estimating the proportion of true null hypotheses with application to dna microarray data summary we consider the problem of estimating the proportion of true null hypotheses 0 i n a multiple hypothesis set up the tests are based on observed p values we first review published estimators based on the estimator that was suggested by schweder and spjotvoll then we derive new estimators based on nonparametric maximum likelihood estimation of the p value density restricting to decreasing and convex decreasing densities the estimators of 0 are all derived under the assumption of independent test statistics their performance under dependence is investigated in a simulation study we find that the estimators are relatively robust with respect to the assumption of independence and work well also for test statistics with moderate dependence

modularity of simple termination of term rewriting systems with shared constructors abstract kurihara m and a ohuchi modularity of simple termination of term rewriting systems with shared constructors theoretical computer science 103 1992 273 282 a term rewriting system is simply terminating if there exists a simplification ordering showing its termination let r and r be term rewriting systems which share no defined symbol but may share constructors constructors are function symbols which do not occur at the leftmost position in left hand sides of rewrite rules the rest of the function symbols are defined symbols in this paper we prove that r u r is simply terminating if and only if both r and r are so 1 introduction a property p of term rewriting systems trss 4 6 is modular if r u r has the property p if and only if both r0 and r have that property starting with toyama 141 several authors studied modular aspects of trss under the disjointness condition which requires that

modularity in term rewriting revisited we revisit modularity in term rewriting which for the last 25 years has been a very active and fruitful research field starting with the pioneering works of yoshihito toyama on the modularity of confluence and the non modularity of termination he thus initiated an extremely productive line of research with many non trivial and deep results striking counterexamples and a substantial amount of systematic theoretical foundations methodological principles and novel proof techniques in this focused summary we will revisit the modularity analysis for ordinary term rewriting systems considering various confluence and termination properties and restricting ourselves mainly to the case of disjoint unions we will summarize known results on the non modularity of various confluence and termination properties and exhibit crucial ideas constructions and phenomena later on we will also briefly consider various extensions applications related questions and open problems as well as recent developments

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

size power and false discovery rates modern scientific technology has provided a new class of large scale simultaneous inference problems with thousands of hypothesis tests to consider at the same time microarrays epitomize this type of technology but similar situations arise in proteomics spectroscopy imaging and social science surveys this paper uses false discovery rate methods to carry out both size and power calculations on large scale problems a simple empirical bayes approach allows the false discovery rate fdr analysis to proceed with a minimum of frequentist or bayesian modeling assumptions closed form accuracy formulas are derived for estimated false discovery rates and used to compare different methodologies local or tail area fdr s theoretical permutation or empirical null hypothesis estimates two microarray data sets as well as simulations are used to evaluate the methodology the power diagnostics showing why nonnull cases might easily fail to appear on a list of significant discoveries

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

optimal multiple testing under a gaussian prior on the effect sizes we develop a new method for large scale frequentist multiple testing with bayesian prior information we find optimal formula see text value weights that maximize the average power of the weighted bonferroni method due to the nonconvexity of the optimization problem previous methods that account for uncertain prior information are suitable for only a small number of tests for a gaussian prior on the effect sizes we give an efficient algorithm that is guaranteed to find the optimal weights nearly exactly our method can discover new loci in genome wide association studies and compares favourably to competitors an open source implementation is available

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

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

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

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

semiunitary precoding for spatially correlated mimo channels the focus of this paper is on spatial precoding in correlated multiantenna channels where the number of data streams is adapted independent of the number of transmit antennas towards the goal of a low complexity implementation a statistical semiunitary precoder is studied where the precoder matrix evolves fairly slowly with respect to the channel evolution while prior work on statistical precoding has focussed on information theoretic limits most of these computations result in complicated functional dependencies of the mutual information with the channel statistics that do not explicitly reveal the impact of statistics on performance in contrast estimates that are directly in terms of the channel statistics are obtained here for the relative mutual information loss of a semiunitary precoder with respect to a perfect channel information benchmark based on these estimates matching metrics are developed that capture the degree of matching of a channel to the precoder structure continuously and allow ordering two matrix channels in terms of their mutual information performance while these metrics are based on bounds numerical studies are used to show that the proposed metrics capture the performance tradeoffs accurately the main conclusion of this work is a simple to state fundamental principle in the context of signaling design for single user mimo systems the best channel for the statistical precoder is the channel that is matched to it

