the measure theoretic identity underlying transient fluctuation theorems we prove a measure theoretic identity that underlies all transient fluctuation theorems tfts for entropy production and dissipated work in inhomogeneous deterministic and stochastic processes including those of evans and searles crooks and seifert the identity is used to deduce a tautological physical interpretation of tfts in terms of the arrow of time and its generality reveals that the self inverse nature of the various trajectory and process transformations historically relied upon to prove tfts while necessary for these theorems from a physical standpoint it is however not necessary from a mathematical one the moment generating functions of thermodynamic variables appearing in the identity are shown to converge in general only in a vertical strip in the complex plane with the consequence that a tft that holds over arbitrary timescales may fail to give rise to an asymptotic fluctuation theorem for any possible speed of the corresponding large deviation principle the case of strongly biased birth death chains is presented to illustrate this phenomenon we also discuss insights obtained from our measure theoretic formalism into the results of saha et al on the breakdown of tfts for driven brownian particles

testing hypotheses in order in certain circumstances one wishes to test one hypothesis only if certain other hypotheses have been rejected this ordering of hypotheses simplifies the task of controlling the probability of rejecting any true hypothesis in an example from an observational study a treated group is shown to be further from both of two control groups than the two control groups are from each other

resampling based multiple testing methods with covariate adjustment application to investigation of antiretroviral drug susceptibility identifying genetic mutations that cause clinical resistance to antiretroviral drugs requires adjustment for potential confounders such as the number of active drugs in a hiv infected patient s regimen other than the one of interest motivated by this problem we investigated resampling based methods to test equal mean response across multiple groups defined by hiv genotype after adjustment for covariates we consider construction of test statistics and their null distributions under two types of model parametric and semiparametric the covariate function is explicitly specified in the parametric but not in the semiparametric approach the parametric approach is more precise when models are correctly specified but suffer from bias when they are not the semiparametric approach is more robust to model misspecification but may be less efficient to help preserve type i error while also improving power in both approaches we propose resampling approaches based on matching of observations with similar covariate values matching reduces the impact of model misspecification as well as imprecision in estimation these methods are evaluated via simulation studies and applied to a data set that combines results from a variety of clinical studies of salvage regimens our focus is on relating hiv genotype to viral susceptibility to abacavir after adjustment for the number of active antiretroviral drugs excluding abacavir in the patient s regimen

tests for high dimensional covariance matrices we propose tests for sphericity and identity of high dimensional covariance matrices the tests are nonparametric without assuming a specific parametric distribution for the data they can accommodate situations where the data dimension is much larger than the sample size namely the large p small n situations we demonstrate by both theoretical and empirical studies that the tests have good properties for a wide range of dimensions and sample sizes we applied the proposed test on a microarray dataset on yorkshire gilts and tested for the covariance structure for the expression levels for sets of genes

experimental study of the fluctuation theorem in a nonequilibrium steady state the fluctuation theorem ft quantifies the probability of second law violations in small systems over short time scales while this theorem has been experimentally demonstrated for systems that are perturbed from an initial equilibrium state there are a number of studies suggesting that the theorem applies asymptotically in the long time limit to systems in a nonequilibrium steady state the asymptotic application of the ft to such nonequilibrium steady states has been referred to in the literature as the steady state fluctuation theorem or ssft in this paper we demonstrate experimentally the application of the ft to nonequilibrium steady states using a colloidal particle localized in a translating optical trap furthermore we show for this colloidal system that the ft holds under nonequilibrium steady states for all time and not just in the long time limit as in the ssft

energy representation for nonequilibrium brownian like systems steady states and fluctuation relations stochastic dynamics in the energy representation is used as a method to represent nonequilibrium brownian like systems it is shown that the equation of motion for the energy of such systems can be taken in the form of the langevin equation with multiplicative noise properties of the steady states are examined by solving the fokker planck equation for the energy distribution functions the generalized integral fluctuation theorem is deduced for the systems characterized by the shifted probability flux operator from this theorem a number of entropy and fluctuation relations such as the evans searles fluctuation theorem the hatano sasa identity and the jarzynski s equality are derived

gene identification using true discovery rate degree of association sets and estimates corrected for regression to the mean analyses intended to identify genes with expression that is associated with some clinical outcome or state are often based on ranked p values from tests of point null hypotheses of no association van de wiel and kim take the innovative approach of testing the interval null hypotheses that the degree of association for a gene is less than some value of interest against the alternative that it is greater combining this idea with the false discovery rate controlling methods of storey taylor and siegmund gives a computationally simple way to identify true discovery rate degree of association tdrda sets of genes among which a specified proportion are expected to have an absolute association of a specified degree or more this leads to a gene ranking method that uses the maximum lower bound degree of association for which each gene belongs to a tdrda set estimates of each gene s actual degree of association with approximate correction for selection bias due to regression to the mean rm can be derived using simple bivariate normal theory and efron and tibshirani s empirical bayes approach for a given data set all possible tdrda sets can be displayed along with the gene ranking and the rm corrected estimates of degree of association in a concise graphical summary

