correction to on skew information in the above titled paper ibid vol 50 no 8 pp 1778 1782 aug 04 changes were made to figure 2 theorem 1

comments on conjectures of trace inequalities on a generalized wigner yanase skew information abstract furuichi yanagi and kuriyama gave three conjectures of trace inequalities on the wigner yanase dyson skew information and a generalized wigner yanase skew information furuichi et al 2009 1 and yanagi found a counterexample showing that two of the three conjectures don t hold yanagi 2010 6 in this note we show that the last conjecture does not hold in general in addition we show that in the case of 2 2 matrices the conjecture is true

metric adjusted skew information we extend the concept of wigner yanase dyson skew information to something we call metric adjusted skew information of a state with respect to a conserved observable this skew information is intended to be a non negative quantity bounded by the variance of an observable in a state that vanishes for observables commuting with the state we show that the skew information is a convex function on the manifold of states it also satisfies other requirements proposed by wigner and yanase for an effective measure of information content of a state relative to a conserved observable we establish a connection between the geometrical formulation of quantum statistics as proposed by chentsov and morozova and measures of quantum information as introduced by wigner and yanase and extended in this article we show that the set of normalized morozova chentsov functions describing the possible quantum statistics is a bauer simplex and determine its extreme points we determine a particularly simple skew information the skew information parametrized by a 0 1 and show that the convex cone this family generates coincides with the set of all metric adjusted skew informations

out of time order fluctuation dissipation theorem we prove a generalized fluctuation dissipation theorem for a certain class of out of time ordered correlators otocs with a modified statistical average which we call bipartite otocs for general quantum systems in thermal equilibrium the difference between the bipartite and physical otocs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the wigner yanase skew information within this difference the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear response function that involves a time reversed process we show that the theorem can be generalized to higher order n partite otocs as well as in the form of generalized covariance

higher entropic uncertainty relations for anti commuting observables uncertainty relations provide one of the most powerful formulations of the quantum mechanical principle of complementarity yet very little is known about such uncertainty relations for more than two measurements here we show that sufficient unbiasedness for a set of binary observables in the sense of mutual anticommutation is good enough to obtain maximally strong uncertainty relations in terms of the shannon entropy we also prove nearly optimal relations for the collision entropy this is the first systematic and explicit approach to finding an arbitrary number of measurements for which we obtain maximally strong uncertainty relations our results have immediate applications to quantum cryptography

wigner yanase information on quantum state space the geometric approach in the search of appropriate riemannian metrics on quantum state space the concept of statistical monotonicity or contraction under coarse graining has been proposed by chentsov the metrics with this property have been classified by petz all the elements of this family of geometries can be seen as quantum analogs of fisher information although there exists a number of general theorems shedding light on this subject many natural questions also stemming from applications are still open in this paper we discuss a particular member of the family the wigner yanase information using a well known approach that mimics the classical pull back approach to fisher information we are able to give explicit formulas for the geodesic distance the geodesic path the sectional and scalar curvatures associated to wigner yanase information moreover we show that this is the only monotone metric for which such an approach is possible

uncertainty relation associated with a monotone pair skew information abstract we derive a trace inequality leading to an uncertainty relation based on the monotone pair skew information introduced by furuichi as the monotone pair skew information generalizes the wigner yanase dyson skew information as well as some other skew information our result also extends a few known results on the uncertainty relations particularly it reduces to that of luo yanagi and furuichi et al in the special cases

monotone riemannian metrics and relative entropy on noncommutative probability spaces we use the relative modular operator to define a generalized relative entropy for any convex operator function g on 0 satisfying g 1 0 we show that these convex operator functions can be partitioned into convex subsets each of which defines a unique symmetrized relative entropy a unique family parametrized by density matrices of continuous monotone riemannian metrics a unique geodesic distance on the space of density matrices and a unique monotone operator function satisfying certain symmetry and normalization conditions we describe these objects explicitly in several important special cases including g w log w which yields the familiar logarithmic relative entropy the relative entropies riemannian metrics and geodesic distances obtained by our procedure all contract under completely positive trace preserving maps we then define and study the maximal contraction associated with these quantities