inverse source problem in an oblate spheroidal geometry the canonical inverse source problem of reconstructing an unknown source whose region of support is describable as a spheroidal oblate or prolate volume from knowledge of the far field radiation pattern it generates is formulated and solved within the framework of the inhomogeneous scalar helmholtz equation via a linear inversion framework in hilbert spaces particular attention is paid to the analysis and computer illustration of flat aperture like sources whose support is approximated by an oblate spheroidal volume

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

comments on fast direct solution of method of moments linear system in the above named work a new algorithm is presented for direct non iterative frequency domain method of moments mom calculations based on block wise compression of the impedance matrix the storage requirements and computational complexity of the algorithm are claimed to be n3 2 and n2 respectively if n is the number of unknowns for a mom surface discretization that is fixed with respect to the wavelength a more rigorous analysis explicitly using the asymptotic expression for the number of degrees of freedom dof in the interaction between groups of scatterers is presented here showing that this should be n3 2log n and n2log2 n respectively the complexity analysis applies to problems that can be formulated as a surface integral equation sie on surfaces in or between homogeneous media such as a ship or an airplane it does not apply to volume discretization mom or multilayer problems the results presented here are also relevant for block wise compression methods using iterative solvers since the compressed impedance matrix is the same consequently the above complexity analysis applies to very large problems well beyond the reach of even the largest existent computers for moderate size problems the measured complexity is lower

a bayesian discovery procedure we discuss a bayesian discovery procedure for multiple comparison problems we show that under a coherent decision theoretic framework a loss function combining true positive and false positive counts leads to a decision rule based on a threshold of the posterior probability of the alternative under a semi parametric model for the data we show that the bayes rule can be approximated by the optimal discovery procedure odp recently introduced by storey 2007a improving the approximation leads us to a bayesian discovery procedure bdp which exploits the multiple shrinkage in clusters implied by the assumed nonparametric model we compare the bdp and the odp estimates in a simple simulation study and in an assessment of differential gene expression based on microarray data from tumor samples we extend the setting of the odp by discussing modifications of the loss function that lead to different single thresholding statistics finally we provide an application of the previous arguments to dependent spatial data

influence of environment richness on the increase of mimo capacity with number of antennas we study the capacity of mimo systems with uniform linear arrays in complex media as the number of antennas increases the distance between adjacent antennas is kept constant the transfer matrix describing the channel is expressed in terms of the antennas and the physical characteristics of the environment using direct scattering theory we prove that the capacity increases logarithmically when the number of antennas in the system belongs to a large interval of intermediate values we then take the case where the number of antennas is large and we study the effects on the capacity of adding a new scatterer using a city model with buildings of different sizes randomly distributed in space we show numerically that initially the capacity increases at a nearly linear rate as the number of antennas increases after a certain threshold the capacity growth becomes logarithmic we show that the number of antennas where this transition occurs increases as the number of buildings increases

on the modularity of termination of term rewriting systems it is well known that termination is not a modular property of term rewriting systems i e it is not preserved under disjoint union the objective of this paper is to provide a uniform framework for sufficient conditions which ensure the modularity of termination we will prove the following result whenever the disjoint union of two terminating term rewriting systems is nonterminating then one of the systems is not ce terminating i e it loses its termination property when extended with the rules cons x y x and cons x y y and the other is collapsing this result has already been achieved by gramlich 7 for finitely branching term rewriting systems a more sophisticated approach is necessary however to prove it in full generality most of the known sufficient criteria for the preservation of termination 24 15 13 7 follow as corollaries from our result and new criteria are derived this paper particularly settles the open question whether simple termination is modular in general we will moreover shed some light on modular properties of combined systems with shared constructors for instance it will be shown that the above result does not carry over to constructor sharing systems

