the graph model for conflict resolution with incomplete fuzzy reciprocal preference relations abstract within the paradigm of the graph model for conflict resolution gmcr fuzzy reciprocal preference relations fprs can be usually employed to handle decision makers dms certain and uncertain preferences due to lack of time limited expertise or dynamic factors the dms fuzzy preferences over the alternatives or states may be incomplete thus a new preference relation the incomplete fuzzy reciprocal preference relation ifpr is proposed to deal with both complete and incomplete fuzzy preferences within gmcr in this study one key contribution is that according to dms attitude to risk associated with incomplete fuzzy preferences four extended sets of stability definitions are put forward for providing a nuanced description of human behavior for both two dm and n dm conflict models furthermore the interrelationships of solution concepts within and across the four extensions of stability definitions are investigated finally an illustrative example the potential large scale export of water from lake gisborne canada is used to show the usefulness of gmcr with incomplete fuzzy reciprocal preference relations

multiple testing for pattern identification with applications to microarray time course experiments in time course experiments it is often desirable to identify genes that exhibit a specific pattern of differential expression over time and thus gain insights into the mechanisms of the underlying biological processes two challenging issues in the pattern identification problem are i how to combine the simultaneous inferences across multiple time points and ii how to control the multiplicity while accounting for the strong dependence we formulate a compound decision theoretic framework for set wise multiple testing and propose a data driven procedure that aims to minimize the missed set rate subject to a constraint on the false set rate the hidden markov model proposed in yuan and kendziorski 2006 is generalized to capture the temporal correlation in the gene expression data both theoretical and numerical results are presented to show that our data driven procedure controls the multiplicity provides an optimal way of combining simultaneous inferences across multiple time points and greatly i

fuzzy preferences in the graph model for conflict resolution a new framework for the graph model for conflict resolution is developed so that decision makers dms with fuzzy preferences can be included in conflict models a graph model is both a formal representation for multiple participant multiple objective decision problems and a set of analysis procedures that add insights into them within the new framework graph models can include and integrate into the analysis both certain and uncertain information about dms preferences one key contribution of this study is to extend the four basic stability definitions for two or more dms to models with fuzzy preferences together fuzzy nash stability fuzzy general metarationality fuzzy symmetric metarationality and fuzzy sequential stability provide anuanced description of human behavior a state is fuzzy stable for a dm if a move to any other state is not sufficiently likely to yield an outcome which the dm prefers where sufficiency is measured according to a fuzzy satisficing threshold that is the characteristic of the dm a fuzzy equilibrium which is an outcome that is fuzzy stable for all dms therefore represents a possible resolution of the strategic conflict the practical application and interpretation of these new stability definitions are illustrated with an example

consistent classification of nonstationary time series using stochastic wavelet representations consider the situation when we have training data containing many time series having known group membership and testing data with unknown group membership the goals are to find timescale features using training data that can best separate the groups and to use these highly discriminant features to classify test data we propose a method for classification using a bias corrected nondecimated wavelet transform wavelets are ideal for identifying highly discriminant local time and scale features the observed signals will be treated as realizations of locally stationary wavelet processes under which we define and rigorously estimate the evolutionary wavelet spectrum timescale decomposition of variance the evolutionary wavelet spectrum which contains the second moment information on the signals is used as the classification signature for each test time series we compute the empirical wavelet spectrum and its divergence from the wavelet spectrum of each group the test time series is then assigned

false discovery control in large scale spatial multiple testing summary the paper develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals we consider both pointwise and clusterwise spatial analyses and derive oracle procedures which optimally control the false discovery rate false discovery exceedance and false cluster rate a data driven finite approximation strategy is developed to mimic the oracle procedures on a continuous spatial domain our multiple testing procedures are asymptotically valid and can be effectively implemented using bayesian computational algorithms for analysis of large spatial data sets numerical results show that the procedures proposed lead to more accurate error control and better power performance than conventional methods we demonstrate our methods for analysing the time trends in tropospheric ozone in eastern usa

multiple testing with heterogeneous multinomial distributions summary standard false discovery rate fdr procedures can provide misleading inference when testing multiple null hypotheses with heterogeneous multinomial data for example in the motivating study the goal is to identify species of bacteria near the roots of wheat plants rhizobacteria that are moderately or strongly associated with productivity however standard procedures discover the most abundant species even when their association is weak and fail to discover many moderate and strong associations when the species are not abundant this article provides a new fdr controlling method based on a finite mixture of multinomial distributions and shows that it tends to discover more moderate and strong associations and fewer weak associations when the data are heterogeneous across tests the new method is applied to the rhizobacteria data and performs favorably over competing methods

estimating the null and the proportion of nonnull effects in large scale multiple comparisons an important issue raised by efron in the context of large scale multiple comparisons is that in many applications the usual assumption that the null distribution is known is incorrect and seemingly negligible differences in the null may result in large differences in subsequent studies this suggests that a careful study of estimation of the null is indispensable in this article we consider the problem of estimating a null normal distribution and a closely related problem estimation of the proportion of nonnull effects we develop an approach based on the empirical characteristic function and fourier analysis the estimators are shown to be uniformly consistent over a wide class of parameters we investigate the numerical performance of the estimators using both simulated and real data in particular we apply our procedure to the analysis of breast cancer and human immunodeficiency virus microarray datasets the estimators perform favorably compared with existing methods