nonharmonic fourier series and spectral theory we consider the problem of using functions g x exp ix 1 x to form biorthogonal expansions in the spaces lp 7r sr for various values of p the work of paley and wiener and of levinson considered conditions of the form ix ni a p which insure that g is part of a biorthogonal system and the resulting biorthogonal expansions are pointwise equiconvergent with ordinary fourier series norm convergence is obtained for p 2 in this paper rather than imposing an explicit growth condition we assume that x n is a multiplier sequence on lp t 7t conditions are given insuring that g inherits both norm and pointwise convergence properties of ordinary fourier series further xn and gn are shown to be the eigenvalues and eigenfunctions of an unbounded operator a which is closely related to a differential operator i a generates a strongly continuous group and a2 generates a strongly continuous semigroup half range expansions involving cos x x or sin x n x on 0 7t are also shown to arise from linear operators which generate semigroups many of these results are obtained using the functional calculus for well bounded operators

a split and merge bayesian variable selection approach for ultrahigh dimensional regression summary we propose a bayesian variable selection approach for ultrahigh dimensional linear regression based on the strategy of split and merge the approach proposed consists of two stages split the ultrahigh dimensional data set into a number of lower dimensional subsets and select relevant variables from each of the subsets and aggregate the variables selected from each subset and then select relevant variables from the aggregated data set since the approach proposed has an embarrassingly parallel structure it can be easily implemented in a parallel architecture and applied to big data problems with millions or more of explanatory variables under mild conditions we show that the approach proposed is consistent i e the true explanatory variables can be correctly identified by the approach as the sample size becomes large extensive comparisons of the approach proposed have been made with penalized likelihood approaches such as the lasso elastic net sure independence screening and iterative sure independence screening the numerical results show that the approach proposed generally outperforms penalized likelihood approaches the models selected by the approach tend to be more sparse and closer to the true model

trace inequalities on a generalized wigner yanase skew information abstract we introduce a generalized wigner yanase skew information and then derive the trace inequality related to the uncertainty relation this inequality is a non trivial generalization of the uncertainty relation derived by s luo for the quantum uncertainty quantity excluding the classical mixture in addition several trace inequalities on our generalized wigner yanase skew information are argued

schrodinger uncertainty relation wigner yanase dyson skew information and metric adjusted correlation measure abstract in this paper we give schrodinger type uncertainty relation using the wigner yanase dyson skew information in addition we give schrodinger type uncertainty relation by use of a two parameter extended correlation measure we finally show a further generalization of schrodinger type uncertainty relation by use of the metric adjusted correlation measure these results generalize our previous result in phys rev a 82 2010 034101

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

wigner yanase skew information and uncertainty relations the wigner araki yanase theorem puts a limitation on the measurement of observables in the presence of a conserved quantity and the notion of wigner yanase skew information quantifies the amount of information on the values of observables not commuting with the conserved quantity we demonstrate that the statistical idea underlying the skew information is the fisher information in the theory of statistical estimation a quantum cramer rao inequality and a new uncertainty relation in terms of the skew information are established which shed considerable new light on the relationships between quantum measurement and statistical inference the result is applied to estimating the evolution speed of quantum states

quantum covariance quantum fisher information and the uncertainty relations in this paper the relation between quantum covariances and quantum fisher informations is studied this study is applied to generalize a recently proved uncertainty relation based on quantum fisher information the proof given here considerably simplifies the previously proposed proofs and leads to more general inequalities

a note on a generalization of the luo s uncertainty relation we give the trace inequalities as a generalization of the uncertainty relation improved by s luo these inequalities are refinements of the trace inequality conjectured by furuichi et al