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

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

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

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

on optimality of stepdown and stepup multiple test procedures consider the multiple testing problem of testing k null hypotheses where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption attention is restricted to procedures that control the familywise error rate in the strong sense and which satisfy a monotonicity condition under these assumptions we prove certain maximin optimality results for some well known stepdown and stepup procedures

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

fast direct solution of method of moments linear system a novel algorithm the compressed block decomposition cbd is presented for highly accelerated direct noniterative method of moments mom solution of electromagnetic scattering and radiation problems the algorithm is based on a block wise subdivision of the mom impedance matrix impedance matrix subblocks corresponding to distant subregions of the problem geometry are not calculated directly but approximated in a compressed form subsequently the matrix is decomposed preserving the compression examples are presented of typical problems in the range of 5000 to 70000 unknowns the total execution time for the largest problem is about 1 h and 20 min for a single excitation vector the main strength of the method is for problems with multiple excitation vectors monostatic rcs computations due to the negligible extra cost for each new excitation for radiation and scattering problems in free space the numerical complexity of the algorithm is shown to be n 2 and the storage requirements scale with n 3 2

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

modularity in noncopying term rewriting it is known that termination and completeness are not modular properties of term rewriting systems the disjoint union of terminating complete term rewriting systems need not be terminating complete in this paper we introduce a class of noncopying term rewriting systems as a new term based formalism for a kind of graph rewriting systems and prove that this class enjoys the modularity of termination and of completeness actually our results are stronger in the sense that the disjointness condition is relaxed for allowing the systems to share constructors and some defined symbols while preserving the main results

capacity scaling of wireless ad hoc networks shannon meets maxwell in this paper we characterize the information theoretic capacity scaling of wireless ad hoc networks with randomly distributed nodes by using an exact channel model from maxwell s equations we successfully resolve the conflict in the literature between the linear capacity scaling by ozgur and the degrees of freedom limit given as the ratio of the network diameter and the wavelength by franceschetti in dense networks where the network area is fixed the capacity scaling is given as the minimum of and the degrees of freedom limit to within an arbitrarily small exponent in extended networks where the network area is linear in the capacity scaling is given as the minimum of and the degrees of freedom limit to within an arbitrarily small exponent hence we recover the linear capacity scaling by ozgur if in dense networks and if in extended networks otherwise the capacity scaling is given as the degrees of freedom limit characterized by franceschetti for achievability a modified hierarchical cooperation is proposed based on a lower bound on the capacity of multiple input multiple output channel between two node clusters using our channel model

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

degrees of freedom of a communication channel using dof singular values a fundamental problem in any communication system is given a communication channel between a transmitter and a receiver how many independent signals can be exchanged between them arbitrary communication channels that can be described by linear compact channel operators mapping between normed spaces are examined in this paper the well known notions of degrees of freedom dof at level and essential dimension of such channels are developed in this general setting we argue that the dof at level and the essential dimension fundamentally limit the number of independent signals that can be exchanged between the transmitter and the receiver we also generalize the concept of singular values of compact operators to be applicable to compact operators defined on arbitrary normed spaces which do not necessarily carry a hilbert space structure we show how these generalized singular values which we call dof singular values can be used to calculate the dof at level and the essential dimension of compact operators that describe communication channels we describe physically realistic channels that require such general channel models

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

spatio temporal coding for wireless communication multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels this paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed a compact model is developed for the multiple input multiple output mimo dispersive spatially selective wireless communication channel the multivariate information capacity is analyzed for high signal to noise ratio snr conditions the mimo channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components the number of input antennas or the number of output antennas this desirable result is contrasted with the lower capacity slope of the well studied case with multiple antennas at only one side of the radio link a spatio temporal vector coding stvc communication structure is suggested as a means for achieving mimo channel capacity the complexity of stvc motivates a more practical reduced complexity discrete matrix multitone dmmt space frequency coding approach both of these structures are shown to be asymptotically optimum an adaptive lattice trellis coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the dmmt channel experimental examples that support the theoretical results are presented

discrete sequential boundaries for clinical trials summary pocock 1977 o brien fleming 1979 and slud wei 1982 have proposed different methods to construct discrete sequential boundaries for clinical trials these methods require that the total number of decision times be specified in advance in the present paper we propose a more flexible way to construct discrete sequential boundaries the method is based on the choice of a function a t which characterizes the rate at which the error level ac is spent the boundary at a decision time is determined by a t and by past and current decision times but does not depend on the future decision times or the total number of decision times

