shrinkage priors for bayesian prediction we investigate shrinkage priors for constructing bayesian predictive distributions it is shown that there exist shrinkage predictive distributions asymptotically dominating bayesian predictive distributions based on the jeffreys prior or other vague priors if the model manifold satisfies some differential geometric conditions kullback leibler divergence from the true distribution to a predictive distribution is adopted as a loss function conformal transformations of model manifolds corresponding to vague priors are introduced we show several examples where shrinkage predictive distributions dominate bayesian predictive distributions based on vague priors

essential self adjointness of the graph laplacian we study the operator theory associated with such infinite graphs g as occur in electrical networks in fractals in statistical mechanics and even in internet search engines our emphasis is on the determination of spectral data for a natural laplace operator associated with the graph in question this operator will depend not only on g but also on a prescribed positive real valued function c defined on the edges in g in electrical network models this function c will determine a conductance number for each edge we show that the corresponding laplace operator is automatically essential self adjoint by this we mean that is defined on the dense subspace d of all the real valued functions on the set of vertices g0 with finite support in the hilbert space l2 g0 the conclusion is that the closure of the operator is self adjoint in l2 g0 and so in particular that it has a unique spectral resolution determined by a projection valued measure on the borel subsets of the infinite half line we

non perturbative anderson localization in heavy tailed potentials via large deviations moment analysis we study a class of anderson hamiltonians with heavy tailed independent and identically distributed random potential on graphs with sub exponential growth of the balls and of the number of self avoiding paths connecting pairs of points we show that for a class of marginal distributions anderson localization occurs non perturbatively i e for any nonzero amplitude of the potential like in one dimensional systems the proof is based on the moment analysis of the green functions via large deviations estimates

hilbert schmidt lower bounds for estimators on matrix lie groups for atr deformable template representations of observed imagery model the variability of target pose via the actions of the matrix lie groups on rigid templates in this paper we study the construction of minimum mean squared error estimators on the special orthogonal group so n for pose estimation due to the nonflat geometry of so n the standard bayesian formulation of optimal estimators and their characteristics requires modifications by utilizing hilbert schmidt metric defined on gl n a larger group containing so n a mean squared criterion is defined on so n the hilbert schmidt estimate hse is defined to be a minimum mean squared error estimator restricted to so n the expected error associated with the hse is shown to be a lower bound called the hilbert schmidt bound hsb on the error incurred by any other estimator analysis and algorithms are presented for evaluating the hse and the hsb in cases of both ground based and airborne targets

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

clutter invariant atr one of the central problems in automated target recognition is to accommodate the infinite variety of clutter in real military environments the principle focus of our paper is on the construction of metric spaces where the metric measures the distance between objects of interest invariant to the infinite variety of clutter such metrics are formulated using second order random field models our results indicate that this approach significantly improves detection classification rates of targets in clutter

fractional moment methods for anderson localization with saw representation the green function contains much information about physical systems mathematically the fractional moment method fmm developed by aizenman and molchanov connects the green function and the transport of electrons in the anderson model recently it has been discovered that the green function on a graph can be represented using self avoiding walks on a graph which allows us to connect localization properties in the system and graph properties we discuss fmm in terms of the self avoiding walks on a general graph the only general condition being that the graph has a uniform bound on the vertex degree

geometry of deformed exponential families invariant dually flat and conformal geometries an information geometrical foundation is established for the deformed exponential families of probability distributions two different types of geometrical structures an invariant geometry and a flat geometry are given to a manifold of a deformed exponential family the two different geometries provide respective quantities such as deformed free energies entropies and divergences the class belonging to both the invariant and flat geometries at the same time consists of exponential and mixture families theq families are characterized from the viewpoint of the invariant and flat geometries the q exponential family is a unique class that has the invariant and flat geometries in the extended class of positive measures furthermore it is the only class of which the riemannian metric is conformally connected with the invariant fisher metric

localization criteria for anderson models on locally finite graphs we prove spectral and dynamical localization for anderson models on locally finite graphs using the fractional moment method our theorems extend earlier results on localization for the anderson model on d we establish geometric assumptions for the underlying graph such that localization can be proven in the case of sufficiently large disorder