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

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

online rules for control of false discovery rate and false discovery exceedance multiple hypothesis testing is a core problem in statistical inference and arises in almost every scientific field given a set of null hypotheses mathcal h n h 1 ldots h n benjamini and hochberg j r stat soc ser b stat methodol 57 1995 289 300 introduced the false discovery rate mathrm fdr which is the expected proportion of false positives among rejected null hypotheses and proposed a testing procedure that controls mathrm fdr below a pre assigned significance level nowadays mathrm fdr is the criterion of choice for large scale multiple hypothesis testing in this paper we consider the problem of controlling mathrm fdr in an online manner concretely we consider an ordered possibly infinite sequence of null hypotheses mathcal h h 1 h 2 h 3 ldots where at each step i the statistician must decide whether to reject hypothesis h i having access only to the previous decisions this model was introduced by foster and stine j r stat soc ser b stat methodol 70 2008 429 444 we study a class of generalized alpha investing procedures first introduced by aharoni and rosset j r stat soc ser b stat methodol 76 2014 771 794 we prove that any rule in this class controls online mathrm fdr provided p values corresponding to true nulls are independent from the other p values earlier work only established mathrm mfdr control next we obtain conditions under which generalized alpha investing controls mathrm fdr in the presence of general p values dependencies we also develop a modified set of procedures that allow to control the false discovery exceedance the tail of the proportion of false discoveries finally we evaluate the performance of online procedures on both synthetic and real data comparing them with offline approaches such as adaptive benjamini hochberg

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

exact calculations for false discovery proportion with application to least favorable configurations in a context of multiple hypothesis testing we provide several new exact calculations related to the false discovery proportion fdp of step up and step down procedures for step up procedures we show that the number of erroneous rejections conditionally on the rejection number is simply a binomial variable which leads to explicit computations of the c d f the s th moment and the mean of the fdp the latter corresponding to the false discovery rate fdr for step down procedures we derive what is to our knowledge the first explicit formula for the fdr valid for any alternative c d f of the p values we also derive explicit computations of the power for both step up and step down procedures these formulas are explicit in the sense that they only involve the parameters of the model and the c d f of the order statistics of i i d uniform variables the p values are assumed either independent or coming from an equicorrelated multivariate normal model and an additional mixture model for the true false hypotheses is used this new approach is used to investigate new results which are of interest in their own right related to least most favorable configurations for the fdr and the variance of the fdp

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

total positivity properties of absolute value multinormal variables with applications to confidence interval estimates and related probabilistic inequalities total positivity properties of multivariate densities are useful in deducing positive dependence of random vector components and related probability inequalities in this paper we determine necessary and sufficient conditions for total positivity of absolute value multinormal variables the results are applied to obtain positive dependence and associated inequalities for the multinormal and related distributions e g the multivariate t and wishart distributions inequalities of this type yield bounds for multivariate confidence set probabilities

multiple testing via fdrl for large scale imaging data the multiple testing procedure plays an important role in detecting the presence of spatial signals for large scale imaging data typically the spatial signals are sparse but clustered this paper provides empirical evidence that for a range of commonly used control levels the conventional fdr procedure can lack the ability to detect statistical significance even if the p values under the true null hypotheses are independent and uniformly distributed more generally ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of the fdr procedure this paper first introduces a scalar quantity to characterize the extent to which the lack of identification phenomenon lip of the fdr procedure occurs second we propose a new multiple comparison procedure called fdrl to accommodate the spatial information of neighboring p values via a local aggregation of p values theoretical properties of the fdrl procedure are investigated under weak dependence of p values it is shown that the fdrl procedure alleviates the lip of the fdr procedure thus substantially facilitating the selection of more stringent control levels simulation evaluations indicate that the fdrl procedure improves the detection sensitivity of the fdr procedure with little loss in detection specificity the computational simplicity and detection effectiveness of the fdrl procedure are illustrated through a real brain fmri dataset