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

on the church rosser property for the direct sum of term rewriting systems the direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols it is shown that if two term rewriting systems both have the chruch rosser property then the direct sum of these systems also has this property

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

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

signal recovery with cost constrained measurements we are concerned with the problem of optimally measuring an accessible signal under a total cost constraint in order to estimate a signal which is not directly accessible an important aspect of our formulation is the inclusion of a measurement device model where each device has a cost depending on the number of amplitude levels that the device can reliably distinguish we also assume that there is a cost budget so that it is not possible to make a high amplitude resolution measurement at every point we investigate the optimal allocation of cost budget to the measurement devices so as to minimize estimation error this problem differs from standard estimation problems in that we are allowed to design the number and noise levels of the measurement devices subject to the cost constraint our main results are presented in the form of tradeoff curves between the estimation error and the cost budget although our primary motivation and numerical examples come from wave propagation problems our formulation is also valid for other measurement problems with similar budget limitations where the observed variables are related to the unknown variables through a linear relation we discuss the effects of signal to noise ratio distance of propagation and the degree of coherence correlation of the waves on these tradeoffs and the optimum cost allocation our conclusions not only yield practical strategies for designing optimal measurement systems under cost constraints but also provide insights into measurement aspects of certain inverse problems

statistical discoveries and effect size estimation abstract current methods of statistical inference are correct but incomplete small probability of wrong null hypothesis rejections can be misunderstood definitive rejections of null hypotheses as well as interval assessments of effect sizes are impossible in single cases with significance probabilities like 05 sufficiently large sets of independent experiments and attained significance levels p values should be registered from such data it is possible to calculate least upper bounds for proportions of fallacies in sets of null hypothesis rejections or effect size assessments a provisional rejection of a null hypothesis in a one tailed test or a one sided confidence interval showing a nonzero effect is here called a discovery consider a large number n of independent experiments with r discoveries for r rejections of null hypotheses the proportion of fallacies q has least upper bound q max n r 1 1 1 for r confidence intervals the proportion of fallacies is e n r assumi

degrees of freedom region of the mimo x channel we provide achievability as well as converse results for the degrees of freedom region of a multiple input multiple output mimo x channel i e a system with two transmitters two receivers each equipped with multiple antennas where independent messages need to be conveyed over fixed channels from each transmitter to each receiver the inner and outer bounds on the degrees of freedom region are tight whenever integer degrees of freedom are optimal for each message with m 1 antennas at each node we find that the total sum rate degrees of freedom are bounded above and below as 1 les eta x les 4 3 if m 1 and channel matrices are nondegenerate then the precise degrees of freedom eta x 4 3 m thus the mimo x channel has noninteger degrees of freedom when m is not a multiple of 3 simple zero forcing without dirty paper encoding or successive decoding suffices to achieve the 4 3 m degrees of freedom if the channels vary with time frequency then the channel with single antennas m 1 at all nodes has exactly 4 3 degrees of freedom the key idea for the achievability of the degrees of freedom is interference alignment i e signal spaces are aligned at receivers where they constitute interference while they are separable at receivers where they are desired we also explore the increase in degrees of freedom when some of the messages are made available to a transmitter or receiver in the manner of cognitive radio

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

field dimensions and polarization gains in electromagnetic systems the dimensions of electromagnetic fields on linear planar and volumetric observation manifolds are studied by rigorously deriving and counting all the significant modes to linearly represent the fields with great accuracy the fields are received with either full scattering or azimuthal scattering only both the uni polarized scalar wave case and the fully polarized vector wave case are investigated the ratio of the field dimensions between the two cases gives rise to what is usually called the polarization gain in the literature by tackling the problem from a purely electromagnetics perspective this work offers an alternative approach of assessing the mimo degrees of freedom limit in addition to a heuristic approach utilized by a recent study involving almost no approximation during the analysis the results here bring improvement in terms of rigor and accuracy over those from the heuristic approach additionally by using some numerical examples this paper also explains how the field dimensions and the polarization gains should be properly interpreted in the context of realistic mimo applications