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

metric adjusted skew information and uncertainty relation abstract we show that an uncertainty relation for wigner yanase dyson skew information proved by yanagi 2010 10 can hold for an arbitrary quantum fisher information under some conditions this is a refinement of the result of gibilisco and isola 2011 4

generalized intelligent states and squeezing the robertson schrodinger uncertainty relation for two observables a and b is shown to be minimized in the eigenstates of the operator a ib being a complex number such states called generalized intelligent states gis can exhibit arbitrarily strong squeezing of a or b the time evolution of gis is stable for hamiltonians which admit linear in a and b invariants systems of gis for the su 1 1 and su 2 groups are constructed and discussed it is shown that su 1 1 gis contain all the perelomov coherent states cs and the barut and girardello cs while the spin cs are a subset of su 2 gis cs for an arbitrary semisimple lie group can be considered as a gis for the quadratures of the weyl generators

on a correspondence between regular and non regular operator monotone functions abstract we prove the existence of a bijection between the regular and the non regular operator monotone functions satisfying a certain functional equation as an application we give a new proof of the operator monotonicity of certain functions related to the wigner yanase dyson skew information

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

weak superadditivity of skew information we revisit the superadditivity conjecture for skew information which has recently been disproved by hansen 2007 j stat phys 126 643 we establish two weak forms of superadditivity which are conjectured to be optimal our results show that in a certain sense the superadditivity is true with 50 off

an imputation regularized optimization algorithm for high dimensional missing data problems and beyond missing data are frequently encountered in high dimensional problems but they are usually difficult to deal with by using standard algorithms such as the expectation maximization algorithm and its variants to tackle this difficulty some problem specific algorithms have been developed in the literature but there still lacks a general algorithm this work is to fill the gap we propose a general algorithm for high dimensional missing data problems the algorithm works by iterating between an imputation step and a regularized optimization step at the imputation step the missing data are imputed conditionally on the observed data and the current estimates of parameters and at the regularized optimization step a consistent estimate is found via the regularization approach for the minimizer of a kullback leibler divergence defined on the pseudocomplete data for high dimensional problems the consistent estimate can be found under sparsity constraints the consistency of the averaged estimate for the true parameter can be established under quite general conditions the algorithm is illustrated by using high dimensional gaussian graphical models high dimensional variable selection and a random coefficient model

the capacity of the quantum channel with general signal states it is shown that the capacity of a classical quantum channel with arbitrary possibly mixed states equals the maximum of the entropy bound with respect to all a priori distributions this completes the recent result of hausladen jozsa schumacher westmoreland and wootters 1996 who proved the equality for the pure state channel

a generalized skew information and uncertainty relation a generalized skew information is defined and a generalized uncertainty relation is established with the help of a trace inequality which was recently proven by fujii in addition we prove the trace inequality conjectured by luo and zhang finally we point out that theorem 1 in s luo and q zhang ieee trans inf theory vol 50 pp 1778 1782 no 8 aug 2004 is incorrect in general by giving a simple counter example

covariance and fisher information in quantum mechanics variance and fisher information are ingredients of the cramer rao inequality we regard fisher information as a riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and fisher information in this approach we show that there is a kind of dual one to one correspondence between the candidates of the two concepts we emphasize that fisher information is obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold

polynomial splines and their tensor products in extended linear modeling 1994 wald memorial lecture analysis of variance type models are considered for a regression function or for the logarithm of a probability function conditional probability function density function conditional density function hazard function conditional hazard function or spectral density function polynomial splines are used to model the main effects and their tensor products are used to model any interaction components that are included in the special context of survival analysis the baseline hazard function is modeled and nonproportionality is allowed in general the theory involves the l 2 rate of convergence for the fitted model and its components the methodology involves least squares and maximum likelihood estimation stepwise addition of basis functions using rao statistics stepwise deletion using wald statistics and model selection using the bayesian information criterion cross validation or an independent test set publicly available software written in c and interfaced to s s plus is used to apply this methodology to real data

born jordan quantization and the uncertainty principle the weyl correspondence and the related wigner formalism lie at the core of traditional quantum mechanics we discuss here an alternative quantization scheme the idea of which goes back to born and jordan and which has recently been revived in another context namely time frequency analysis we show in particular that the uncertainty principle does not enjoy full symplectic covariance properties in the born and jordan scheme as opposed to what happens in the weyl quantization