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

functional integral approach for multiplicative stochastic processes we present a functional formalism to derive a generating functional for correlation functions of a multiplicative stochastic process represented by a langevin equation we deduce a path integral over a set of fermionic and bosonic variables without performing any time discretization the usual prescriptions to define the wiener integral appear in our formalism in the definition of green s functions in the grassman sector of the theory we also study nonperturbative constraints imposed by becchi rouet and stora symmetry brs and supersymmetry on correlation functions we show that the specific prescription to define the stochastic process is wholly contained in tadpole diagrams therefore in a supersymmetric theory the stochastic process is uniquely defined since tadpole contributions cancels at all order of perturbation theory

stepup procedures controlling generalized fwer and generalized fdr in many applications of multiple hypothesis testing where more than one false rejection can be tolerated procedures controlling error rates measuring at least k false rejections instead of at least one for some fixed k 1 can potentially increase the ability of a procedure to detect false null hypotheses the k fwer a generalized version of the usual familywise error rate fwer is such an error rate that has recently been introduced in the literature and procedures controlling it have been proposed a further generalization of a result on the k fwer is provided in this article in addition an alternative and less conservative notion of error rate the k fdr is introduced in the same spirit as the k fwer by generalizing the usual false discovery rate fdr a k fwer procedure is constructed given any set of increasing constants by utilizing the kth order joint null distributions of the p values without assuming any specific form of dependence among all the p values procedures controlling the k fdr are also developed by using the kth order joint null distributions of the p values first assuming that the sets of null and nonnull p values are mutually independent or they are jointly positively dependent in the sense of being multivariate totally positive of order two mtp2 and then discarding that assumption about the overall dependence among the p values

sequential selection procedures and false discovery rate control summary we consider a multiple hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block of hypotheses a rejection rule in this setting amounts to a procedure for choosing the stopping point k this setting is inspired by the sequential nature of many model selection problems where choosing a stopping point or a model is equivalent to rejecting all hypotheses up to that point and none thereafter we propose two new testing procedures and prove that they control the false discovery rate in the ordered testing setting we also show how the methods can be applied to model selection by using recent results on p values in sequential model selection settings

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

a bottom up approach to testing hypotheses that have a branching tree dependence structure with error rate control modern statistical analyses often involve testing large numbers of hypotheses in many situations these hypotheses may have an underlying tree structure that both helps determine the order that te

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

hierarchical false discovery rate controlling methodology we discuss methodology for controlling the false discovery rate fdr in complex large scale studies that involve testing multiple families of hypotheses the tested hypotheses are arranged in a tree of disjoint subfamilies and the subfamilies of hypotheses are hierarchically tested by the benjamini and hochberg fdr controlling bh procedure we derive an approximation for the multiple family fdr for independently distributed test statistics q the level at which the bh procedure is applied times the number of families tested plus the number of discoveries divided by the number of discoveries plus 1 we provide a universal bound for the fdr of the discoveries in the new hierarchical testing approach 2 1 44 q and demonstrate in simulations that when the data has an hierarchical structure the new testing approach can be considerably more powerful than the bh procedure

the simes method for multiple hypothesis testing with positively dependent test statistics abstract the simes method for testing intersection of more than two hypotheses is known to control the probability of type i error only when the underlying test statistics are independent although this method is more powerful than the classical bonferroni method it is not known whether it is conservative when the test statistics are dependent this article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple hypothesis testing situations the simes method indeed controls the probability of type i error this extends some results established very recently in the special case of two hypotheses

wavelet thresholding with bayesian false discovery rate control la procedure du false discovery rate fdr est aujourd hui une methode largement repandue pour gerer les questions de multiplicite liees a des donnees multidimensionnelles la definition du fdr trouveune interpretation naturelle dans le cadre bayesien a savoir la proportion attendue d hypotheses nulles rejetees a tort a seuil de significativite donne dans cet article nous proposons de controler le fdr positif par une approche bayesienne dont la regle de rejet est basee sur les probabilites posterieures des hypotheses nulles le lien entre les degres de significativite bayesiens et frequentistes a ete etudie dans plusieurs contextes ici nous elargissons la comparaison aux tests multiples avec controle du fdr et illustrons la procedure par une application au seuillage en ondelettes le probleme consiste a recuperer un signal a partir de mesures bruitees ceci implique d extraire des coefficients d ondelettes resultant du vrai signal et peut etre formule comme un probleme de test d hypotheses multiples nous utilisons des exemples simules pour comparer les performances de notre approche a la procedure de benjamini et hochberg 1995 nous illustrons egalement cette methode au moyen de donnees issues de l analyse spectrale par resonance magnetique nucleaire du cerveau humain

correlated z values and the accuracy of large scale statistical estimates we consider large scale studies in which there are hundreds or thousands of correlated cases to investigate each represented by its own normal variate typically a z value a familiar example is provided by a microarray experiment comparing healthy with sick subjects expression levels for thousands of genes this paper concerns the accuracy of summary statistics for the collection of normal variates such as their empirical cdf or a false discovery rate statistic it seems like we must estimate an n by n correlation matrix n the number of cases but our main result shows that this is not necessary good accuracy approximations can be based on the root mean square correlation over all n n 1 2 pairs a quantity often easily estimated a second result shows that z values closely follow normal distributions even under nonnull conditions supporting application of the main theorem practical application of the theory is illustrated for a large leukemia microarray study

