testing are clusters rather than individual locations the investigator may know a priori these more natural units or an approximation to them we suggest testing these cluster units rather than individual locations thus increasing the signal to noise ratio within the unit tested as well as reducing the number of hypothesis tests conducted because the signal may be absent from part of each cluster we define a cluster as containing a signal if the signal is present somewhere within the cluster we suggest controlling the false discovery rate fdr on clusters i e the expected proportion of clusters rejected erroneously out of all clusters rejected or its extension to general weights wfdr we int

a stochastic process approach to false discovery control this paper extends the theory of false discovery rates fdr pioneered by benjamini and hochberg j roy statist soc ser b 57 1995 289 300 we develop a framework in which the false discovery proportion fdp the number of false rejections divided by the number of rejections is treated as a stochastic process after obtaining the limiting distribution of the process we demonstrate the validity of a class of procedures for controlling the false discovery rate the expected fdp we construct a confidence envelope for the whole fdp process from these envelopes we derive confidence thresholds for controlling the quantiles of the distribution of the fdp as well as controlling the number of false discoveries we also investigate methods for estimating the p value distribution

estimating the false discovery rate using the stochastic approximation algorithm testing of multiple hypotheses involves statistics that are strongly dependent in some applications but most work on this subject is based on the assumption of independence we propose a new method for estimating the false discovery rate of multiple hypothesis tests in which the density of test scores is estimated parametrically by minimizing the kullback leibler distance between the unknown density and its estimator using the stochastic approximation algorithm and the false discovery rate is estimated using the ensemble averaging method our method is applicable under general dependence between test statistics numerical comparisons between our method and several competitors conducted on simulated and real data examples show that our method achieves more accurate control of the false discovery rate in almost all scenarios

the control of the false discovery rate in multiple testing under dependency 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 a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

coding in the block erasure channel in this correspondence we study an m ary block erasure channel with b blocks where with probability epsi a block of l coded symbols is erased the behavior of the error probability of coded systems over such channels is studied and we show that if the code is diversity wise maximum distance separable its word error probability is equal to the outage probability which admits a very simple expression this correspondence is intended to complement the error probability analysis in previous work by lapidoth and shed some light on the design of coding schemes for nonergodic channels

multifrequency trellis coding with low delay for fading channels an l frequency trellis coding scheme designed for fading channels that provides diversity up to order l is described l frequency coding is advantageous over channel coding schemes that achieve implicit time diversity through trellis coding in conjunction with time interleaving because it requires negligible end to end delay the authors derive an upper bound for the probability of symbol error of the l frequency code based on this upper bound they then deduce the design criteria for optimum l frequency codes a numerical approximation to this upper bound and the design of a two state and two four state two frequency codes are presented through simulations it was found that relative to the traditional dual frequency diversity approach the two state and four state codes achieve 3 and 4 db coding gains respectively this energy efficiency gain can be translated into a spectral efficiency gain a brief discussion on the difference in code design techniques for the gaussian channel and the fading channel is also presented

low density parity check codes for nonergodic block fading channels we design powerful low density parity check ldpc codes with iterative decoding for the block fading channel we first study the case of maximum likelihood decoding and show that the design criterion is rather straightforward since optimal constructions for maximum likelihood decoding do not perform well under iterative decoding we introduce a new family of full diversity ldpc codes that exhibit near outage limit performance under iterative decoding for all block lengths this family competes favorably with multiplexed parallel turbo codes for nonergodic channels

evaluating the performance of convolutional codes over block fading channels this correspondence considers union upper bound techniques for error control codes with limited interleaving over block fading rician channels a modified bounding technique is presented that relies on limiting the conditional union bound before averaging over the fading process this technique although analytically not very attractive provides tight and hence useful numerical results

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

fast robust model selection in large datasets large datasets are increasingly common in many research fields in particular in the linear regression context it is often the case that a huge number of potential covariates are available to explain a response variable and the first step of a reasonable statistical analysis is to reduce the number of covariates this can be done in a forward selection procedure that includes selecting the variable to enter deciding to retain it or stop the selection and estimating the augmented model least squares plus t tests can be fast but the outcome of a forward selection might be suboptimal when there are outliers in this article we propose a complete algorithm for fast robust model selection including considerations for huge sample sizes because simply replacing the classical statistical criteria with robust ones is not computationally possible we develop simplified robust estimators selection criteria and testing procedures for linear regression the robust estimator is a one step weighted m estimato

false discovery control with p value weighting we present a method for multiple hypothesis testing that maintains control of the false discovery rate while incorporating prior information about the hypotheses the prior information takes the form of p value weights if the assignment of weights is positively associated with the null hypotheses being false the procedure improves power except in cases where power is already near one even if the assignment of weights is poor power is only reduced slightly as long as the weights are not too large we also provide a similar method to control false discovery exceedance