fuzzy option prioritization for the graph model for conflict resolution abstract a fuzzy option prioritization technique is developed to efficiently model uncertain preferences of dms in strategic conflicts as fuzzy preferences by using the decision makers dms fuzzy truth values of preference statements at feasible states within the framework of the graph model for conflict resolution the preference statements of a dm express desirable combinations of options or courses of action and are listed in order of importance a fuzzy truth value is a truth degree expressed as a number between 0 and 1 capturing uncertainty in the truth of a preference statement at a feasible state a fuzzy preference formula is introduced based on the fuzzy truth values of preference statements and it is established that the output of this formula is a fuzzy preference relation it is shown that fuzzy option prioritization can also be used when the truth values of preference statements at feasible states are completely based on boolean logic thereby generating a crisp preference over feasible states that is the same as would be found by employing the existing crisp option prioritization making the crisp option prioritization technique a special case of the fuzzy option prioritization methodology to demonstrate how this methodology can be employed to represent fuzzy preferences in real world decision problems fuzzy option prioritization is applied to an actual dispute over groundwater contamination that took place in elmira ontario canada

multiple testing for neuroimaging via hidden markov random field traditional voxel level multiple testing procedures in neuroimaging mostly p value based often ignore the spatial correlations among neighboring voxels and thus suffer from substantial loss of power we extend the local significance index based procedure originally developed for the hidden markov chain models which aims to minimize the false nondiscovery rate subject to a constraint on the false discovery rate to three dimensional neuroimaging data using a hidden markov random field model a generalized expectation maximization algorithm for maximizing the penalized likelihood is proposed for estimating the model parameters extensive simulations show that the proposed approach is more powerful than conventional false discovery rate procedures we apply the method to the comparison between mild cognitive impairment a disease status with increased risk of developing alzheimer s or another dementia and normal controls in the fdg pet imaging study of the alzheimer s disease neuroimaging initiative

stochastic blockmodels and community structure in networks stochastic blockmodels have been proposed as a tool for detecting community structure in networks as well as for generating synthetic networks for use as benchmarks most blockmodels however ignore variation in vertex degree making them unsuitable for applications to real world networks which typically display broad degree distributions that can significantly affect the results here we demonstrate how the generalization of blockmodels to incorporate this missing element leads to an improved objective function for community detection in complex networks we also propose a heuristic algorithm for community detection using this objective function or its non degree corrected counterpart and show that the degree corrected version dramatically outperforms the uncorrected one in both real world and synthetic networks

power enhanced multiple decision functions controlling family wise error and false discovery rates improved procedures in terms of smaller missed discovery rates mdr for performing multiple hypotheses testing with weak and strong control of the family wise error rate fwer or the false discovery rate fdr are developed and studied the improvement over existing procedures such as the sidak procedure for fwer control and the benjamini hochberg bh procedure for fdr control is achieved by exploiting possible differences in the powers of the individual tests results signal the need to take into account the powers of the individual tests and to have multiple hypotheses decision functions which are not limited to simply using the individual p values as is the case for example with the sidak bonferroni or bh procedures they also enhance understanding of the role of the powers of individual tests or more precisely the receiver operating characteristic roc functions of decision processes in the search for better multiple hypotheses testing procedures a decision theoretic framework is utilized and through auxiliary randomizers the procedures could be used with discrete or mixed type data or with rank based nonparametric tests this is in contrast to existing p value based procedures whose theoretical validity is contingent on each of these p value statistics being stochastically equal to or greater than a standard uniform variable under the null hypothesis proposed procedures are relevant in the analysis of high dimensional large m small n data sets arising in the natural physical medical economic and social sciences whose generation and creation is accelerated by advances in high throughput technology notably but not limited to microarray technology

simultaneous testing of grouped hypotheses finding needles in multiple haystacks in large scale multiple testing problems data are often collected from heterogeneous sources and hypotheses form into groups that exhibit different characteristics conventional approaches including the pooled and separate analyses fail to efficiently utilize the external grouping information we develop a compound decision theoretic framework for testing grouped hypotheses and introduce an oracle procedure that minimizes the false nondiscovery rate subject to a constraint on the false discovery rate it is shown that both the pooled and separate analyses can be uniformly improved by the oracle procedure we then propose a data driven procedure that is shown to be asymptotically optimal simulation studies show that our procedures enjoy superior performance and yield the most accurate results in comparison with both the pooled and separate procedures a real data example with grouped hypotheses is studied in detail using different methods both theoretical and numerical results demonstrate that exploit