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

fiber density estimation from single q shell diffusion imaging by tensor divergence diffusion weighted magnetic resonance imaging provides information about the nerve fiber bundle geometry of the human brain while the inference of the underlying fiber bundle orientation only requires single q shell measurements the absolute determination of their volume fractions is much more challenging with respect to measurement techniques and analysis unfortunately the usually employed multi compartment models cannot be applied to single q shell measurements because the compartment s diffusivities cannot be resolved this work proposes an equation for fiber orientation densities that can infer the absolute fraction up to a global factor this equation which is inspired by the classical mass preservation law in fluid dynamics expresses the fiber conservation associated with the assumption that fibers do not terminate in white matter simulations on synthetic phantoms show that the approach is able to derive the densities correctly for various configurations experiments with a pseudo ground truth phantom show that even for complex brain like geometries the method is able to infer the densities correctly in vivo results with 81 healthy volunteers are plausible and consistent a group analysis with respect to age and gender show significant differences such that the proposed maps can be used as a quantitative measure for group and longitudinal analysis

composition operators from bloch type spaces into qk type spaces supposeis an analytic map of the unit disk d into itself x is a banach space of analytic functions on d define the composition operator c cf f for all f x in this paper the boundedness and compactness of the composition operators from bloch spaces into qk p q and qk 0 p q spaces are discussed where 0 keywords composition operator analytic function bspace k carleson measure compact k carleson measure

controlling variable selection by the addition of pseudovariables we propose a new approach to variable selection designed to control the false selection rate fsr defined as the proportion of uninformative variables included in selected models the method works by adding a known number of pseudovariables to the real dataset running a variable selection procedure and monitoring the proportion of pseudovariables falsely selected information obtained from bootstrap like replications of this process is used to estimate the proportion of falsely selected real variables and to tune the selection procedure to control the fsr

some probability inequalities for ordered rm mtp sb 2 random variables a proof of the simes conjecture some new probability inequalities involving the ordered components of an mtp 2 random vector are derived which provide an analytical proof of an important conjecture in the field of multiple hypothesis testing this conjecture has been mostly validated so far using simulation

compact composition operators on the bloch space necessary and sufficient conditions are given for a composition operator cof f o q to be compact on the bloch space w and on the little bloch space o weakly compact composition operators on o are shown to be compact if q e o is a conformal mapping of the unit disk d into itself whose image q d approaches the unit circle t only in a finite number of nontangential cusps then co is compact on 7o on the other hand if there is a point of t n q d at which q d does not have a cusp then co is not compact

denoising functional mr images a comparison of wavelet denoising and gaussian smoothing we present a general wavelet based denoising scheme for functional magnetic resonance imaging fmri data and compare it to gaussian smoothing the traditional denoising method used in fmri analysis one dimensional wavelab thresholding routines were adapted to two dimensional 2 d images and applied to 2 d wavelet coefficients to test the effect of these methods on the signal to noise ratio snr we compared the snr of 2 d fmri images before and after denoising using both gaussian smoothing and wavelet based methods we simulated a fmri series with a time signal in an active spot and tested the methods on noisy copies of it the denoising methods were evaluated in two ways by the average temporal snr inside the original activated spot and by the shape of the spot detected by thresholding the temporal snr maps denoising methods that introduce much smoothness are better suited for low snrs but for images of reasonable quality they are not preferable because they introduce heavy deformations wavelet based denoising methods that introduce less smoothing preserve the sharpness of the images and retain the original shapes of active regions we also performed statistical parametric mapping on the denoised simulated time series as well as on a real fmri data set false discovery rate control was used to correct for multiple comparisons the results show that the methods that produce smooth images introduce more false positives the less smoothing wavelet based methods although generating more false negatives produce a smaller total number of errors than gaussian smoothing or wavelet based methods with a large smoothing effect

dependency and false discovery rate asymptotics some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step up procedure lsu for testing n hypotheses when test statistics are dependent in this paper we investigate the expected error rate eer and the false discovery rate fdr in some extreme parameter configurations when n tends to infinity for test statistics being exchangeable under null hypotheses all results are derived in terms of p values in a general setup we present a series of results concerning the interrelation of simes rejection curve and the limiting empirical distribution function of the p values main objects under investigation are largest limiting crossing points between these functions which play a key role in deriving explicit formulas for eer and fdr as specific examples we investigate equi correlated normal and t variables in more detail and compute the limiting eer and fdr theoretically and numerically a surprising limit behavior occurs if these models tend to independence