adaptive false discovery rate control under independence and dependence in the context of multiple hypothesis testing the proportion 0 of true null hypotheses in the pool of hypotheses to test often plays a crucial role although it is generally unknown a priori a testing procedure using an implicit or explicit estimate of this quantity in order to improve its efficency is called adaptive in this paper we focus on the issue of false discovery rate fdr control and we present new adaptive multiple testing procedures with control of the fdr in a first part assuming independence of the p values we present two new procedures and give a unified review of other existing adaptive procedures that have provably controlled fdr we report extensive simulation results comparing these procedures and testing their robustness when the independence assumption is violated the new proposed procedures appear competitive with existing ones the overall best though is reported to be storey s estimator albeit for a specific parameter setting that does not appear to have been considered before in a second part we propose adaptive versions of step up procedures that have provably controlled fdr under positive dependence and unspecified dependence of the p values respectively in the latter case while simulations only show an improvement over non adaptive procedures in limited situations these are to our knowledge among the first theoretically founded adaptive multiple testing procedures that control the fdr when the p values are not independent

optimal detection of functional connectivity from high dimensional eeg synchrony data computing phase locking values between eeg signals is a popular method for quantifying functional connectivity however this method involves large scale high resolution datasets which impose a serious multiple testing problem standard multiple testing methods fail to exploit the information from the complex dependence structure that varies across hypotheses in spectral temporal and spatial dimensions and result in a severe loss of power they tend to control the false positives at the cost of hiding true positives we introduce a new approach called optimal discovery procedure odp for identifying synchrony that is statistically significant odp maximizes the number of true positives for a given number of false positives and thus offers a theoretical optimum for detecting significant synchrony in a multiple testing situation we demonstrate the utility of this method with plv data obtained from a visual search study we also present simulation analysis to confirm the validity and relevance of using odp in comparison with the standard fdr method for given configurations of true synchrony we also compare the effectiveness of odp with our previously published investigation of hierarchical fdr method singh and phillips 2010

asymptotic results on adaptive false discovery rate controlling procedures based on kernel estimators the false discovery rate fdr is a commonly used type i error rate in multiple testing problems it is defined as the expected false discovery proportion fdp that is the expected fraction of false positives among rejected hypotheses when the hypotheses are independent the benjamini hochberg procedure achieves fdr control at any pre specified level by construction fdr control offers no guarantee in terms of power or type ii error a number of alternative procedures have been developed including plug in procedures that aim at gaining power by incorporating an estimate of the proportion of true null hypotheses in this paper we study the asymptotic behavior of a class of plug in procedures based on kernel estimators of the density of the p values as the number m of tested hypotheses grows to infinity in a setting where the hypotheses tested are independent we prove that these procedures are asymptotically more powerful in two respects i a tighter asymptotic fdr control for any target fdr level and ii a broader range of target levels yielding positive asymptotic power we also show that this increased asymptotic power comes at the price of slower non parametric convergence rates for the fdp these rates are of the form m k 2k 1 where k is determined by the regularity of the density of the p value distribution or equivalently of the test statistics distribution these results are applied to one and two sided tests statistics for gaussian and laplace location models and for the student model

straight to the source detecting aggregate objects in astronomical images with proper error control the next generation of telescopes coming online in the next decade will acquire terabytes of image data each night collectively these large images will contain billions of interesting objects which astronomers call sources one critical task for astronomers is to construct from the image data a detailed source catalog that gives the sky coordinates and other properties of all detected sources the source catalog is the primary data product produced by most telescopes and serves as an important input for studies that build and test new astrophysical theories to construct an accurate catalog the sources must first be detected in the image a variety of effective source detection algorithms exist in the astronomical literature but few if any provide rigorous statistical control of error rates a variety of multiple testing procedures exist in the statistical literature that can provide rigorous error control over pixelwise errors but these do not provide control over errors at the level of sources

reduction of excessive energy in the four noded membrane quadrilateral element part i linear theory compressible materials abstract the objective of the paper is to set forth in a consistent manner reasons for the appearance of excessive energy in the four noded membrane quadrilateral element and to propose a formulation leading to simple and reliable elements that are less sensitive to distortions of the geometrical shape by presenting the differential geometry emphasis is placed upon those geometrical attributes which are inherently related to the quadrilateral a modified version of the functional of hu washizu is employed for the discretization appropriate approximations for the displacements rotations are chosen and the physical meaning of the various parameters is identified a systematic procedure is followed for the approximation of stress and strain the convergence of the formulation is investigated by examining the inf sup condition and applying the patch test also results of numerical examples and comparisons with other elemental formulations are presented

bounds on the error probability of block codes over the q ary erasure channel in this paper tight bounds on the block error probability of linear block codes over order q finite fields for the q ary erasure channel under maximum likelihood ml decoding are developed upper bounds are obtained for uniform parity check ensembles sparse parity check ensembles general parity check ensembles e g gallager regular nonbinary low density parity check ensembles and for any given linear code with known distance spectrum the tightness of the upper bounds is confirmed both by the comparison with simple lower bounds and for gallager low density parity check ensembles by extensive monte carlo simulations exploiting the derived bounds it is shown how already for short blocks and small q 2 sparse ensembles attain block error probabilities close to those of idealized maximum distance separable mds codes down to low error probabilities whereas in the same regime binary codes show visible losses with respect to the singleton bound thanks to the accurate performance estimates the developed bounds can support the design of near optimum erasure correcting codes with short and moderate lengths