electromagnetic degrees of freedom in 2 d scattering environments the electromagnetic em degrees of freedom dof of a noise limited system in two dimensions with random multiple scattering is evaluated numerically following a rigorous dof theory first developed by miller and piestun for optical systems the received em fields are efficiently calculated by fast multipole method fmm and the ensemble average of the dof number is obtained through monte carlo simulation technique the results show that the average em dof number is strongly dependent on the sizes of the transmit volume the receive volume and the scattering region in particular the average number of dof generally increases with both the transmit and receive volumes however this increase is a non linear process and will not continue indefinitely as the transmit volume or the receive volume expands an upper bound of the average dof number is expected due to noise effects due to the lack of criteria for choosing a critical parameter involved in miller and piestun s original dof definition a modified definition is also considered even though the modified definition is snr dependent it provides a clearer physical meaning of the dof in addition the simulations also suggest that it might not be appropriate to ignore the influence of the snr on the dof number when the system concerned is of general form and relative small where no critical point of the channel quality can be identified a logarithmic dependence of the dof number on the total source power is demonstrated for such systems

on sampling and coding for distributed acoustic sensing the issue of how to efficiently represent the data collected by a network of microphones recording spatio temporal acoustic wave fields is addressed each sensor node in the network samples the sound field quantizes the samples and transmits the encoded samples to some central unit which computes an estimate of the original sound field based on the information received from all the microphones our analysis is based on the spectral properties of the sound field which are induced by the physics of wave propagation and have a significant impact on the efficiency of the chosen sampling lattice and coding scheme as field acquisition by a sensor network typically implies spatio temporal sampling of the field a multidimensional sampling theorem for homogeneous random fields with compactly supported spectral measures is proved to assess the loss of information implied by source coding rate distortion functions for various coding schemes and sampling lattices are determined in particular centralized coding independent coding and some multiterminal schemes are compared under the assumption of spectral whiteness of the sound field it is shown that sampling with a quincunx lattice followed by independent coding is optimal as it achieves the lower bound given by centralized coding

the optimal discovery procedure a new approach to simultaneous significance testing summary the neyman pearson lemma provides a simple procedure for optimally testing a single hypothesis when the null and alternative distributions are known this result has played a major role in the development of significance testing strategies that are used in practice most of the work extending single testing strategies to multiple tests has focused on formulating and estimating new types of significance measures such as the false discovery rate these methods tend to be based on p values that are calculated from each test individually ignoring information from the other tests i show here that one can improve the overall performance of multiple significance tests by borrowing information across all the tests when assessing the relative significance of each one rather than calculating p values for each test individually the optimal discovery procedure is introduced which shows how to maximize the number of expected true positive results for each fixed number of expected false positive results the optimality that is achieved by this procedure is shown to be closely related to optimality in terms of the false discovery rate the optimal discovery procedure motivates a new approach to testing multiple hypotheses especially when the tests are related as a simple example a new simultaneous procedure for testing several normal means is defined this is surprisingly demonstrated to outperform the optimal single test procedure showing that a method which is optimal for single tests may no longer be optimal for multiple tests connections to other concepts in statistics are discussed including stein s paradox shrinkage estimation and the bayesian approach to hypothesis testing

generalizing simes test and hochberg s stepup procedure in a multiple testing problem where one is willing to tolerate a few false rejections procedure controlling the familywise error rate fwer can potentially be improved in terms of its ability to detect false null hypotheses by generalizing it to control the k fwer the probability of falsely rejecting at least k null hypotheses for some fixed k 1 simes test for testing the intersection null hypothesis is generalized to control the k fwer weakly that is under the intersection null hypothesis and hochberg s stepup procedure for simultaneous testing of the individual null hypotheses is generalized to control the k fwer strongly that is under any configuration of the true and false null hypotheses the proposed generalizations are developed utilizing joint null distributions of the k dimensional subsets of the p values assumed to be identical the generalized simes test is proved to control the k fwer weakly under the multivariate totally positive of order two mtp 2 condition j multivariate analysis 10 1980 467 498 of the joint null distribution of the p values by generalizing the original simes inequality it is more powerful to detect k or more false null hypotheses than the original simes test when the p values are independent a stepdown procedure strongly controlling the k fwer a version of generalized holm s procedure that is different from and more powerful than ann statist 33 2005 1138 1154 with independent p values is derived before proposing the generalized hochberg s procedure the strong control of the k fwer for the generalized hochberg s procedure is established in situations where the generalized simes test is known to control its k fwer weakly