symmetric path integrals for stochastic equations with multiplicative noise a langevin equation with multiplicative noise is an equation schematically of the form dq dt f q e q xi where e q xi is gaussian white noise whose amplitude e q depends on q itself i show how to convert such equations into path integrals the definition of the path integral depends crucially on the convention used for discretizing time and i specifically derive the correct path integral when the convention used is the natural time symmetric one whose time derivatives are q sub t q sub t delta sub t delta t and coordinates are q sub t q sub t delta sub t 2 this is the convention that permits standard manipulations of calculus on the action like naive integration by parts it has sometimes been assumed in the literature that a stratonovich langevin equation can be quickly converted to a path integral by treating time as continuous but using the rule theta t 0 1 2 i show that this prescription fails when the amplitude e q is q dependent c 2000 the american physical society

multiple tests based on a gaussian approximation of the unitary events method with delayed coincidence count the unitary events ue method is one of the most popular and efficient methods used over the past decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons the detection of coincidences is usually based on binned coincidence count grun 1996 which is known to be subject to loss in synchrony detection grun diesmann grammont riehle aertsen 1999 this defect has been corrected by the multiple shift coincidence count grun et al 1999 the statistical properties of this count have not been further investigated until this work the formula being more difficult to deal with than the original binned count first we propose a new notion of coincidence count the delayed coincidence count which is equal to the multiple shift coincidence count when discretized point processes are involved as models for the spike trains moreover it generalizes this notion to nondiscretized point processes allowing us to propose a new gaussian approximation of the count since unknown parameters are involved in the approximation we perform a plug in step where unknown parameters are replaced by estimated ones leading to a modification of the approximating distribution finally the method takes the multiplicity of the tests into account via a benjamini and hochberg approach benjamini hochberg 1995 to guarantee a prescribed control of the false discovery rate we compare our new method mtgaue multiple tests based on a gaussian approximation of the unitary events and the ue method proposed in grun et al 1999 over various simulations showing that mtgaue extends the validity of the previous method in particular mtgaue is able to detect both profusion and lack of coincidences with respect to the independence case and is robust to changes in the underlying model furthermore mtgaue is applied on real data

hierarchical testing of variable importance a frequently encountered challenge in high dimensional regression is the detection of relevant variables variable selection suffers from instability and the power to detect relevant variables is typically low if predictor variables are highly correlated when taking the multiplicity of the testing problem into account the power diminishes even further to gain power and insight it can be advantageous to look for influence not at the level of individual variables but rather at the level of clusters of highly correlated variables we propose a hierarchical approach variable importance is first tested at the coarsest level corresponding to the global null hypothesis the method then tries to attribute any effect to smaller subclusters or even individual variables the smallest possible clusters which still exhibit a significant influence on the response variable are retained it is shown that the proposed testing procedure controls the familywise error rate at a prespecified level simultaneously over all resolution levels the method has power comparable to the bonferroni holm procedure on the level of individual variables and dramatically larger power for coarser resolution levels the best resolution level is selected adaptively

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

conditional association and unidimensionality in monotone latent variable models latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables usually assuming the conditional independence of the observable variables given the latent variables these models play an important role in educational measurement and psychometrics in sociology and in population genetics and are implicit in some work on systems reliability we study a broad class of latent variable models namely the monotone unidimensional models in which the latent variable is a scalar the observable variables are conditionally independent given the latent variable and the conditional distribution of the observables given the latent variable is stochastically increasing in the latent variable all models in this class imply a new strong form of positive dependence among the observable variables namely conditional positive association this positive dependence condition may be used to test whether any model in this class can provide an adequate fit to observed data various applications generalizations and a numerical example are discussed

detecting differentially expressed genes in microarrays using bayesian model selection dna microarrays open up a broad new horizon for investigators interested in studying the genetic determinants of disease the high throughput nature of these arrays where differential expression for thousands of genes can be measured simultaneously creates an enormous wealth of information but also poses a challenge for data analysis because of the large multiple testing problem involved the solution has generally been to focus on optimizing false discovery rates while sacrificing power the drawback of this approach is that more subtle expression differences will be missed that might give investigators more insight into the genetic environment necessary for a disease process to take hold we introduce a new method for detecting differentially expressed genes based on a high dimensional model selection technique bayesian anova for microarrays bam which strikes a balance between false rejections and false nonrejections the basis of the new approach involves a weighted average of generalized ridge