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

weighted false discovery rate control in large scale multiple testing abstractthe use of weights provides an effective strategy to incorporate prior domain knowledge in large scale inference this article studies weighted multiple testing in a decision theoretical framework we develop oracle and data driven procedures that aim to maximize the expected number of true positives subject to a constraint on the weighted false discovery rate the asymptotic validity and optimality of the proposed methods are established the results demonstrate that incorporating informative domain knowledge enhances the interpretability of results and precision of inference simulation studies show that the proposed method controls the error rate at the nominal level and the gain in power over existing methods is substantial in many settings an application to a genome wide association study is discussed supplementary materials for this article are available online

determining the density of states for classical statistical models a random walk algorithm to produce a flat histogram we describe an efficient monte carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models the density of states is modified at each step when the energy level is visited to produce a flat histogram by carefully controlling the modification factor we allow the density of states to converge to the true value very quickly even for large systems from the density of states at the end of the random walk we can estimate thermodynamic quantities such as internal energy and specific heat capacity by calculating canonical averages at any temperature using this method we not only can avoid repeating simulations at multiple temperatures but we can also estimate the free energy and entropy quantities that are not directly accessible by conventional monte carlo simulations this algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability as with the multicanonical monte carlo technique our method overcomes the tunneling barrier between coexisting phases at first order phase transitions in this paper we apply our algorithm to both first and second order phase transitions to demonstrate its efficiency and accuracy we obtained direct simulational estimates for the density of states for two dimensional ten state potts models on lattices up to 200 x 200 and ising models on lattices up to 256 x 256 our simulational results are compared to both exact solutions and existing numerical data obtained using other methods applying this approach to a three dimensional j spin glass model we estimate the internal energy and entropy at zero temperature and using a two dimensional random walk in energy and order parameter space we obtain the rough canonical distribution and energy landscape in order parameter space preliminary data suggest that the glass transition temperature is about 1 2 and that better estimates can be obtained with more extensive application of the method this simulational method is not restricted to energy space and can be used to calculate the density of states for any parameter by a random walk in the corresponding space

modeling fuzzy and interval fuzzy preferences within a graph model framework a methodology is developed to model a decision maker s dm s fuzzy and or interval fuzzy preference over feasible scenarios or states within the framework of the graph model for conflict resolution this technique uses the dm s fuzzy relative importance of its preference statements and their fuzzy truth values for the feasible states in a conflict under uncertain conditions a preference statement of a dm is a preferable combination of dm s options or courses of action the fuzzy importance for one preference statement over another a value in the interval 0 1 is interpreted as the degree to which the first preference statement is more important than the second to the dm a fuzzy truth value of a preference statement at a feasible state is a number in the interval 0 1 that represents the degree to which the statement is true at the state when the dm is confident in its pairwise fuzzy importance degrees over the preference statements and their fuzzy truth values at the feasible states the methodology provides a fuzzy preference over the states when there is an ordinary or crisp importance ordering of preference statements and when the truth values of preference statements are classical or crisp at the feasible states the technique generates a crisp preference over the states the methodology is illustrated using a case study

hypothesis test for normal mixture models the em approach normal mixture distributions are arguably the most important mixture models and also the most technically challenging the likelihood function of the normal mixture model is unbounded based on a set of random samples unless an artificial bound is placed on its component variance parameter moreover the model is not strongly identifiable so it is hard to differentiate between over dispersion caused by the presence of a mixture and that caused by a large variance and it has infinite fisher information with respect to mixing proportions there has been extensive research on finite normal mixture models but much of it addresses merely consistency of the point estimation or useful practical procedures and many results require undesirable restrictions on the parameter space we show that an em test for homogeneity is effective at overcoming many challenges in the context of finite normal mixtures we find that the limiting distribution of the em test is a simple function of the 0 5 2 0 5 2 and 2 distributions when the mixing variances are equal but unknown and the 2 when variances are unequal and unknown simulations show that the limiting distributions approximate the finite sample distribution satisfactorily two genetic examples are used to illustrate the application of the em test

efficient monte carlo and greedy heuristic for the inference of stochastic block models we present an efficient algorithm for the inference of stochastic block models in large networks the algorithm can be used as an optimized markov chain monte carlo mcmc method with a fast mixing time and a much reduced susceptibility to getting trapped in metastable states or as a greedy agglomerative heuristic with an almost linear o nln2n complexity where n is the number of nodes in the network independent of the number of blocks being inferred we show that the heuristic is capable of delivering results which are indistinguishable from the more exact and numerically expensive mcmc method in many artificial and empirical networks despite being much faster the method is entirely unbiased towards any specific mixing pattern and in particular it does not favor assortative community structures

the effect of correlation in false discovery rate estimation the objective of this paper is to quantify the effect of correlation in false discovery rate analysis specifically we derive approximations for the mean variance distribution and quantiles of the standard false discovery rate estimator for arbitrarily correlated data this is achieved using a negative binomial model for the number of false discoveries where the parameters are found empirically from the data we show that correlation may increase the bias and variance of the estimator substantially with respect to the independent case and that in some cases such as an exchangeable correlation structure the estimator fails to be consistent as the number of tests becomes large

