asymptotically optimal quantizers for detection of i i d the asymptotic probability of error for quantization in maximum likelihood tests is analyzed the authors assume quantizers with large numbers of levels generated from a companding function a theorem that relates the companding function to the asymptotic probability of error is proved the companding function is then optimized

worst and average case privacy breaches in randomization mechanisms in a variety of contexts randomization is regarded as an effective technique to conceal sensitive information viewing randomization mechanisms as information theoretic channels we start from a semantic notion of security which expresses absence of any privacy breach above a given level of seriousness irrespective of any background information represented as a prior probability on the secret inputs we first examine this notion according to two dimensions worst vs average case single vs repeated observations in each case we characterize the security level achievable by a mechanism in a simple fashion that only depends on the channel matrix and specifically on certain measures of distance between its rows like norm 1 distance and chernoff information we next clarify the relation between our worst case security notion and differential privacy dp we show that while the former is in general stronger the two coincide if one confines to background information that can be factorized into the product of independent priors over individuals we finally turn our attention to expected utility in the sense of ghosh et al in the case of repeated independent observations we characterize the exponential growth rate of any reasonable utility function in the particular case the mechanism provides dp we study the relation of the utility rate with we offer either exact expressions or upper bounds for utility rate that apply to practically interesting cases such as the truncated geometric mechanism

anonymity protocols as noisy channels we consider a framework in which anonymity protocols are interpreted as noisy channels in the information theoretic sense and we explore the idea of using the notion of capacity as a measure of the loss of anonymity such idea was already suggested by moskowitz newman and syverson in their analysis of the covert channel that can be created as a result of non perfect anonymity we consider the case in which some leak of information is intended by design and we introduce the notion of conditional capacity to rule out this factor thus retrieving a natural correspondence with the notion of anonymity furthermore we show how to compute the capacity and the conditional capacity when the anonymity protocol satisfies certain symmetries we also investigate how the adversary can test the system to try to infer the user s identity and we study how his probability of success depends on the characteristics of the channel we then illustrate how various notions of anonymity can be expressed in this framework and show the relation with some definitions of probabilistic anonymity in literature finally we show how to compute the matrix of the channel and hence the capacity and conditional capacity using model checking

arimoto renyi conditional entropy and bayesian m ary hypothesis testing this paper gives upper and lower bounds on the minimum error probability of bayesian m ary hypothesis testing in terms of the arimoto renyi conditional entropy of an arbitrary order alpha the improved tightness of these bounds over their specialized versions with the shannon conditional entropy alpha 1 is demonstrated in particular in the case where m is finite we show how to generalize fano s inequality under both the conventional and list decision settings as a counterpart to the generalized fano s inequality allowing m to be infinite a lower bound on the arimoto renyi conditional entropy is derived as a function of the minimum error probability explicit upper and lower bounds on the minimum error probability are obtained as a function of the arimoto renyi conditional entropy for both positive and negative alpha furthermore we give upper bounds on the minimum error probability as functions of the renyi divergence in the setup of discrete memoryless channels we analyze the exponentially vanishing decay of the arimoto renyi conditional entropy of the transmitted codeword given the channel output when averaged over a random coding ensemble

stable and invariant adjusted profile likelihood and directed likelihood for curved exponential models summary for curved exponential models the modified profile likelihood and the modified directed likelihood are approximated with error o n 1 under ordinary repeated sampling by explicitly defined and invariant quantities which do not require specification of an ancillary and which are stable in the sense of having the appropriate conditionality property with respect to any reasonable ancillary

second variation of zhang s λ invariant on the moduli space of curves we compute the second variation of the invariant recently introduced by s zhang on the complex moduli space mg of curves of genus g 2 using work of n kawazumi as a result we prove that 8g 4 is equal up to a constant to the invariant introduced some time ago by r hain and d reed we deduce some consequences for example we calculate the invariant for each hyperelliptic curve expressing it in terms of the petersson norm of the discriminant modular form 1 introduction recently independently s zhang 27 and n kawazumi 16 introduced a new interesting real valued function on the moduli space mg of complex curves of genus g 2 its value at a curve x m g is given as follows let h 0 x x be the space of holomorphic differentials on x equipped with the