detection of the number of signals using the benjamini hochberg procedure this paper presents a novel approach to detect multiple signals embedded in noisy observations from a sensor array we formulate the detection problem as a multiple hypothesis test to control the global level of the multiple test we apply the false discovery rate fdr criterion proposed by benjamini and hochberg compared to the classical familywise error rate fwe criterion the fdr controling procedure leads to a significant gain in power for large size problems in addition we apply the bootstrap technique to estimate the observed significance level required by the fdr controling procedure simulations show that the fdr controling procedure always provides higher probability of correct detection than the fwe controling procedure furthermore the reliability of the proposed test procedure is not affected by the gain in power of the test

on false discovery control under dependence a popular framework for false discovery control is the random effects model in which the null hypotheses are assumed to be independent this paper generalizes the random effects model to a conditional dependence model which allows dependence between null hypotheses the dependence can be useful to characterize the spatial structure of the null hypotheses asymptotic properties of false discovery proportions and numbers of rejected hypotheses are explored and a large sample distributional theory is obtained

familywise robustness criteria for multiple comparison procedures a criticism of multiple comparison procedures is that the family of inferences over which an error rate is controlled is often arbitrarily selected yet the conclusion may depend heavily on the choice of the family such ambiguity is most likely in large exploratory studies requiring numerous simultaneous inferences in ambiguous situations it is desirable that results of multiple comparison procedures depend little on the chosen family to assess this we propose several familywise robustness criteria to evaluate such procedures and we find some of their properties theoretically and by simulation procedures that control the false discovery rate seem to be familywise robust

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

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

α investing a procedure for sequential control of expected false discoveries summary investing is an adaptive sequential methodology that encompasses a large family of procedures for testing multiple hypotheses all control mfdr which is the ratio of the expected number of false rejections to the expected number of rejections mfdr is a weaker criterion than the false discovery rate which is the expected value of the ratio we compensate for this weakness by showing that investing controls mfdr at every rejected hypothesis investing resembles spending that is used in sequential trials but it has a key difference when a test rejects a null hypothesis investing earns additional probability towards subsequent tests investing hence allows us to incorporate domain knowledge into the testing procedure and to improve the power of the tests in this way investing enables the statistician to design a testing procedure for a specific problem while guaranteeing control of mfdr

composition type operator from bergman space to μ bloch type space in cn abstract let be a holomorphic self map of b and h b a composition type operator t is defined by t f f we can regard this operator as a generalization of a multiplication operator and a composition operator for normal functions some necessary and sufficient conditions are given for which t is a bounded or compact operator from bergman space to bloch type space on the unit ball of c n as a corollary we obtain the pointwise multiplier from bergman space to bloch type space on b

large scale multiple testing under dependence summary the paper considers the problem of multiple testing under dependence in a compound decision theoretic framework the observed data are assumed to be generated from an underlying two state hidden markov model we propose oracle and asymptotically optimal datadriven procedures that aim to minimize the false non discovery rate fnr subject to a constraint on the false discovery rate fdr it is shown that the performance of a multiple testing procedure can be substantially improved by adaptively exploiting the dependence structure among hypotheses and hence conventional fdr procedures that ignore this structural information are inefficient both theoretical properties and numerical performances of the procedures proposed are investigated it is shown that the procedures proposed control fdr at the desired level enjoy certain optimality properties and are especially powerful in identifying clustered non null cases the new procedure is applied to an influenza like illness surveillance study for detecting the timing of epidemic periods

state dependent diffusion thermodynamic consistency and its path integral formulation the friction coefficient of a particle can depend on its position as it does when the particle is near a wall we formulate the dynamics of particles with such state dependent friction coefficients in terms of a general langevin equation with multiplicative noise whose evaluation requires the introduction of specific rules two common conventions the ito and the stratonovich provide alternative rules for evaluation of the noise but other conventions are possible we show that the requirement that a particle s distribution function approach the boltzmann distribution at long times dictates that a drift term must be added to the langevin equation this drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise we explore the consequences of this result in a number of examples with spatially varying diffusion coefficients we also derive a path integral representation for arbitrary interpretation of the noise and use it in a perturbative study of correlations in a simple system

the p filter multilayer false discovery rate control for grouped hypotheses summary in many practical applications of multiple testing there are natural ways to partition the hypotheses into groups by using the structural spatial or temporal relatedness of the hypotheses and this prior knowledge is not used in the classical benjamini hochberg procedure for controlling the false discovery rate fdr when one can define possibly several such partitions it may be desirable to control the group fdr simultaneously for all partitions as special cases the finest partition divides the n hypotheses into n groups of one hypothesis each and this corresponds to controlling the usual notion of fdr whereas the coarsest partition puts all n hypotheses into a single group and this corresponds to testing the global null hypothesis we introduce the p filter which takes as input a list of n p values and m 1 partitions of hypotheses and produces as output a list of n or fewer discoveries such that the group fdr is provably simultaneously controlled for all partitions importantly since the partitions are arbitrary our procedure can also handle multiple partitions which are non hierarchical the p filter generalizes two classical procedures when m 1 choosing the finest partition into n singletons we exactly recover the benjamini hochberg procedure whereas choosing instead the coarsest partition with a single group of size n we exactly recover the simes test for the global null hypothesis we verify our findings with simulations that show how this technique can not only lead to the aforementioned multilayer fdr control but also lead to improved precision of rejected hypotheses we present some illustrative results from an application to a neuroscience problem with functional magnetic resonance imaging data where hypotheses are explicitly grouped according to predefined regions of interest in the brain thus allowing the scientist to employ field specific prior knowledge explicitly and flexibly