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications in this paper we extend our previous work on the stochastic block model a commonly used generative model for social and biological networks and the problem of inferring functional groups or communities from the topology of the network we use the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram we describe in detail properties of the detectability undetectability phase transition and the easy hard phase transition for the community detection problem our analysis translates naturally into a belief propagation algorithm for inferring the group memberships of the nodes in an optimal way i e that maximizes the overlap with the underlying group memberships and learning the underlying parameters of the block model finally we apply the algorithm to two examples of real world networks and discuss its performance

infinite degree corrected stochastic block model in stochastic block models which are among the most prominent statistical models for cluster analysis of complex networks clusters are defined as groups of nodes with statistically similar link probabilities within and between groups a recent extension by karrer and newman karrer and newman phys rev e 83 016107 2011 incorporates a node degree correction to model degree heterogeneity within each group although this demonstrably leads to better performance on several networks it is not obvious whether modeling node degree is always appropriate or necessary we formulate the degree corrected stochastic block model as a nonparametric bayesian model incorporating a parameter to control the amount of degree correction that can then be inferred from data additionally our formulation yields principled ways of inferring the number of groups as well as predicting missing links in the network that can be used to quantify the model s predictive performance on synthetic data we demonstrate that including the degree correction yields better performance on both recovering the true group structure and predicting missing links when degree heterogeneity is present whereas performance is on par for data with no degree heterogeneity within clusters on seven real networks with no ground truth group structure available we show that predictive performance is about equal whether or not degree correction is included however for some networks significantly fewer clusters are discovered when correcting for degree indicating that the data can be more compactly explained by clusters of heterogenous degree nodes

optimal detection of heterogeneous and heteroscedastic mixtures the problem of detecting heterogeneous and heteroscedastic gaussian mixtures is considered the focus is on how the parameters of heterogeneity heteroscedasticity and proportion of non null component influence the difficulty of the problem we establish an explicit detection boundary which separates the detectable region where the likelihood ratio test is shown to reliably detect the presence of non null effect from the undetectable region where no method can do so in particular the results show that the detection boundary changes dramatically when the proportion of nonnull component shifts from the sparse regime to the dense regime furthermore it is shown that the higher criticism test which does not require the specific information of model parameters is optimally adaptive to the unknown degrees of heterogeneity and heteroscedasticity in both the sparse and dense cases

multiple testing of composite null hypotheses in heteroscedastic models in large scale studies the true effect sizes often range continuously from zero to small to large and are observed with heteroscedastic errors in practical situations where the failure to reject small deviations from the null is inconsequential specifying an indifference region or forming composite null hypotheses can greatly reduce the number of unimportant discoveries in multiple testing the heteroscedasticity issue poses new challenges for multiple testing with composite nulls in particular the conventional framework in multiple testing which involves rescaling or standardization is likely to distort the scientific question we propose the concept of a composite null distribution for heteroscedastic models and develop an optimal testing procedure that minimizes the false nondiscovery rate subject to a constraint on the false discovery rate the proposed approach is different from conventional methods in that the effect size statistical significance and multiplicity issues are addressed in

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

a direct approach to sparse discriminant analysis in ultra high dimensions summary sparse discriminant methods based on independence rules such as the nearest shrunken centroids classifier tibshirani et al 2002 and features annealed independence rules fan fan 2008 have been proposed as computationally attractive tools for feature selection and classification with high dimensional data a fundamental drawback of these rules is that they ignore correlations among features and thus could produce misleading feature selection and inferior classification we propose a new procedure for sparse discriminant analysis motivated by the least squares formulation of linear discriminant analysis to demonstrate our proposal we study the numerical and theoretical properties of discriminant analysis constructed via lasso penalized least squares our theory shows that the method proposed can consistently identify the subset of discriminative features contributing to the bayes rule and at the same time consistently estimate the bayes classification direction even when the dimension can grow faster than any polynomial order of the sample size the theory allows for general dependence among features simulated and real data examples show that lassoed discriminant analysis compares favourably with other popular sparse discriminant proposals

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

hierarchical recognition of sparse patterns in large scale simultaneous inference summary we study how to accurately separate signals from noisy data and determine the patterns of the selected signals controlling the inflation of false positive errors is an important issue in largescale simultaneous inference but has not been addressed in the pattern recognition literature we develop a decision theoretic framework and formulate the sparse pattern recognition problem as a simultaneous inference problem with multiple decision trees oracle and adaptive classifiers are proposed for maximizing the expected number of true positives subject to a constraint on the overall false positive rate existing results on multiple testing are extended by allowing more than two states of nature hierarchical decision making and new error rate concepts

semi supervised novelty detection a common setting for novelty detection assumes that labeled examples from the nominal class are available but that labeled examples of novelties are unavailable the standard inductive approach is to declare novelties where the nominal density is low which reduces the problem to density level set estimation in this paper we consider the setting where an unlabeled and possibly contaminated sample is also available at learning time we argue that novelty detection in this semi supervised setting is naturally solved by a general reduction to a binary classification problem in particular a detector with a desired false positive rate can be achieved through a reduction to neyman pearson classification unlike the inductive approach semi supervised novelty detection ssnd yields detectors that are optimal e g statistically consistent regardless of the distribution on novelties therefore in novelty detection unlabeled data have a substantial impact on the theoretical properties of the decision rule we validate the practical utility of ssnd with an extensive experimental study we also show that ssnd provides distribution free learning theoretic solutions to two well known problems in hypothesis testing first our results provide a general solution to the general two sample problem that is the problem of determining whether two random samples arise from the same distribution second a specialization of ssnd coincides with the standard p value approach to multiple testing under the so called random effects model unlike standard rejection regions based on thresholded p values the general ssnd framework allows for adaptation to arbitrary alternative distributions in multiple dimensions