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

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

a double angular propagation model with cluster scattering a statistical multipath propagation model is developed in the double angular domain to include effects of both angle of departure and angle of arrival the model is characterized by a discrete stochastic double angular spectrum of the green s function between two volumes that communicate with each other in the presence of cluster scattering the whole modeling process is a combination of theories assumptions and numerical verification by rigorous full wave electromagnetic simulations notably an uncorrelated scattering assumption for received fields is extended to the double angular domain and the transport theory plays a key role defining the statistical properties of the spectrum of the green s function the spectrum is eventually modeled as a random matrix whose entries are uncorrelated zero mean complex laplacian random variables the real and imaginary parts of the matrix entries are independent and identically distributed and the variance profile follows the reduced incident intensity of the waves through random media the parameters of the model are completely obtained from bulk statistical knowledge of the scattering environments and the resulting model demonstrates good performance on em dof and mimo capacity estimation

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

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

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

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

on electromagnetics and information theory some connections are described between electromagnetic theory and information theory identifying some unavoidable limitations imposed by the laws of electromagnetism to communication systems starting from this result the role of the degrees of freedom of the field in radiating systems is investigated different classes of antennas use the available degrees of freedom in different ways in particular a multiple input multiple output antenna is a radiating system conveying statistically independent information on more than one degree of freedom of the field applications of the theory to antenna synthesis and antenna characterization in complex environments are shown

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

degrees of freedom in multiple antenna channels a signal space approach multiple antenna systems that are limited by the area and geometry of antenna arrays are considered given these physical constraints the limit on the available number of spatial degrees of freedom is derived the commonly used statistical multiple input multiple output mimo model is inadequate antenna theory is applied to take into account the area and geometry constraints and to define the spatial signal space so as to interpret experimental channel measurements in an array independent but manageable description of the physical environment based on these modeling strategies for a spherical array of effective aperture a in a physical environment of angular spread spl omega in solid angle the number of spatial degrees of freedom is shown to be a spl omega for uni polarized antennas and 2a spl omega for tri polarized antennas together with the 2wt degrees of freedom for a system of bandwidth w transmitting in an interval t the total degrees of freedom of a multiple antenna channel is therefore 4wta spl omega

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

capacity scaling and spectral efficiency in wide band correlated mimo channels the dramatic linear increase in ergodic capacity with the number of antennas promised by multiple input multiple output mimo wireless communication systems is based on idealized channel models representing a rich scattering environment is such scaling sustainable in realistic scattering scenarios existing physical models although realistic are intractable for addressing this problem analytically due to their complicated nonlinear dependence on propagation path parameters such as the angles of arrival and delays in this paper we leverage a recently introduced virtual representation of physical models that is essentially a fourier series representation of wide band mimo channels in terms of fixed virtual angles and delays motivated by physical considerations we propose a d connected model for correlated channels defined by a virtual spatial channel matrix consisting of d nonvanishing diagonals with independent and identically distributed i i d gaussian entries the parameter d provides a meaningful and tractable measure of the richness of scattering we derive general bounds for the coherent ergodic capacity and investigate capacity scaling with the number of antennas and bandwidth in the large antenna regime we show that linear capacity scaling is possible if d scales linearly with the number of antennas this in turn is possible if the number of resolvable paths grows quadratically with the number of antennas the capacity saturates for linear growth in the number of paths fixed d the ergodic capacity does not depend on frequency selectivity of the channel in the wide band case increasing bandwidth tightens the bounds and hastens the convergence of scaling behavior for large bandwidth the capacity scales linearly with the signal to noise ratio snr as well we also provide an explicit characterization of the wide band slope recently proposed by verdu numerical results are presented to illustrate the key theoretical results