representations and properties of generalized ar statistics coherent states and robertson uncertainty relations the generalization of ar statistics including bosonic and fermionic sectors is performed by means of the so called jacobson generators the corresponding fock spaces are constructed the bargmann representations are also considered for the bosonic ar statistics two inequivalent bargmann realizations are developed the first resp second realization induces in a natural way coherent states recognized as gazeau klauder resp klauder perelomov ones in the fermionic case the bargamnn realization leads to the klauder perelomov coherent states for each considered realization the inner product of two analytic functions is defined with respect to a measure explicitly computed the jacobson generators are realized as differential operators it is shown that the obtained coherent states minimize the robertson schr dinger uncertainty relation

a dynamical uncertainty principle in von neumann algebras by operator monotone functions suppose that a1 an are observables selfadjoint matrices and is a state density matrix in this case the standard uncertainty principle proved by robertson gives a bound for the quantum generalized variance namely for det cov aj ak using the commutators aj ak this bound is trivial when n is odd recently a dierent inequality of robertson type has been proved by the authors with the help of the theory of operator monotone functions in this case the bound makes use of the commutators a j and is non trivial for any n in the present paper we generalize this new result to the von neumann algebra case nevertheless the proof appears to simplify all the existing ones

stochastic approximation with discontinuous dynamics and state dependent noise w p 1 and weak convergence abstract stochastic approximations of the form xn 1 xn anh xn n are treated where h might not be continuous and the noise sequence n might depend on xn an averaging and an ordinary differential equation method are combined to get w p 1 convergence for both the above algorithm and for the case where the interates are projected back onto a bounded set g if they ever leave it two examples are developed the first being an automata problem where the dynamics are not smooth and the noise is state dependent and the second a robbins monro process with observation averaging which causes the noise to be state dependent each example is typical of a larger class the results hold if an is a sequence of random variables an being dependent on xi i n if an 0 but an2

uncertainty principle with quantum fisher information in this paper we prove a lower bound for the determinant of the covariance matrix of quantum mechanical observables which was conjectured by gibilisco et al and has the interpretation of uncertainty the lower bound is given in terms of the commutator of the state and the observables and quantum fisher information generated by an operator monotone function

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

on a refinement of heisenberg uncertainty relation by means of quantum fisher information abstract we show that an uncertainty relation proved by luo and yanagi and related to wigner yanase dyson information cannot hold for an arbitrary quantum fisher information we show that by changing a costant a similar trace inequality holds in full generality

monotone metrics on matrix spaces abstract the study of monotone inner products under stochastic mappings on the space of matrices was initiated by morozova and chentsov motivated by information geometry they did not show a monotone metric but proposed several candidates the main result of the present paper is to provide an abundance of monotone metrics by means of operator monotone functions and to characterize them it turns out that there is a correspondence between monotone metrics and operator means in the sense of kubo and ando it follows that all proposals of morozova and chentsov are indeed monotone metrics

state extended uncertainty relations a scheme for construction of uncertainty relations for n observables and m states is presented several lowest order inequalities are displayed and briefly discussed for two states and and canonical observables the entangled extension of the heisenberg relation reads p 2 q 2 p 2 q 2

principle of maximum fisher information from hardy s axioms applied to statistical systems consider a finite sized multidimensional system in a parameter state a the system is in either a state of equilibrium or general non equilibrium and may obey either classical or quantum physics l hardy s mathematical axioms provide a basis for the physics obeyed by any such system one axiom is that the number n of distinguishable states a in the system obeys n max this assumes that n is known as deterministic prior knowledge however most observed systems suffer statistical fluctuations for which n is therefore only known approximately then what happens if the scope of the axiom n max is extended to include such observed systems it is found that the state a of the system must obey a principle of maximum fisher information i imax this is important because many physical laws have been derived assuming as a working hypothesis that i imax these derivations include uses of the principle of extreme physical information epi examples of such derivations were of the de broglie wave hypothesis quantum wave equations maxwell s equations new laws of biology e g of coulomb force directed cell development and of in situ cancer growth and new laws of economic fluctuation and investment that the principle i imax itself derives from suitably extended hardy axioms thereby eliminates its need to be assumed in these derivations thus uses of i imax and epi express physics at its most fundamental level its axiomatic basis in math