large deviations of connected components in the stochastic block model we study the stochastic block model which is often used to model community structures and study community detection algorithms we consider the case of two blocks in regard to its largest connected component and largest biconnected component respectively we are especially interested in the distributions of their sizes including the tails down to probabilities smaller than 10 ensuremath 800 for this purpose we use sophisticated markov chain monte carlo simulations to sample graphs from the stochastic block model ensemble we use these data to study the large deviation rate function and conjecture that the large deviation principle holds further we compare the distribution to the well known erd ifmmode mbox h o else h o fi s r enyi ensemble where we notice subtle differences at and above the percolation threshold

optimal screening and discovery of sparse signals with applications to multistage high throughput studies summary a common feature in large scale scientific studies is that signals are sparse and it is desirable to narrow down significantly the focus to a much smaller subset in a sequential manner we consider two related data screening problems one is to find the smallest subset such that it virtually contains all signals and another is to find the largest subset such that it essentially contains only signals these screening problems are closely connected to but distinct from the more conventional signal detection or multiple testing problems we develop phase transition diagrams to characterize the fundamental limits in simultaneous inference and derive data driven screening procedures which control the error rates with near optimality properties applications in the context of multistage high throughput studies are discussed

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

signal classification for the integrative analysis of multiple sequences of large scale multiple tests the integrative analysis of multiple data sets is becoming increasingly important in many fields of research when the same features are studied in several independent experiments it can often be useful to analyse jointly the multiple sequences of multiple tests that result it is frequently necessary to classify each feature into one of several categories depending on the null and non null configuration of its corresponding test statistics the paper studies this signal classification problem motivated by a range of applications in large scale genomics two new types of misclassification rate are introduced and two oracle procedures are developed to control each type while also achieving the largest expected number of correct classifications corresponding data driven procedures are also proposed proved to be asymptotically valid and optimal under certain conditions and shown in numerical experiments to be nearly as powerful as the oracle procedures in an application to psychiatric genetics the procedures proposed are used to discover genetic variants that may affect both bipolar disorder and schizophrenia as well as variants that may help to distinguish between these conditions

distribution of diameters for erdős renyi random graphs we study the distribution of diameters d of erd s renyi random graphs with average connectivity c the diameter d is the maximum among all the shortest distances between pairs of nodes in a graph and an important quantity for all dynamic processes taking place on graphs here we study the distribution p d numerically for various values of c in the nonpercolating and percolating regimes using large deviation techniques we are able to reach small probabilities like 10 100 which allow us to obtain the distribution over basically the full range of the support for graphs up to n 1000 nodes for values c 1 the distribution is more complex and no complete analytical results are available for this parameter range p d exhibits an inflection point which we found to be related to a structural change of the graphs for all values of c we determined the finite size rate function d n and were able to extrapolate numerically to n indicating that the large deviation principle holds

preference relations on a set of fuzzy utilities as a basis for decision making abstract in fuzzy decision problems we often encounter situations of choosing among alternatives which are assigned fuzzy utilities these problems have been approached using fuzzy implications or direct comparisons among fuzzy utilities in the literature however there are few attempts to investigate the issues addressing reasonable choice or reasonable ordering using fuzzy sets theory this paper first introduces some fundamental properties of fuzzy binary relations and certain conditions of reasonable orderings of fuzzy utilities then a method for constructing a fuzzy preference relation on a given set of fuzzy utilities is proposed for the sake of rational decision making this procedure employs the concepts of the extended minimum and the hamming distance between the greatest upper sets or the greatest lower sets of fuzzy utilities finally it is shown that the proposed fuzzy preference relations have reasonable properties as fuzzy orderings for decision making

fast algorithm to calculate density of states an algorithm to calculate the density of states based on the well known wang landau method is introduced independent random walks are performed in different restricted ranges of energy and the resultant density of states is modified by a function of time f t ensuremath propto t ensuremath 1 for large time as a consequence the calculated density of state g m e t approaches asymptotically the exact value g mathit ex e as ensuremath propto t ensuremath 1 2 avoiding the saturation of the error it is also shown that the growth of the interface of the energy histogram belongs to the random deposition universality class

new monte carlo algorithm entropic sampling we present a new monte carlo sampling algorithm with which one can obtain any desired distribution of the sampling in one monte carlo simulation the free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm the main idea is to sample directly the entropy of a system at infinite temperature importance sampling is shown to be a particular case of the new algorithm the algorithm is tested against the exact partition function of the ital l 4 simple cubic ising model a comparison with the multicanonical ensemble for the ital l 12 ital q 10 potts model shows that the new algorithm is more general and more efficient