support vector machines for dyadic data we describe a new technique for the analysis of dyadic data where two sets of objects row and column objects are characterized by a matrix of numerical values that describe their mutual relationships the new technique called potential support vector machine p svm is a large margin method for the construction of classifiers and regression functions for the column objects contrary to standard support vector machine approaches the p svm minimizes a scale invariant capacity measure and requires a new set of constraints as a result the p svm method leads to a usually sparse expansion of the classification and regression functions in terms of the row rather than the column objects and can handle data and kernel matrices that are neither positive definite nor square we then describe two complementary regularization schemes the first scheme improves generalization performance for classification and regression tasks the second scheme leads to the selection of a small informative set of row support objects and can be applied to feature selection benchmarks for classification regression and feature selection tasks are performed with toy data as well as with several real world data sets the results show that the new method is at least competitive with but often performs better than the benchmarked standard methods for standard vectorial as well as true dyadic data sets in addition a theoretical justification is provided for the new approach

effective action for stochastic partial differential equations stochastic partial differential equations spdes are the basic tool for modeling systems where noise is important spdes are used for models of turbulence pattern formation and the structural development of the universe itself it is reasonably well known that certain spdes can be manipulated to be equivalent to nonquantum field theories that nevertheless exhibit deep and important relationships with quantum field theory in this paper we systematically extend these ideas we set up a functional integral formalism and demonstrate how to extract all the one loop physics for an arbitrary spde subject to arbitrary gaussian noise it is extremely important to realize that gaussian noise does not imply that the field variables undergo gaussian fluctuations and that these nonquantum field theories are fully interacting the limitation to one loop is not as serious as might be supposed experience with quantum field theories qfts has taught us that one loop physics is often quite adequate to give a good description of the salient issues the limitation to one loop does however offer marked technical advantages because at one loop almost any field theory can be rendered finite using zeta function technology we can sidestep the complications inherent in the martin siggia rose formalism the spde analog of the becchi rouet stora tyutin formalism used in qft and instead focus attention on a minimalist approach that uses only the physical fields this direct approach is the spde analog of canonical quantization using physical fields after setting up the general formalism for the characteristic functional partition function we show how to define the effective action to all loops and then focus on the one loop effective action and its specialization to constant fields the effective potential the physical interpretation of the effective action and effective potential for spdes is addressed and we show that key features carry over from qft to the case of spdes an important result is that the amplitude of the two point function governing the noise acts as the loop counting parameter and is the analog of planck s constant in this spde context we derive a general expression for the one loop effective potential of an arbitrary spde subject to translation invariant gaussian noise and compare this with the one loop potential for qft

joint mean and covariance estimation with unreplicated matrix variate data abstractit has been proposed that complex populations such as those that arise in genomics studies may exhibit dependencies among observations as well as among variables this gives rise to the challenging problem of analyzing unreplicated high dimensional data with unknown mean and dependence structures matrix variate approaches that impose various forms of inverse covariance sparsity allow flexible dependence structures to be estimated but cannot directly be applied when the mean and covariance matrices are estimated jointly we present a practical method utilizing generalized least squares and penalized inverse covariance estimation to address this challenge we establish consistency and obtain rates of convergence for estimating the mean parameters and covariance matrices the advantages of our approaches are i dependence graphs and covariance structures can be estimated in the presence of unknown mean structure ii the mean structure becomes more efficiently estimated when accounting for

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

accumulation tests for fdr control in ordered hypothesis testing abstractmultiple testing problems arising in modern scientific applications can involve simultaneously testing thousands or even millions of hypotheses with relatively few true signals in this article we consider the multiple testing problem where prior information is available for instance from an earlier study under different experimental conditions that can allow us to test the hypotheses as a ranked list to increase the number of discoveries given an ordered list of n hypotheses the aim is to select a data dependent cutoff k and declare the first k hypotheses to be statistically significant while bounding the false discovery rate fdr generalizing several existing methods we develop a family of accumulation tests to choose a cutoff k that adapts to the amount of signal at the top of the ranked list we introduce a new method in this family the hingeexp method which offers higher power to detect true signals compared to existing techniques our theoretical results prove that these metho

chip chip data model and analysis summary chip chip or chip on chip is a technology for isolation and identification of genomic sites occupied by specific dna binding proteins in living cells the chip chip signals can be obtained over the whole genome by tiling arrays where a peak shape is generally observed around a protein binding site in this article we describe the chip chip process and present a probability model for chip chip data we then propose a model based method for recognizing the peak shapes for the purpose of detecting protein binding sites we also investigate the issue of bandwidth in nonparametric kernel smoothing method