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

an informational characterization of schrodinger s uncertainty relations heisenberg s uncertainty relations employ commutators of observables to set fundamental limits on quantum measurement the information concerning incompatibility non commutativity of observables is well included but that concerning correlation is missing schrodinger s uncertainty relations remedy this defect by supplementing the correlation in terms of anti commutators however both heisenberg s uncertainty relations and schrodinger s uncertainty relations are expressed in terms of variances which are not good measures of uncertainty in general situations e g when mixed states are involved by virtue of the wigner yanase skew information we will establish an uncertainty relation along the spirit of schrodinger from a statistical inference perspective and propose a conjecture the result may be interpreted as a quantification of certain aspect of the celebrated wigner araki yanase theorem for quantum measurement which states that observables not commuting with a conserved quantity cannot be measured exactly

inequalities for positive module operators on von neumann algebras we establish the cauchy schwarz and golden thompson inequalities for module operators a generalization of a noncommutative conditional expectation on a von neumann algebra we apply these inequalities to the bennett inequality and an uncertainty relation a generalization of the schrodinger uncertainty relation for conditional expectations we establish the cauchy schwarz and golden thompson inequalities for module operators a generalization of a noncommutative conditional expectation on a von neumann algebra we apply these inequalities to the bennett inequality and an uncertainty relation a generalization of the schrodinger uncertainty relation for conditional expectations

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

information geometry of density matrices and state estimation given a pure state vector x and a density matrix the function defines a probability density on the space of pure states parameterised by density matrices the associated fisher rao information measure is used to define a unitary invariant riemannian metric on the space of density matrices an alternative derivation of the metric based on square root density matrices and trace norms is provided this is applied to the problem of quantum state estimation in the simplest case of unitary parameter estimation new higher order corrections to the uncertainty relations applicable to general mixed states are derived

quantum information inequalities via tracial positive linear maps abstract we present some generalizations of quantum information inequalities involving tracial positive linear maps between c algebras among several results we establish a noncommutative heisenberg uncertainty relation more precisely we show that if a b is a tracial positive linear map between c algebras a is a density element and a b are self adjoint operators of a such that sp i 1 2 a b 1 2 m m for some scalers 0 m m then under some conditions 0 1 v a v b 1 2 k m m a b a b where k m m a b is the kantorovich constant of the operator i 1 2 a b 1 2 and v x is the generalized variance of x in addition we use some arguments differing from the scalar theory to present some inequalities related to the generalized correlation and the generalized wigner yanase dyson skew information

improvement of uncertainty relations for mixed states we study a possible improvement of uncertainty relations the heisenberg uncertainty relation employs commutator of a pair of conjugate observables to set the limit of quantum measurement of the observables the schrodinger uncertainty relation improves the heisenberg uncertainty relation by adding the correlation in terms of anti commutator however both relations are insensitive whether the state used is pure or mixed we improve the uncertainty relations by introducing additional terms which measure the mixtureness of the state for the momentum and position operators as conjugate observables and for the thermal state of quantum harmonic oscillator it turns out that the equalities in the improved uncertainty relations hold

uncertainty principle and quantum fisher information ii heisenberg and schrodinger uncertainty principles give lower bounds for the product of variances var a var b if the observables a b are not compatible namely if the commutator a b is not zero in this paper we prove an uncertainty principle in schrodinger form where the bound for the product of variances var a var b depends on the area spanned by the commutators i a and i b with respect to an arbitrary quantum version of the fisher information

completeness and basis properties of complex exponentials this paper is concerned with what might be termed the fine structure of the completeness and basis properties of complex exponentials we give new criteria for two sequences to have the same excess in the sense of paley and wiener a result that illuminates and supplements a well known completeness criterion of levinson and new examples and counterexamples pertaining to riesz bases

renyi formulation of the entropic uncertainty principle for povms uncertainty relations for a pair of arbitrary measurements are posed in the form of inequalities using the renyi entropies the formulation deals with povm measurements on finite dimensional hilbert space both the entropic uncertainty relations with state dependent and state independent bounds are presented the results are illustrated on the example of measurements for state discrimination

some inequalities for norms on matrices and operators we study several inequalities for norms on matrices in particular for the hilbert schmidt and operator norms these inequalities occur when comparing norms of the products xy and yx for matrices x and y with suitable assumptions we also point out some trace inequalities