adjusted versions of profile likelihood and directed likelihood and extended likelihood several adjusted and invariant versions of profile likelihood and of directed likelihood short for signed log likelihood ratio are discussed these adjusted versions which fall into two groups are closely related to modified profile likelihood and modified directed likelihood the first group has the advantage of not requiring an explicit specification of an ancillary but partly at a cost of a loss of asymptotic accuracy in comparison with the modified versions the second group consists of some asymptotically sharpened versions of modified profile likelihood furthermore a concept of extended likelihood is proposed which associates a likelihood like function to certain combinants

asymptotic geometry of multiple hypothesis testing we present a simple geometrical interpretation for the solution to the multiple hypothesis testing problem in the asymptotic limit under this interpretation the optimal decision rule is a nearest neighbor classifier on the probability simplex

constrained epsilon minimax test for simultaneous detection and classification a constrained epsilon minimax test is proposed to detect and classify nonorthogonal vectors in gaussian noise with a general covariance matrix and in presence of linear interferences this test is epsilon minimax in the sense that it has a small loss of optimality with respect to the purely theoretical and incalculable constrained minimax test which minimizes the maximum classification error probability subject to a constraint on the false alarm probability this loss is even more negligible as the signal to noise ratio is large furthermore it is also an epsilon equalizer test since its classification error probabilities are equalized up to a negligible difference when the signal to noise ratio is sufficiently large an asymptotically equivalent test with a very simple form is proposed this equivalent test coincides with the generalized likelihood ratio test when the vectors to classify are strongly separated in term of euclidean distance numerical experiments on active user identification in a multiuser system confirm the theoretical findings

higher arithmetic intersection theory abstract we give a new definition of higher arithmetic chow groups for smooth projective varieties defined over an arithmetic field which is similar to gillet and soule s definition of arithmetic chow groups we also give a compact description of the intersection theory of such groups a consequence of this theory is the definition of a heigh pairing between two higher algebraic cycles of complementary dimensions whose real regulator class is zero this description agrees with beilinson s height pairing for the classical arithmetic chow groups we also give examples of higher arithmetic intersection pairing in dimension zero

discriminating quantum states the multiple chernoff distance we consider the problem of testing multiple quantum hypotheses rho 1 otimes n ldots rho r otimes n where an arbitrary prior distribution is given and each of the r hypotheses is n copies of a quantum state it is known that the minimal average error probability p e decays exponentially to zero that is p e exp xi n o n however this error exponent xi is generally unknown except for the case that r 2 in this paper we solve the long standing open problem of identifying the above error exponent by proving nussbaum and szkola s conjecture that xi min i neq j c rho i rho j the right hand side of this equality is called the multiple quantum chernoff distance and c rho i rho j max 0 leq s leq1 log operatorname tr rho i s rho j 1 s has been previously identified as the optimal error exponent for testing two hypotheses rho i otimes n versus rho j otimes n the main ingredient of our proof is a new upper bound for the average error probability for testing an ensemble of finite dimensional but otherwise general quantum states this upper bound up to a states dependent factor matches the multiple state generalization of nussbaum and szkola s lower bound specialized to the case r 2 we give an alternative proof to the achievability of the binary hypothesis chernoff distance which was originally proved by audenaert et al

variation of mixed hodge structure i around 1970 griffiths introduced the notion of a variation of hodge structure on a complex manifold s see 17 w 2 it constitutes the axiomatization of the features possessed by the local systems of cohomology associated to a family of compact k ihler manifolds esp smooth projective varieties parametrized by s these are for a variation of hodge structure u of weight m 0 a locally constant sheaf u of q vector spaces or u of real vector spaces 1 hodge filtration horizontality a decreasing filtration o r of gs by holomorphic subbundles such that the evident connection v on takes o p into q 2 hodge decompositions if gs denotes the sheaf of functions on s and if