optimal sample size for multiple testing the case of gene expression microarrays we consider the choice of an optimal sample size for multiple comparison problems the motivating application is the choice of the number of microarray experiments to be carried out when learning about differential gene expression however the approach is valid in any application that involves multiple comparisons in a large number of hypothesis tests we discuss two decision problems in the context of this setup the sample size selection and the decision about the multiple comparisons we adopt a decision theoretic approach using loss functions that combine the competing goals of discovering as many differentially expressed genes as possible while keeping the number of false discoveries manageable for consistency we use the same loss function for both decisions the decision rule that emerges for the multiple comparison problem takes the exact form of the rules proposed in the recent literature to control the posterior expected falsediscovery rate for the sample size selection we combine the expe

quadratic variational framework for signal design on the 2 sphere this paper introduces a quadratic variational framework for solving a broad class of signal design problems on the 2 sphere the functional to be extremized combines energy concentration measures using a weighting function in the spatial domain multiplicative weights in the spectral domain and a total energy constraint this leads to two formulations of the signal design problem on the 2 sphere one a fredholm integral equation in the spatial domain and the other an infinite matrix equation in the spectral domain the framework is illustrated by deriving the key equations for the two classical spatio spectral concentration problems on the 2 sphere and for an isotropic filter design that maximizes the filtered energy in addition using the proposed framework we formulate a joint 3 d beamforming application which achieves optimal directivity and spatial resolution simultaneously

minimum rate sampling and reconstruction of signals with arbitrary frequency support we examine the question of reconstruction of signals from periodic nonuniform samples this involves discarding samples from a uniformly sampled signal in some periodic fashion we give a characterization of the signals that can be reconstructed at exactly the minimum rate once a nonuniform sampling pattern has been fixed we give an implicit characterization of the reconstruction system and a design method by which the ideal reconstruction filters may be approximated we demonstrate that for certain spectral supports the minimum rate can be approached or achieved using reconstruction schemes of much lower complexity than those arrived at by using spectral slicing as in earlier work previous work on multiband signals have typically been those for which restrictive assumptions on the sizes and positions of the bands have been made or where the minimum rate was approached asymptotically we show that the class of multiband signals which can be reconstructed exactly is shown to be far larger than previously considered when approaching the minimum rate this freedom allows us in certain cases to have a far less complex reconstruction system

impact of scattering on the capacity diversity and propagation range of multiple antenna channels the impact of scattering condition and array configuration on performances are inseparable in early analyses of multiple antenna systems an array independent scattering model is introduced where three basic scattering mechanisms are modeled performance results become more intrinsic property of the scattering channel itself for linear arrays of length l in an environment of total angle spread omega the ergodic capacity is shown to increase linearly with l omega for large arrays when antenna arrays reduce to practical sizes the capacity scaling depends on the signal to noise ratio snr as well this implies that the number of antennas used should also depend on the snr in terms of outage capacity the tradeoff between spatial multiplexing gain and diversity gain is shown to be very sensitive to the underlying scattering mechanisms finally as omega varies with the propagation range the tradeoff among multiplexing gain diversity gain and propagation range is studied

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

why does the kronecker model result in misleading capacity estimates many recent works that study the performance of multiple input multiple output mimo systems in practice assume a kronecker model where the variances of the channel entries upon decomposition on to the transmit and the receive eigenbases admit a separable form measurement campaigns however show that the kronecker model results in poor estimates for capacity motivated by these observations a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better in this paper we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates the transmit and or the receive eigenbases using tools from random matrix theory we then establish the theoretical basis behind the kronecker mismatch at the low and the high snr extremes 1 sparsity of the dominant statistical degrees of freedom dof in the true channel at the low snr extreme and 2 nonregularity of the sparsity structure disparities in the distribution of the dof across the rows and the columns at the high snr extreme