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

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

geometries of quantum states the quantum analog of the fisher information metric of a probability simplex is searched and several riemannian metrics on the set of positive definite density matrices are studied some of them appeared in the literature in connection with cramer rao type inequalities or the generalization of the berry phase to mixed states they are shown to be stochastically monotone here all stochastically monotone riemannian metrics are characterized by means of operator monotone functions and it is proven that there exist a maximal and a minimal among them a class of metrics can be extended to pure states and a constant multiple of the fubini study metric appears in the extension

a robertson type uncertainty principle and quantum fisher information let a1 an be complex self adjoint matrices and let be a density matrix the robertson uncertainty principle det cov ah aj det i 2 tr a h aj gives a bound for the quantum generalized variance in terms of the commutators ah aj the right side matrix is antisymmetric and therefore the bound is trivial equal to zero in the odd case n 2m 1 let f be an arbitrary normalized symmetric operator monotone function and let h i f be the associated quantum fisher information we have conjectured the inequality det cov ah aj det f 0 hi a h i a j i f

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

concrete examples of operator monotone functions obtained by an elementary method without appealing to lowner integral representation we study concrete examples of operator monotone functions obtained by an elementary method without appealing to lowner integral representation

how to distinguish quantum covariances using uncertainty relations abstract to each operator monotone function it is possible to associate a quantum version of the classical covariance we show that i only for regular quantum covariances one can prove non trivial uncertainty relations ii the usual quantum covariance gives the best inequalities in this setting

a trace inequality arising from quantum information theory abstract we introduce a skew information of lieb s type s f g a x tr f a xg a x tr f a g a x 2 for selfadjoint matrices a x we give conditions for f and g so that sf g is positive or negative as another important application we settle the problem posed by yanagi furuichi and kuriyama from quantum information theory

a resampling based stochastic approximation method for analysis of large geostatistical data the gaussian geostatistical model has been widely used in modeling of spatial data however it is challenging to computationally implement this method because it requires the inversion of a large covariance matrix particularly when there is a large number of observations this article proposes a resampling based stochastic approximation method to address this challenge at each iteration of the proposed method a small subsample is drawn from the full dataset and then the current estimate of the parameters is updated accordingly under the framework of stochastic approximation since the proposed method makes use of only a small proportion of the data at each iteration it avoids inverting large covariance matrices and thus is scalable to large datasets the proposed method also leads to a general parameter estimation approach maximum mean log likelihood estimation which includes the popular maximum log likelihood estimation mle approach as a special case and is expected to play an important role

order in a multidimensional system we show that any convex k dimensional system has a level of order r that is proportional to its level of fisher information i the proportionality constant is 1 8 the square of the longest chord connecting two surface points of the system this result follows solely from the requirement that r decrease under small perturbations caused by a coarse graining of the system the form for r is generally unitless allowing the order for different phenomena or different representations e g using time vs frequency of a given phenomenom to be compared objectively order r is also invariant to uniform magnification of the system the monotonic contraction properties of r and i define an arrow of time and imply that they are entropies in addition to their usual status as informations this also removes the need for data and therefore an observer in derivations of nonparticipatory phenomena that utilize i simple graphical examples of the new order measure show that it measures as well the level of complexity in the system finally an application to cell growth during enforced distortion shows that a single hydrocarbon chain can be distorted into a membrane having equal order or complexity such membranes are prime constituents of living cells