asymptotic normality of the posterior in relative entropy we show that the relative entropy between a posterior density formed from a smooth likelihood and prior and a limiting normal form tends to zero in the independent and identically distributed case the mode of convergence is in probability and in mean applications to code lengths in stochastic complexity and to sample size selection are discussed

single observation unbiased priors this paper studies a class of default priors which we call single observation unbiased priors soup a prior for a parameter is a soup if the corresponding posterior mean of the parameter based on a single observation is an unbiased estimator of the parameter we prove that under mild regularity conditions a default prior for a convolution parameter is noninformative in the sense of yielding a posterior inference invariant under amalgamation only if it is a soup therefore when amalgamation invariance is desirable as in our motivating example of performing imputation for census undercount soup is the only possible coherent noninformative prior for bayesian predictions that will be utilized under aggregation the use of soup also mutually calibrates bayesian and frequentist inferences for aggregates of convolution parameters across many small areas we describe approaches that identify soups in many common models in particular a constructive duality method that identifies soups in pairs of distribution families we introduce o completeness a necessary and sufficient condition for a prior distribution to be uniquely characterized by the corresponding posterior mean uniqueness of the soup is determined by the o completeness of the dual family o completeness of a natural exponential family is implied by its completeness hence the diaconis ylvisaker characterization of the conjugate prior for natural exponential families via linear posterior expectation is a direct consequence of the completeness of such families for most of the examples we have examined the inverse of the variance function is the soup for the mean parameter of the corresponding family suggesting that hartigan s results on asymptotic unbiasedness can be generalized to some families with discrete parameters we also discuss a possible extension of berger s result on the inadmissibility of unbiased estimators as the nonexistence of soup can be a first step in establishing such inadmissibility

asymptotic performance analysis of bayesian target recognition this article investigates the asymptotic performance of bayesian target recognition algorithms using deformable template representations rigid computer aided design cad models represent the underlying targets low dimensional matrix lie groups rotation and translation extend them to particular instances remote sensors observing the targets are modeled as projective transformations converting three dimensional scenes into random images bayesian target recognition corresponds to hypothesis selection in the presence of nuisance parameters its performance is quantified as the bayes error analytical expressions for this error probability in small noise situations are derived yielding asymptotic error rates for exponential error probability decay

on coherence in parametric density estimation summary in parametric density estimation the existence of a prior distribution on the parameter dictates the use of the corresponding predictive density function as estimate this paper argues that in a decision theory approach to parameter density estimation any loss function introduced should lead to this predictive result for situations where prior information is available the kullbackleibler directed divergence has this coherence property whereas the corresponding symmetric divergence does not the role of a recently suggested sequential improvement criterion in density estimation is also discussed

goodness of prediction fit for multivariate linear models abstract using both frequentist and bayesian techniques predicting densities are derived for future observations from a multivariate linear model with matrix normal error terms all the candidates belong to a general location scale family of predicting densities an analytic comparison is undertaken using a kullback leibler loss by citing an optimal member of a subclass including most of these predicting densities as members the subclass is based on an invariant student t random matrix and the optimal member is the bayesian predictive density corresponding to a jeffreys noninformative prior information based numerical comparisons illustrate the nature of the dominance

on the generalization of the likelihood function and the likelihood principle abstract the parametric likelihood and likelihood principle lp play a central role in parametric methodology and in the foundations of statistics the main purpose of this article is to extend the concepts of likelihood and lp to general inferential aims and models covering for example prediction and empirical bayes models the likelihood function is the joint distribution of the data and the unobserved variables of inferential interest considered as a function of the parameters and these inferential variables lp is based on this likelihood and the principles of sufficiency sp and conditionality cp are modified such that the equivalence sp and cp lp is valid generalizing birnbaum s theorem