likelihood for component parameters for a statistical model with data likelihood for the scalar or vector full parameter 0 of dimension p say is typically well defined and easily computed in this paper we investigate likelihood for a component parameter 0 of dimension d p and make use of the recent likelihood theory that has been successful in producing highly accurate third order p values for scalar parameters of continuous models the theory leads under moderate regularity to a definitive third order determination of likelihood for a component parameter 0 of dimension d where 1 d p we use the simple location model on the plane with standard normal errors to motivate the development the example exhibits most of the key characteristics of the general case and the recent theory then extends the determination of likelihood to the general context for the scalar interest parameter case with d 1 the usual determinations are typically of second order accuracy the example indicates how the new determination achieves third order accuracy the implementation is straightforward and uses familiar ingredients to other determinations such as the full maximum likelihood value o the constrained value o given 0 and the observed information j o for a complementing nuisance parameter 0 it does however require a special version of the nuisance information j o a version calibrated relative to a symmetric choice of the exponential type reparameterisation 0 underlying the recent theory but this is easily computed various examples are given and the motivating example is discussed in detail

a note on the relation between modified profile likelihood and the cox reid adjusted profile likelihood summary an adjustment to the profile likelihood proposed by cox reid 1987 when the parameters are orthogonal is shown to agree with modified profile likelihood in a number of instances in which the parameters are not orthogonal several examples of the phenomenon are given in the case of composite transformation models with invariant parameter as the parameter of interest it is shown that the cox reid adjustment agrees with modified profile likelihood in a large deviation sense if lebesgue measure is rightinvariant necessary and sufficient conditions for equivalence in the moderate deviation sense of modified profile likelihood and the cox reid adjusted profile likelihood are

on the asymptotics of m hypothesis bayesian detection in two hypothesis detection problems with i i d observations the minimum error probability decays exponentially with the amount of data with the constant in the exponent equal to the chernoff distance between the probability distributions characterizing the hypotheses we extend this result to the general m hypothesis bayesian detection problem where zero cost is assigned to correct decisions and find that the bayesian cost function s exponential decay constant equals the minimum chernoff distance among all distinct pairs of hypothesized probability distributions

asymptotics of degenerations of mixed hodge structures abstract we construct a hermitian metric on the classifying spaces of graded polarized mixed hodge structures and prove analogs of the strong distance estimate 6 between an admissible period map and the approximating nilpotent orbit we also consider the asymptotic behavior of the biextension metric introduced by hain 12 analogs of the norm estimates of 19 and the asymptotics of the naive limit hodge filtration considered in 21

asymptotics of the archimedean height pairing let x be a compact kahler manifold of dimension n let a and b be two analytic submanifolds of dimensions p and q respectivelly assume p q n 1 a and b intersect cleanly at a submanifold m of dimension m let a t be a differentiable deformation of a a 0 for the complex number t around 0 such that a t b o for t 0 and the deformation a t is analytic in a neighborhood of m let g b be a green s current of b smooth on x b we prove the asymptotic formula a t g b e log t 2 o 1 where e m c m tx ta tb the asymptotics suggest that e is an obstruction to the existence of positive green s currents

on optimum and nearly optimum data quantization for signal detection the application of companding approximation theory to the quantization of data for detection of coherent signals in a noisy environment is considered this application is twofold allowing for greater simplicity in both analysis and design of quantizers for detection systems most computational methods for designing optimum most efficient quantizers for signal detection systems are iterative and are extremely sensitive to initial conditions companding approximation theory is used here to obtain suitable initial conditions for this problem furthermore the companding approximation idea is applied to design suboptimum quantizers which are nearly as efficient as optimum quantizers when the number of levels is large in this design iteration is not needed to derive the parameters of the quantizer and the design procedure is very simple in this paper we explore this approach numerically and demonstrate its effectiveness for designing and analyzing quantizers in detection systems