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

entropy of stochastic blockmodel ensembles stochastic blockmodels are generative network models where the vertices are separated into discrete groups and the probability of an edge existing between two vertices is determined solely by their group membership in this paper we derive expressions for the entropy of stochastic blockmodel ensembles we consider several ensemble variants including the traditional model as well as the newly introduced degree corrected version karrer et al phys rev e 83 016107 2011 which imposes a degree sequence on the vertices in addition to the block structure the imposed degree sequence is implemented both as soft constraints where only the expected degrees are imposed and as hard constraints where they are required to be the same on all samples of the ensemble we also consider generalizations to multigraphs and directed graphs we illustrate one of many applications of this measure by directly deriving a log likelihood function from the entropy expression and using it to infer latent block structure in observed data due to the general nature of the ensembles considered the method works well for ensembles with intrinsic degree correlations i e with entropic origin as well as extrinsic degree correlations which go beyond the block structure

improved estimation of the noncentrality parameter distribution from a large number of t statistics with applications to false discovery rate estimation in microarray data analysis summary given a large number of t statistics we consider the problem of approximating the distribution of noncentrality parameters ncps by a continuous density this problem is closely related to the control of false discovery rates fdr in massive hypothesis testing applications e g microarray gene expression analysis our methodology is similar to but improves upon the existing approach by ruppert nettleton and hwang 2007 biometrics 63 483 495 we provide parametric nonparametric and semiparametric estimators for the distribution of ncps as well as estimates of the fdr and local fdr in the parametric situation we assume that the ncps follow a distribution that leads to an analytically available marginal distribution for the test statistics in the nonparametric situation we use convex combinations of basis density functions to estimate the density of the ncps a sequential quadratic programming procedure is developed to maximize the penalized likelihood the smoothing parameter is selected with the approximate network information criterion a semiparametric estimator is also developed to combine both parametric and nonparametric fits simulations show that under a variety of situations our density estimates are closer to the underlying truth and our fdr estimates are improved compared with alternative methods data based simulations and the analyses of two microarray datasets are used to evaluate the performance in realistic situations

oracle and adaptive compound decision rules for false discovery rate control we develop a compound decision theory framework for multiple testing problems and derive an oracle rule based on the z values that minimizes the false nondiscovery rate fnr subject to a constraint on the false discovery rate fdr we show that many commonly used multiple testing procedures which are p value based are inefficient and propose an adaptive procedure based on the z values the z value based adaptive procedure asymptotically attains the performance of the z value oracle procedure and is more efficient than the conventional p value based methods we investigate the numerical performance of the adaptive procedure using both simulated and real data in particular we demonstrate our method in an analysis of the microarray data from a human immunodeficiency virus study that involves testing a large number of hypotheses simultaneously

the optimal power puzzle scrutiny of the monotone likelihood ratio assumption in multiple testing summary in single hypothesis testing power is a nondecreasing function of type i error rate hence it is desirable to test at the nominal level exactly to achieve optimal power the optimal power puzzle arises from the fact that for multiple testing under the false discovery rate paradigm such a monotonic relationship may not hold in particular exact false discovery rate control may lead to a less powerful testing procedure if a test statistic fails to fulfil the monotone likelihood ratio condition in this article we identify different scenarios wherein the condition fails and give caveats for conducting multiple testing in practical settings we study an important assumption that has been used implicitly in the multiple testing literature in the context of false discovery rate analysis benjamini hochberg 1995 we show that the assumption can be violated in many important settings the goal of this article is to explicitly state the assumption to bridge the gap in conventional methodological development rigorously investigate the legitimacy of the assumption in various settings and give caveats for conducting multiple testing in practice to identify this assumption it is helpful to first examine closely the framework of single hypothesis testing suppose we want to test h0 versus h1 based on the observed value of a continuous random variable x a binary decision rule 0 1 divides the sample space s into two regions s s0 s1 such that 0 when x s0 and 1 when x s1 l ett be a function of x with small values indicating evidence against h0 the critical region s1 can be expressed as s1 x s t x t 1 g1 t respectively since t increasesint and t decreasesint weconcludethat t decreasesin t thereforetheoptimalchoice

extended likelihood approach to large scale multiple testing summary to date only frequentist bayesian and empirical bayes approaches have been studied for the large scale inference problem of testing simultaneously hundreds or thousands of hypotheses their derivations start with some summarizing statistics without modelling the basic responses as a consequence testing procedures have been developed without necessarily checking model assumptions and empirical null distributions are needed to avoid the problem of rejecting all null hypotheses when the sample sizes are large nevertheless these procedures may not be statistically efficient we present the multiple testing problem as a multiple prediction problem of whether a null hypothesis is true or not we introduce hierarchical random effect models for basic responses and show how the extended likelihood is built it is shown that the likelihood prediction has a certain oracle property the extended likelihood leads to new testing procedures which are optimal for the usual loss function in hypothesis testing the new tests are based on certain shrinkage t statistics and control the local probability of false discovery for individual tests to maintain the global frequentist false discovery rate and have no need to consider an empirical null distribution for the shrinkage t statistics conditions are given when these false rates vanish three examples illustrate how to use the likelihood method in practice a numerical study shows that the likelihood approach can greatly improve existing methods and finding the best fitting model is crucial for the behaviour of test procedures