the maximum likelihood prior consider an estimate theta of a parameter theta based on repeated observations from a family of densities f theta evaluated by the kullback leibler loss function k theta theta int log f theta f theta f theta the maximum likelihood prior density if it exists is the density for which the corresponding bayes estimate is asymptotically negligibly different from the maximum likelihood estimate the bayes estimate corresponding to the maximum likelihood prior is identical to maximum likelihood for exponential families of densities in predicting the next observation the maximum likelihood prior produces a predictive distribution that is asymptotically at least as close in expected truncated kullback leibler distance to the true density as the density indexed by the maximum likelihood estimate it frequently happens in more than one dimension that maximum likelihood corresponds to no prior density and in that case the maximum likelihood estimate is asymptotically inadmissible and may be improved upon by using the estimate corresponding to a least favorable prior as in brown the asymptotic risk for an arbitrary estimate near maximum likelihood is given by an expression involving derivatives of the estimator and of the information matrix admissibility questions for these near ml estimates are determined by the existence of solutions to certain differential equations

geometry of an accelerated model with censored data from the geometrical point of view a statistical model can be considered as a manifold with parameter plays the role of a coordinate system in this paper the geometrical quantities of a statistical model equipped with k step stress accelerated life test and progressively type ii censoring are obtained where censoring is allowed not only at each stress change time but also at each failure time as an application of these quantities the asymptotic expansions of the bayesian prediction are investigated finally some computation and simulation results are presented to illustrate our main results

a new proof of localization in the anderson tight binding model we give a new proof of exponential localization in the anderson tight binding model which uses many ideas of the frohlich martinelli scoppola and spencer proof but is technically simpler particularly the probabilistic estimates

multiple target direction of arrival tracking a new algorithm is presented for estimating the directions of arrival of signals from an unknown number of moving signal sources the parameter space is a countable union of cartesian products of the torus each product space corresponding to a different number of signals reaching the sensor array a bayesian posterior probability measure is defined on this parameter space by combining the sensor array manifold models with the von mises prior on source motion the estimates are generated empirically using a random sampling algorithm based on jump diffusion processes and the results are presented from an implementation on a dap510 massively parallel computer

simultaneous prediction of independent poisson observables simultaneous predictive distributions for independent poisson observables are investigated a class of improper prior distributions for poisson means is introduced the bayesian predictive distributions based on priors from the introduced class are shown to be admissible under the kullback leibler loss a bayesian predictive distribution based on a prior in this class dominates the bayesian predictive distribution based on the jeffreys prior

analysis of the physical laplacian and the heat flow on a locally finite graph we study the physical laplacian and the corresponding heat flow on an infinite locally finite graph with possibly unbounded valence

asymptotically minimax bayes predictive densities given a random sample from a distribution with density function that depends on an unknown parameter 0 we are interested in accurately estimating the true parametric density function at a future observation from the same distribution the asymptotic risk of bayes predictive density estimates with kullback leibler loss function d f f f f log f f is used to examine various ways of choosing prior distributions the principal type of choice studied is minimax we seek asymptotically least favorable predictive densities for which the corresponding asymptotic risk is minimax a result resembling stein s paradox for estimating normal means by maximum likelihood holds for the uniform prior in the multivariate location family case when the dimensionality of the model is at least three the jeffreys prior is minimax though inadmissible the jeffreys prior is both admissible and minimax for one and two dimensional location problems

dynamical localization for discrete anderson dirac operators we establish dynamical localization for random dirac operators on the d dimensional lattice with d in left 1 2 3 right in the three usual regimes large disorder band edge and 1d these operators are discrete versions of the continuous dirac operators and consist in the sum of a discrete free dirac operator with a random potential the potential is a diagonal matrix formed by different scalar potentials which are sequences of independent and identically distributed random variables according to an absolutely continuous probability measure with bounded density and of compact support we prove the exponential decay of fractional moments of the green function for such models in each of the above regimes i e j throughout the spectrum at larger disorder jj for energies near the band edges at arbitrary disorder and jjj in dimension one for all energies in the spectrum and arbitrary disorder dynamical localization in theses regimes follows from the fractional moments method the result in the one dimensional regime contrast with one that was previously obtained for 1d dirac model with bernoulli potential

geometry of exponential family with competing risks and censored data abstract employing the differential geometrical methods in statistics suggested by amari 1985 and amari et al 1987 considering the exponential family with censored data and competing risks as a manifold of a statistical model the geometry of the manifold is investigated based on two information sources as an application of the geometry the asymptotic expansions of the bootstrap prediction bayesian prediction and their risk evaluations are investigated the results show that these expansions are related to the coefficients of connections and metric tensors and the predictive density function is the estimative density function in the asymptotic sense finally taking rayleigh distribution and prostatic cancer data as examples some computation and simulation results are presented to illustrate our main results