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

sublinear capacity scaling laws for sparse mimo channels recent attention on performance analysis of single user multiple input multiple output mimo systems has been on understanding the impact of the spatial correlation model on ergodic capacity in most of these works it is assumed that the statistical degrees of freedom dof in the channel can be captured by decomposing it along a suitable eigenbasis and that the transmitter has perfect knowledge of the statistical dof with an increased interest in large antenna systems in state of the art technologies these implicit channel modeling assumptions in the literature have to be revisited in particular multiantenna measurements have showed that large antenna systems are sparse where only a few dof are dominant enough to contribute towards capacity thus in this work it is assumed that the transmitter can only afford to learn the dominant statistical dof in the channel the focus is on understanding ergodic capacity scaling laws in sparse channels unlike classical results where linear capacity scaling is implicit sparsity of mimo channels coupled with a knowledge of only the dominant dof is shown to result in a new paradigm of sublinear capacity scaling that is consistent with experimental results and physical arguments it is also shown that uniform power signaling over all the antenna dimensions is wasteful and could result in a significant penalty over optimally adapting the antenna spacings in response to the sparsity level of the channel and transmit snr

intrinsic limits of dimensionality and richness in random multipath fields we study the dimensions or degrees of freedom of farfield multipath that is observed in a limited source free region of space the multipath fields are studied as solutions to the wave equation in an infinite dimensional vector space we prove two universal upper bounds on the truncation error of fixed and random multipath fields a direct consequence of the derived bounds is that both fixed and random multipath fields have an effective finite dimension for circular and spherical spatial regions we show that this finite dimension is proportional to the radius and area of the region respectively we use the karhunen loegraveve kl expansion of random multipath fields to quantify the notion of multipath richness the multipath richness is defined as the number of significant eigenvalues in the kl expansion that achieve 99 of the total multipath energy we establish a lower bound on the largest eigenvalue this lower bound quantifies to some extent the well known reduction of multipath richness with reducing the angular power spread of multipath angular power spectrum

on landau s eigenvalue theorem and information cut sets a variation of landau s eigenvalue theorem describing the phase transition of the eigenvalues of a time frequency limiting self adjoint operator is presented the total number of degrees of freedom of square integrable multidimensional bandlimited functions is defined in terms of kolmogorov s n width and computed in some limiting regimes where the original theorem cannot be directly applied results are used to characterize up to order the total amount of information that can be transported in time and space by multiple scattered electromagnetic waves rigorously addressing a question originally posed in the early works of toraldo di francia and gabor applications in the context of wireless communication and electromagnetic sensing are discussed

multiscale compressed block decomposition for fast direct solution of method of moments linear system the multiscale compressed block decomposition algorithm ms cbd is presented for highly accelerated direct non iterative solution of electromagnetic scattering and radiation problems with the method of moments mom the algorithm is demonstrated to exhibit n2 computational complexity and storage requirements scaling with n1 5 for electrically large objects several numerical examples illustrate the efficiency of the method in particular for problems with multiple excitation vectors the largest problem presented in this paper is the monostatic rcs of the nasa almond at 50 ghz for one thousand incidence angles discretized using 442 089 rwg basis functions being entirely algebraic ms cbd is independent of the greens function of the problem

new aspects of electromagnetic information theory for wireless and antenna systems this paper investigates information theoretic characterization via shannon s information capacity and number of degrees of freedom of wave radiation antenna and wireless propagation systems specifically the paper derives from the fundamental physical point of view of maxwell s equations describing electromagnetic fields the shannon information capacity of space time wireless channels formed by electromagnetic sources and receivers in a known background medium the theory is developed first for the case of sources working at a fixed frequency time harmonic case and is expanded later to the more general case of temporally bandlimited systems time domain fields in the bandlimited case we consider separately the two cases of time limited and essentially bandlimited systems and of purely bandlimited systems the developments take into account the physical radiated power constraint in addition to a constraint in the source l 2 norm which acts to avoid antenna superdirectivity based on such radiated power and current l 2 norm constraints we derive the shannon information capacity of canonical wireless and antenna systems in free space for a given additive gaussian noise level as well as an associated number of degrees of freedom resulting from such capacity calculations the derived results also illustrate from a new information theoretic point of view the transition from near to far fields