large deviations of convex hulls of self avoiding random walks a global picture of a random particle movement is given by the convex hull of the visited points we obtained numerically the probability distributions of the volume and surface of the convex hulls of a selection of three types of self avoiding random walks namely the classical self avoiding walk the smart kinetic self avoiding walk and the loop erased random walk to obtain a comprehensive description of the measured random quantities we applied sophisticated large deviation techniques which allowed us to obtain the distributions over a large range of support down to probabilities far smaller than p 10 ensuremath 100 we give an approximate closed form of the so called large deviation rate function mathrm ensuremath phi which generalizes above the upper critical dimension to the previously studied case of the standard random walk further we show correlations between the two observables also in the limits of atypical large or small values

a rate optimal procedure for recovering sparse differences between high dimensional means under dependence the paper considers the problem of recovering the sparse different components between two high dimensional means of column wise dependent random vectors we show that dependence can be utilized to lower the identification boundary for signal recovery moreover an optimal convergence rate for the marginal false nondiscovery rate mfnr is established under dependence the convergence rate is faster than the optimal rate without dependence to recover the sparse signal bearing dimensions we propose a dependence assisted thresholding and excising date procedure which is shown to be rate optimal for the mfnr with the marginal false discovery rate mfdr controlled at a pre specified level extensions of the date to recover the differences in contrasts among multiple population means and differences between two covariance matrices are also provided simulation studies and case study are given to demonstrate the performance of the proposed signal identification procedure

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

covariate assisted ranking and screening for large scale two sample inference author s cai t tony sun wenguang wang weinan abstract two sample multiple testing has a wide range of applications the conventionalpractice first reduces the original observations to a vector of p values and then chooses a cutoffto adjust for multiplicity however this data reduction step could cause significant loss ofinformation and thus lead to suboptimal testing procedures we introduce a new framework fortwo sample multiple testing by incorporating a carefully constructed auxiliary variable in inferenceto improve the power a data driven multiple testing procedure is developed by employinga covariate assisted ranking and screening cars approach that optimally combines the informationfrom both the primary and the auxiliary variables the proposed cars procedureis shown to be asymptotically valid and optimal for false discovery rate control the procedureis implemented in the r package cars numerical results confirm the effectiveness of carsin false discovery rate control and show that it achieves substantial power gain over existingmethods cars is also illustrated through an application to the analysis of a satellite imagingdata set for supernova detection

sample size and power analysis for sparse signal recovery in genome wide association studies genome wide association studies have successfully identified hundreds of novel genetic variants associated with many complex human diseases however there is a lack of rigorous work on evaluating the statistical power for identifying these variants in this paper we consider sparse signal identification in genome wide association studies and present two analytical frameworks for detailed analysis of the statistical power for detecting and identifying the disease associated variants we present an explicit sample size formula for achieving a given false non discovery rate while controlling the false discovery rate based on an optimal procedure sparse genetic variant recovery is also considered and a boundary condition is established in terms of sparsity and signal strength for almost exact recovery of both disease associated variants and nondisease associated variants a data adaptive procedure is proposed to achieve this bound the analytical results are illustrated with a genome wide association study of neuroblastoma

semiparametric inference in mixture models with predictive recursion marginal likelihood predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models in semiparametric mixture models however the algorithm fails to account for any uncertainty in the additional unknown structural parameter as an alternative to existing profile likelihood methods we treat predictive recursion as a filter approximation to fitting a fully bayes model whereby an approximate marginal likelihood of the structural parameter emerges and can be used for inference we call this the predictive recursion marginal likelihood convergence properties of predictive recursion under model mis specification also lead to an attractive construction of this new procedure we show pointwise convergence of a normalized version of this marginal likelihood function simulations compare the performance of this new marginal likelihood approach that of existing profile likelihood methods as well as dirichlet process mixtures in density estimation mixed effects models and an empirical bayes multiple testing application in time series analysis are also considered

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

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

a smooth nonparametric estimate of a mixing distribution using mixtures of gaussians abstract we propose a method of estimating mixing distributions using maximum likelihood over the class of arbitrary mixtures of gaussians subject to the constraint that the component variances be greater than or equal to some minimum value h this approach can lead to estimates of many shapes with smoothness controlled by parameter h we show that the resulting estimate will always be a finite mixture of gaussians each having variance h the nonparametric maximum likelihood estimate can be viewed as a special case with h 0 the method can be extended to estimate multivariate mixing distributions examples and the results of a simulation study are presented