on efficient probability forecasting systems we study the asymptotic behaviour of probability forecasting systems and discuss their usefulness as inferential tools for statistical problems such as model verification and selection our theoretical setting is the prequential or predictive sequential framework proposed by dawid 1984 we study especially the notion of prequential efficiency of a forecasting system and present some new results we focus on plug in or estimative forecasting systems where the forecast distribution is generated by replacing the unknown parameter with an estimate

frequentist prediction intervals and predictive distributions summary we consider parametric frameworks for the prediction of future values of a random variable y based on previously observed data x simple pivotal methods for obtaining calibrated prediction intervals are presented and illustrated frequentist predictive distri butions are defined as confidence distributions and their utility is demonstrated a simple pivotal based approach that produces prediction intervals and predictive distributions with well calibrated frequentist probability interpretations is introduced and efficient simulation methods for producing predictive distributions are considered properties related to an average kullback leibler measure of goodness for predictive or estimated distributions are given the predictive distributions here are shown to be optimal in certain settings with invariance structure and to dominate plug in distributions under certain conditions

absence of diffusion in the anderson tight binding model for large disorder or low energy we prove that the green s function of the anderson tight binding hamiltonian decays exponentially fast at long distances on v with probability 1 we must assume that either the disorder is large or the energy is sufficiently low our proof is based on perturbation theory about an infinite sequence of block hamiltonians and is related to kam methods

dually flat geometries of the deformed exponential family abstract an exponential family is dually flat with respect to amari s 1 connection a deformed exponential family which is a generalization of the exponential family has two dually flat structures called the u geometry and the geometry in the case of an exponential family invariant geometry gives the dually flat structure but for a deformed exponential family one need to consider generalized geometric structures other than the invariant geometry the f g geometry on a statistical manifold is such a generalized geometry defined using a general embedding function f and a positive smooth function g in this paper we present the role of the f g geometry in the study of a deformed exponential family we show that the dually flat u geometry is the f g geometry for suitable choices of f and g further we show that the dully flat geometry is the conformal flattening of the f g geometry for suitable f and g

robust predictive distributions for exponential families summary the bootstrap predictive distribution considered by harris 1989 is modified by replacing the maximum likelihood estimator of the unknown parameter by its minimum hellinger distance estimator the predictive distribution thus obtained is asymptotically superior to the corresponding estimative distribution in terms of the average kullback leibler divergence when the true distribution is in the natural exponential family simulation results are provided for the binomial and normal distributions which suggest that the proposed predictive distributions are robust and can perform better than the likelihood based methods under data contamination

geometry on the statistical manifold induced by the degradation model with soft failure data abstract information geometry discusses the properties of a statistical manifold and is useful for different fields involving neural networks signal processing machine learning optimization and statistics the methods of information geometry are also employed to discuss the geometry on a statistical manifold induced by the reliability model and lifetime testing where the time to failure data are available for analyzing for highly reliable products however it is difficult to obtain failure data in a reasonable period of time for some products there is a gradual loss of performance then it is possible to derive degradation measurements over times this paper investigates the geometry on a statistical manifold induced by the degradation model with few or no failure data the statistical manifold is constructed based on the degradation model the fisher information metric amari chentsov structure affine connection and connection on the manifold are discussed taking the linear model as an example the main results are illustrated where we find that the geometry quantities are closely related to the degradation threshold value parameters of the model and the euler s constant the parameters are estimated by using the multi step estimation method and numerical results are reported

bayesian duality and risk analysis on the statistical manifold of exponential family with censored data abstract information geometry has been attracted wide attentions in the past few decades this paper focuses on the bayesian duality on a statistical manifold derived from the exponential family with data from life tests based on life testing data the statistical manifold is constructed with a new cumulant generating function the bregman divergence between two parameter points is studied the dual coordinate system and dual function are obtained then the dualistic structure on the manifold is discussed the results show that the maximum likelihood estimate can be obtained by minimizing the bregman divergence induced from the dual function the bayesian analysis and prediction are investigated based on informative and non informative priors consider the gamma distribution as an example the closed form representations of the dual coordinate system and dual function are obtained a real data set is employed to illustrate the methodologies and experimental designs developed in this paper