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

the positive false discovery rate a bayesian interpretation and the q value multiple hypothesis testing is concerned with controlling the rate of false positives when testing several hypotheses simultaneously one multiple hypothesis testing error measure is the false discovery rate fdr which is loosely defined to be the expected proportion of false positives among all significant hypotheses the fdr is especially appropriate for exploratory analyses in which one is interested in finding several significant results among many tests in this work we introduce a modified version of the fdr called the positive false discovery rate pfdr we discuss the advantages and disadvantages of the pfdr and investigate its statistical properties when assuming the test statistics follow a mixture distribution we show that the pfdr can be written as a bayesian posterior probability and can be connected to classification theory these properties remain asymptotically true under fairly general conditions even under certain forms of dependence also a new quantity called the q value is introduced and investigated which is a natural bayesian posterior p value or rather the pfdr analogue of the p value 1 introduction when testing a single hypothesis one is usually concerned with controlling the false positive rate while maximizing the probability of detecting an effect when one really exists in statistical terms we maximize the power conditional on the type i error rate being at or below some level the field of multiple hypothesis testing tries to extend this basic paradigm to the situation where several hypotheses are tested simultaneously one must define an appropriate compound error measure according to the rate of false positives one is willing to encounter then a procedure is developed that allows one to control the error rate at a desired level while maintaining the power of each test as much as possible the most commonly controlled quantity when testing multiple hypotheses is the family wise error rate fwer which is the probability of yielding one or more false positives out of all hypotheses tested the most familiar example of this is the bonferroni method if there are m hypothesis tests each test is controlled so that the probability of a false positive is less than or equal to m for some chosen value of it then follows that the overall fwer is less than or equal to m any

sensitivity analysis for the cross match test with applications in genomics the cross match test is an exact distribution free test of no treatment effect on a high dimensional outcome in a randomized experiment the test uses optimal nonbipartite matching to pair 2i subjects into i pairs based on similar outcomes and the cross match statistic a is the number of times that a treated subject was paired with a control rejecting for small values of a if the test is applied in an observational study in which treatments are not randomly assigned then it may be comparing treated and control subjects who are not comparable and thus may falsely reject a true null hypothesis of no treatment effect we develop a sensitivity analysis for the cross match test and apply it in an observational study of the effects of smoking on gene expression levels in addition we develop a sensitivity analysis for several multiple testing procedures using the cross match test and apply it to 1627 molecular function categories in gene ontology

a note on the adaptive control of false discovery rates summary the use of a fixed rejection region for multiple hypothesis testing has been shown to outperform standard fixed error rate approaches when applied to control of the false discovery rate in this work it is demonstrated that if the original step up procedure of benjamini and hochberg is modified to exercise adaptive control of the false discovery rate its performance is virtually identical to that of the fixed rejection region approach in addition the dependence of both methods on the proportion of true null hypotheses is explored with a focus on the difficulties that are involved in the estimation of this quantity

false discovery rate estimation for large scale homogeneous discrete p values large scale homogeneous discrete p values are encountered frequently in high throughput genomics studies and the related multiple testing problems become challenging because most existing methods for the false discovery rate fdr assume continuous p values in this article we study the estimation of the null proportion and fdr for discrete p values with common support in the finite sample setting we propose a novel class of conservative fdr estimators furthermore we show that a broad class of fdr estimators is simultaneously conservative over all support points under some weak dependence condition in the asymptotic setting we further demonstrate the significant improvement of a newly proposed method over existing methods through simulation studies and a case study

estimation of a two component mixture model with applications to multiple testing we consider a two component mixture model with one known component we develop methods for estimating the mixing proportion and the other unknown distribution nonparametrically given i i d data from the mixture model we use ideas from shape restricted function estimation and develop tuning parameter free estimators that are easily implementable and have good finite sample performance we establish the consistency of our procedures distribution free finite sample lower confidence bounds are developed for the mixing proportion the identifiability of the model and the estimation of the density of the unknown mixing distribution are also addressed we discuss the connection with the problem of multiple testing and compare our procedure with some of the existing methods in that area through simulation studies we also analyse two data sets one arising from an application in astronomy and the other from a microarray experiment

on false discovery rate thresholding for classification under sparsity we study the properties of false discovery rate fdr thresholding viewed as a classification procedure the 0 class null is assumed to have a known density while the 1 class alternative is obtained from the 0 class either by translation or by scaling furthermore the 1 class is assumed to have a small number of elements w r t the 0 class sparsity we focus on densities of the subbotin family including gaussian and laplace models nonasymptotic oracle inequalities are derived for the excess risk of fdr thresholding these inequalities lead to explicit rates of convergence of the excess risk to zero as the number m of items to be classified tends to infinity and in a regime where the power of the bayes rule is away from 0 and 1 moreover these theoretical investigations suggest an explicit choice for the target level alpha m of fdr thresholding as a function of m our oracle inequalities show theoretically that the resulting fdr thresholding adapts to the unknown sparsity regime contained in the data this property is illustrated with numerical experiments