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

nonparametric weighted stochastic block models we present a bayesian formulation of weighted stochastic block models that can be used to infer the large scale modular structure of weighted networks including their hierarchical organization our method is nonparametric and thus does not require the prior knowledge of the number of groups or other dimensions of the model which are instead inferred from data we give a comprehensive treatment of different kinds of edge weights i e continuous or discrete signed or unsigned bounded or unbounded as well as arbitrary weight transformations and describe an unsupervised model selection approach to choose the best network description we illustrate the application of our method to a variety of empirical weighted networks such as global migrations voting patterns in congress and neural connections in the human brain

large scale multiple testing of correlations multiple testing of correlations arises in many applications including gene coexpression network analysis and brain connectivity analysis in this article we consider large scale simultaneous testing for correlations in both the one sample and two sample settings new multiple testing procedures are proposed and a bootstrap method is introduced for estimating the proportion of the nulls falsely rejected among all the true nulls we investigate the properties of the proposed procedures both theoretically and numerically it is shown that the procedures asymptotically control the overall false discovery rate and false discovery proportion at the nominal level simulation results show that the methods perform well numerically in terms of both the size and power of the test and it significantly outperforms two alternative methods the two sample procedure is also illustrated by an analysis of a prostate cancer dataset for the detection of changes in coexpression patterns between gene expression levels suppl

inferring the mesoscale structure of layered edge valued and time varying networks many network systems are composed of interdependent but distinct types of interactions which cannot be fully understood in isolation these different types of interactions are often represented as layers attributes on the edges or as a time dependence of the network structure although they are crucial for a more comprehensive scientific understanding these representations offer substantial challenges namely it is an open problem how to precisely characterize the large or mesoscale structure of network systems in relation to these additional aspects furthermore the direct incorporation of these features invariably increases the effective dimension of the network description and hence aggravates the problem of overfitting i e the use of overly complex characterizations that mistake purely random fluctuations for actual structure in this work we propose a robust and principled method to tackle these problems by constructing generative models of modular network structure incorporating layered attributed and time varying properties as well as a nonparametric bayesian methodology to infer the parameters from data and select the most appropriate model according to statistical evidence we show that the method is capable of revealing hidden structure in layered edge valued and time varying networks and that the most appropriate level of granularity with respect to the additional dimensions can be reliably identified we illustrate our approach on a variety of empirical systems including a social network of physicians the voting correlations of deputies in the brazilian national congress the global airport network and a proximity network of high school students

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

constructing confidence intervals for selected parameters in large scale problems it is common practice to select important parameters by a procedure such as the benjamini and hochberg procedure and construct confidence intervals cis for further investigation while the false coverage statement rate fcr for the cis is controlled at a desired level although the well known by cis control the fcr they are uniformly inflated in this paper we propose two methods to construct shorter selective cis the first method produces shorter cis by allowing a reduced number of selective cis the second method produces shorter cis by allowing a prefixed proportion of cis containing the values of uninteresting parameters we theoretically prove that the proposed cis are uniformly shorter than by cis and control the fcr asymptotically for independent data numerical results confirm our theoretical results and show that the proposed cis still work for correlated data we illustrate the advantage of the proposed procedures by analyzing the microarray data from a hiv study

nonparametric bayesian inference of the microcanonical stochastic block model a principled approach to characterize the hidden structure of networks is to formulate generative models and then infer their parameters from data when the desired structure is composed of modules or communities a suitable choice for this task is the stochastic block model sbm where nodes are divided into groups and the placement of edges is conditioned on the group memberships here we present a nonparametric bayesian method to infer the modular structure of empirical networks including the number of modules and their hierarchical organization we focus on a microcanonical variant of the sbm where the structure is imposed via hard constraints i e the generated networks are not allowed to violate the patterns imposed by the model we show how this simple model variation allows simultaneously for two important improvements over more traditional inference approaches 1 deeper bayesian hierarchies with noninformative priors replaced by sequences of priors and hyperpriors which not only remove limitations that seriously degrade the inference on large networks but also reveal structures at multiple scales 2 a very efficient inference algorithm that scales well not only for networks with a large number of nodes and edges but also with an unlimited number of modules we show also how this approach can be used to sample modular hierarchies from the posterior distribution as well as to perform model selection we discuss and analyze the differences between sampling from the posterior and simply finding the single parameter estimate that maximizes it furthermore we expose a direct equivalence between our microcanonical approach and alternative derivations based on the canonical sbm

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

integrating multiplicative preference relations in a multipurpose decision making model based on fuzzy preference relations the aim of this paper is to study the integration of multiplicative preference relation as a preference representation structure in fuzzy multipurpose decision makingproblems assumingfuzzy multipurpose decision makingproblems under di4erent preference representation structures ordering utilities and fuzzy preference relations and using the fuzzy preference relations as uniform representation elements the multiplicative preference relations are incorporated in the decision problem by means of a transformation function between multiplicative and fuzzy preference relations a consistency study of this transformation function which demonstrates that it does not change the informative content of multiplicative preference relation is shown as a consequence a selection process based on fuzzy majority for multipurpose decision makingproblems under multiplicative preference relations is presented to design it an aggregation operator of information called ordered weighted geometric operator is introduced and two choice degrees the quanti7er guided dominance degree and the quanti7er guided non dominance degree are de7ned for multiplicative preference relations c 2001 elsevier science b v all rights reserved