asymptotic theory of sequential estimation differential geometrical approach sequential estimation continues observations until the observed sample satisfies a prescribed criterion its properties are superior on the average to those of nonsequential estimation in which the number of observations is fixed a priori a higher order asymptotic theory of sequential estimation is given in the framework of geometry of multidimensional curved exponential families this gives a design principle of the second order efficient sequential estimation procedure it is also shown that a sequential estimation can be designed to have a covariance stabilizing effect at the same time

the essential spectrum of the laplacian on rapidly branching tessellations in this paper we characterize absence of the essential spectrum of the laplacian under a hyperbolicity assumption for general graphs moreover we present a characterization for absence of the essential spectrum for planar tessellations in terms of curvature

inference for accelerated competing failure models from weibull distribution under type i progressive hybrid censoring this paper considers constant stress accelerated competing failure models under type i progressive hybrid censoring with binomial random removals a weibull distributed life of test units is assumed for a specific cause and by the newton raphson iteration and asymptotic likelihood theory the maximum likelihood estimates mles and asymptotic confidence intervals of the unknown parameters are obtained based on the noninformative prior a gibbs sampling algorithm using adaptive rejection sampling is presented to obtain bayesian estimates and the monte carlo mc method is employed to construct the hpd credible intervals the simulation results are provided to show that bayesian estimates perform better than mles and the change of the removal probability has a significant effect on mles

approximate predictive likelihood summary a predictive likelihood is given which approximates both bayes and maximum likeli hood predictive inference by expansion of a posterior likelihood this synthesizes and extends previous results and is widely applicable the approximation usually differs from exact bayes posterior predictive density by op n 2 and from exact predictive likelihood by op n 1 but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot be found the results are applied to the prediction various treatments of the likelihood function form the basis of parametric inference but until recently few non bayesian attempts have been made to define versions of it suitable for prediction however lauritzen 1974 hinkley 1979 and more recently butler 1986 have proposed rather similar definitions of predictive likelihood based on the idea of conditioning on the value of a sufficient statistic unfortunately they apply only when sufficiency provides a genuine reduction of the data moreover even if for a given problem an exact predictive likelihood exists the calculations needed to derive it can be onerous this paper provides approximations to hinkley lauritzen predictive likelihood accur ate to op n 1 in many cases which are applicable in situations where maximum likelihood estimation is regular they also apply to problems which admit no exact predictive likelihood because sufficiency provides no real reduction of the data the approximations are derived from a posterior predictive density and may if prior informa tion is available be regarded as bayesian procedures their construction requires only the repeated maximization of a likelihood and evaluation of the observed information matrix at the maximum and is fast and accurate using usual numerical maximization methods there is a close connexion with the approximations to posterior moments and marginal densities given by tierney kadane 1986 who suggest the same approxima tion as used here but give no detailed results for prediction section 2 of this paper shows how laplace s method for integrals may be applied to a posterior predictive density to yield approximate predictive likelihood section 3 discusses a connection with conditional inference essentially the same approximation

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

localization at large disorder and at extreme energies an elementary derivation the work presents a short proof of localization under the conditions of either strong disorder 0 or extreme energies for a wide class of self adjoint operators with random matrix elements acting inl 2 spaces a prototypical example is the discrete schrodinger operatorh u 0 x v x onz d d 1 withu 0 x a specified background potential and v x generated as random variables the general results apply to operators with replaced by a non local self adjoint operatort whose matrix elements satisfy y t x y s const uniformly inx for somes 1 localization means here that within a specified energy range the spectrum ofh is of the pure point type or equivalently the wave functions do not spread indefinitely under the unitary time evolution generated byh the effect is produced by strong disorder in either the potential or in the off diagonal matrix elementst x y under rapid decay oft x y the corresponding eigenfunctions are also proven to decay exponentially the method is based on resolvent techniques the central technical ideas include the use of low moments of the resolvent kernel i e g e x y s withs small enough 1 to avoid the divergence caused by the distribution s cauchy tails and an effective use of the simple form of the dependence ofg e x y on the individual matrix elements ofh in elucidating the implications of the fundamental equation h e g e x x 0 x x0 this approach simplifies previous derivations of localization results avoiding the small denominator difficulties which have been hitherto encountered in the subject it also yields some new results which include localization under the following sets of conditions i potentials with an inhomogeneous non random partu 0 x ii the bethe lattice iii operators with very slow decay in the off diagonal terms t x y 1 x y d e and iv localization produced by disordered boundary conditions