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

uncertainty relation on wigner yanase dyson skew information abstract we give a trace inequality related to the uncertainty relation of wigner yanase dyson skew information this inequality corresponds to a generalization of the uncertainty relation derived by s luo 2005 8 for the quantum uncertainty quantity excluding the classical mixture

quantifying the incompatibility of quantum measurements relative to a basis motivated by quantum resource theories we introduce a notion of incompatibility for quantum measurements relative to a reference basis the notion arises by considering states diagonal in that basis and investigating whether probability distributions associated with different quantum measurements can be converted into one another by probabilistic postprocessing the induced preorder over quantum measurements is directly related to multivariate majorization and gives rise to families of monotones i e scalar quantifiers that preserve the ordering for the case of orthogonal measurement we establish a quantitative connection between incompatibility quantum coherence and entropic uncertainty relations we generalize the construction to include arbitrary positive operator valued measurements and report complete families of monotones

on skew information in this paper we show that skew information introduced by wigner and yanase which is a natural informational extension of variance for pure states can be interpreted as a measure of quantum uncertainty by virtue of skew information we establish a new uncertainty relation in the spirit of schrodinger which incorporates both incompatibility encoded in the commutator and correlations encoded in a new correlation measure related to skew information between observables and moreover is stronger than the conventional ones

uncertainty relation on generalized wigner yanase dyson skew information abstract we give a trace inequality related to the uncertainty relation of generalized wigner yanase dyson skew information which is two parameter s extension of our result in 12

bayesian subset modeling for high dimensional generalized linear models this article presents a new prior setting for high dimensional generalized linear models which leads to a bayesian subset regression bsr with the maximum a posteriori model approximately equivalent to the minimum extended bayesian information criterion model the consistency of the resulting posterior is established under mild conditions further a variable screening procedure is proposed based on the marginal inclusion probability which shares the same properties of sure screening and consistency with the existing sure independence screening sis and iterative sure independence screening isis procedures however since the proposed procedure makes use of joint information from all predictors it generally outperforms sis and isis in real applications this article also makes extensive comparisons of bsr with the popular penalized likelihood methods including lasso elastic net sis and isis the numerical results indicate that bsr can generally outperform the penalized likelihood methods the m

jensen divergence based on fisher s information the measure of jensen fisher divergence between probability distributions is introduced and its theoretical grounds set up this quantity in contrast to the remaining jensen divergences grasps the fluctuations of the probability distributions because it is controlled by the local fisher information which is a gradient functional of the distribution so it is appropriate and informative when studying the similarity of distributions mainly for those having oscillatory character the new jensen fisher divergence shares with the jensen shannon divergence the following properties non negativity additivity when applied to an arbitrary number of probability densities symmetry under exchange of these densities vanishing under certain conditions and definiteness even when these densities present non common zeros moreover the jensen fisher divergence is shown to be expressed in terms of the relative fisher information as the jensen shannon divergence does in terms of the kullback leibler or relative shannon entropy finally the jensen shannon and jensen fisher divergences are compared for the following three large non trivial and qualitatively different families of probability distributions the sinusoidal generalized gamma like and rakhmanov hermite distributions which are closely related to the quantum mechanical probability densities of numerous physical systems

on the monotonicity of scalar curvature in classical and quantum information geometry we study the monotonicity under mixing of the scalar curvature for the geometries on the simplex of probability vectors from the results obtained and from numerical data we are led to some conjectures about quantum geometries and wigner yanase dyson information finally we show that this last conjecture implies the truth of the petz conjecture about the monotonicity of the scalar curvature of the bogoliubov kubo mori monotone metric

almost sure convergence of stochastic approximation algorithms with non additive noise abstract stochastic approximation algorithms with non additive noise are discussed in studying strong convergence of such algorithms traditionally one assumes that the iterates return to a bounded or compact set infinitely often or that the function under consideration grows with certain rate the usual projection algorithms require that the bounded projection region is known beforehand it is desirable to weaken these boundedness conditions by introducing randomly varying truncations chen and zhu 1986 achieved this for stochastic approximation algorithms with additive noise here we extend their result to a more general setting