asymptotically optimal matching of multiple sequences to source distributions and training sequences consider a finite set of sources each producing independent identically distributed observations that follow a unique probability distribution on a finite alphabet we study the problem of matching a finite set of observed sequences to the set of sources under the constraint that the observed sequences are produced by distinct sources in general the number of sequences n may be different from the number of sources m and only some k min m n of the observed sequences may be produced by a source from the set of sources of interest we consider two versions of the problem one in which the probability laws of the sources are known and another in which the probability laws of the sources are unspecified but one training sequence from each of the sources is available we show that both these problems can be solved using a sequence of tests that are allowed to produce no match decisions the tests ensure exponential decay of the probabilities of incorrect matching as the sequence lengths increase and minimize the no match decisions both the tests can be implemented using variants of the minimum weight matching algorithm applied to a weighted bipartite graph we also compare the performances obtained using these tests with those obtained using tests that do not consider the constraint that the sequences are produced by distinct sources for the version of the problem in which the probability laws of the sources are known we compute the rejection exponents and error exponents of the tests and show that the tests that make use of the constraint have better exponents than the tests that do not make use of this information

likelihood functions for inference in the presence of a nuisance parameter consider inference about a scalar parameter of interest in the presence of a vector nuisance parameter inference about is often based on a pseudolikelihood function in this paper the general problem of constructing a pseudo loglikelihood function h is considered conditions are given under which h has the same properties as a genuine loglikelihood function for a model without a nuisance parameter when these conditions are satisfied to a given order of approximation h is said to be a jth order local loglikelihood function the theory of local loglikelihood functions is developed and it is shown that second order versions of these have a number of desirable properties several commonly used pseudolikelihood functions are studied from this point of view one commonly used pseudolikelihood function is profile likelihood in which parameters other than 0 are replaced by their maximum likelihood estimates a second aspect of the paper is to consider the use of other estimates in this context examples are given which suggest that inference about may be improved if a method other than maximum likelihood is used particularly when the number of other parameters is large relative to the sample size

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

a 2 sprt based approach to multiple model hypothesis testing for multi distribution detection this paper presents an approach to multiple model hypothesis testing mmht based on 2 sprt 2 mmsrpt for detecting unknown events that may have multiple possible distributions the sequential probability ratio test sprt based mmht method mmsprt is promising because of its efficiency and theoretical validity however it may suffer from sprt s lack of an upper bound on its stopping time especially in the mis specified case the proposed 2 mmsprt algorithm not only copes with this problem but also is in a setting that can provide efficient detection in the sense of minimizing the maximum expected sample size subject to error probability constraints specifically we prove the theoretical validity of 2 sprt for the problem of testing hypotheses with multivariate normal densities moreover we present a technique of forced independence and identical distribution i i d to map the non i i d likelihood ratio sequence to an i i d one which enables us to apply the sprt and 2 sprt effectively to the dynamic case under the linear gaussian assumption with a non identical distribution also 2 mmsprt s detection efficiency under some assumptions approximations is verified performance of 2 mmsprt is evaluated for signal detection and model set selection problems in several scenarios simulation results demonstrate the detection efficiency of the proposed 2 mmsprt compared with the mmsprt and some traditional tests

quantization for decentralized hypothesis testing under communication constraints in a decentralized hypothesis testing network several peripheral nodes observe an environment and communicate their observations to a central node for the final decision the presence of capacity constraints introduces theoretical and practical problems the following problem is addressed given that the peripheral encoders that satisfy these constraints are scalar quantizers how should they be designed in order that the central test to be performed on their output indices is most powerful the scheme is called cooperative design separate encoding since the quantizers process separate observations but have a common goal they seek to maximize a system wide performance measure the bhattacharyya distance of the joint index space as such a criterion is suggested and a design algorithm to optimize arbitrarily many quantizers cyclically is proposed a simplified version of the algorithm namely an independent design separate encoding scheme where the correlation is either absent or neglected for the sake of simplicity is outlined performances are compared through worked examples

complex analytic neron models for arbitrary families of intermediate jacobians given a family of intermediate jacobians for a polarizable variation of integral hodge structure of odd weight on a zariski open subset of a complex manifold we construct an analytic space that naturally extends the family its two main properties are a the horizontal and holomorphic sections are precisely the admissible normal functions without singularities b the graph of any admissible normal function has an analytic closure inside our space as a consequence we obtain a new proof for the zero locus conjecture of m green and p griffiths the construction uses filtered mathcal d modules and m saito s theory of mixed hodge modules it is functorial and does not require normal crossing or unipotent monodromy assumptions

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12