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

composition operators from bloch type spaces to hardy and besov spaces boundedness and compactness of composition operators from bloch type spaces to hardy spaces and analytic besov spaces are characterized by function theoretic properties of their inducing maps for the case of the bloch space the characterizations involve the hyperbolic versions of hardy and besov classes the conditions for the hyperbolic besov classes are then interpreted geometrically when the symbols are univalent and strict inclusion between different hyperbolic besov classes is shown by an example

fluctuation theorem for stochastic systems the fluctuation theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics it has been proved in a number of different ways for thermostatted deterministic nonequilibrium systems in the present paper we show that the fluctuation theorem is also valid for a class of stochastic nonequilibrium systems the theorem is therefore not reliant on the reversibility or the determinism of the underlying dynamics numerical tests verify the theoretical result

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

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

characterization of bayes procedures for multiple endpoint problems and inadmissibility of the step up procedure the problem of multiple endpoint testing for k endpoints is treated as a 2 k finite action problem the loss function chosen is a vector loss function consisting of two components the two components lead to a vector risk one component of the vector risk is the false rejection rate frr that is the expected number of false rejections the other component is the false acceptance rate far that is the expected number of acceptances for which the corresponding null hypothesis is false this loss function is more stringent than the positive linear combination loss function of lehmann ann math statist 28 1957 1 25 and cohen and sackrowitz ann statist 2005 33 126 144 in the sense that the class of admissible rules is larger for this vector risk formulation than for the linear combination risk function in other words fewer procedures are inadmissible for the vector risk formulation the statistical model assumed is that the vector of variables z is multivariate normal with mean vector and known intraclass covariance matrix e the endpoint hypotheses are h i i 0 vs k i i 0 1 k a characterization of all symmetric bayes procedures and their limits is obtained the characterization leads to a complete class theorem the complete class theorem is used to provide a useful necessary condition for admissibility of a procedure the main result is that the step up multiple endpoint procedure is shown to be inadmissible

the transient fluctuation theorem of sample entropy production for general stochastic processes the transient fluctuation theorem for stochastic processes was first put forward by d j searles and d j evans 1999 in the present paper it is rigorously proved that the transient fluctuation theorem tft of sample entropy production which is previously defined by jiang et al 2003 and reid et al 2005 and also called the general action functional up to boundary terms by lebowitz and spohn 1999 holds for general stochastic processes without the assumption of markovian homogeneous or stationary properties then the condition of our theorem is verified for various stochastic processes including homogeneous inhomogeneous markov chains and general diffusion processes among these cases the transient fluctuation theorems for inhomogeneous markov chains and general diffusion processes are rigorously derived for the first time

outlier detection and false discovery rates for whole genome dna matching we define a statistic called the matching statistic for locating regions of the genome that exhibit excess similarity among cases when compared to controls such regions are reasonable candidates for harboring disease genes we find the asymptotic distribution of the statistic while accounting for correlations among sampled individuals we then use the benjamini and hochberg false discovery rate fdr method for multiple hypothesis testing to find regions of excess sharing the p values for each region involve estimated nuisance parameters under appropriate conditions we show that the fdr method based on p values and with estimated nuisance parameters asymptotically preserves the fdr property finally we apply the method to a pilot study on schizophrenia

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

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

supersymmetry approach in the field theory of ergodicity breaking transitions abstract the supersymmetry susy self consistent approximation for the model of non equilibrium thermodynamic system with quenched disorder is derived from the dynamical action calculated by means of generalized second legendre transformation technique the equations for adiabatic and isothermal susceptibilities memory and field induced parameters are obtained on the basis of asymptotic analysis of dynamic dyson equations it is shown that the marginal stability condition that defines the critical point is governed by fluctuations violating fluctuation dissipation theorem fdt the temperature of ergodicity breaking transition is calculated as a function of quenched disorder intensities transformation of superfields related to the mapping between an instanton process and the corresponding causal solution is discussed

cauchy combination test a powerful test with analytic p value calculation under arbitrary dependency structures abstract combining individual p values to aggregate multiple small effects has a long standing interest in statistics dating back to the classic fisher s combination test in modern large scale da