constructive proof of localization in the anderson tight binding model we prove that for large disorder or near the band tails the spectrum of the anderson tight binding hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues the corresponding eigenfunctions are exponentially well localized these results hold in arbitrary dimension and with probability one in one dimension we recover the result that all states are localized for arbitrary energies and arbitrarily small disorder our techniques extend to other physical systems which exhibit localization phenomena such as infinite systems of coupled harmonic oscillators or random schrodinger operators in the continuum

an infinite dimensional geometric structure on the space of all the probability measures equivalent to a given one let m be the set of all probability densities equivalent to a given reference probability measure this set is thought of as the maximal regular i e with strictly positive densities dominated statistical model for each f m we define 1 a banach space l f with unit ball v f and 2 a mapping s f from a subset u f of m onto v f in such a way that the system s f u f f m is an affine atlas on m moreover each parametric exponential model dominated by is a finite dimensional affine submanifold and each parametric statistical model dominated by with a suitable regularity is a submanifold the global geometric framework given by the manifold structure adds some insight to the so called geometric theory of statistical models in particular the present paper gives some of the developments connected with the fisher information metrics rao and the hilbert bundle introduced by amari

spl alpha parallel prior and its properties it is known that the jeffreys prior plays an important role in statistical inference in this paper we generalize the jeffreys prior from the point of view of information geometry and introduce a one parameter family of prior distributions which we named the spl alpha parallel priors the spl alpha parallel prior is defined as the parallel volume element with respect to the spl alpha connection and coincides with the jeffreys prior when spl alpha 0 further we analyze asymptotic behavior of the various estimators such as the projected bayes estimator the estimator obtained by projecting the bayes predictive density onto the original class of distributions and the minimum description length mdl estimator when the spl alpha parallel prior is used the difference of these estimators from maximum likelihood estimator mle due to the spl alpha prior is shown to be regulated by an invariant vector field of the statistical model although the jeffreys prior always exists the existence of spl alpha parallel prior with spl alpha spl ne 0 is not always guaranteed hence we consider conditions for the existence of the spl alpha parallel prior elucidating the conjugate symmetry in a statistical model

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

game theory maximum entropy minimum discrepancy and robust bayesian decision theory we describe and develop a close relationship between two problems that have customarily been regarded as distinct that of maximizing entropy and that of minimizing worst case expected loss using a formulation grounded in the equilibrium theory of zero sum games between decision maker and nature these two problems are shown to be dual to each other the solution to each providing that to the other although topsoe described this connection for the shannon entropy over 20 years ago it does not appear to be widely known even in that important special case we here generalize this theory to apply to arbitrary decision problems and loss functions we indicate how an appropriate generalized definition of entropy can be associated with such a problem and we show that subject to certain regularity conditions the above mentioned duality continues to apply in this extended context this simultaneously provides a possible rationale for maximizing entropy and a tool for finding robust bayes acts we also describe the essential identity between the problem of maximizing entropy and that of minimizing a related discrepancy or divergence between distributions this leads to an extension to arbitrary discrepancies of a well known minimax theorem for the case of kullback leibler divergence the redundancy capacity theorem of information theory for the important case of families of distributions having certain mean values specified we develop simple sufficient conditions and methods for identifying the desired solutions we use this theory to introduce a new concept of generalized exponential family linked to the specific decision problem under consideration and we demonstrate that this shares many of the properties of standard exponential families finally we show that the existence of an equilibrium in our game can be rephrased in terms of a pythagorean property of the related divergence thus generalizing previously announced results for kullback leibler and bregman divergences

information geometry of generalized bayesian prediction using alpha divergences as loss functions in this paper the methods of information geometry are employed to investigate a generalized bayes rule for prediction taking alpha divergences as the loss functions optimality and asymptotic properties of the generalized bayesian predictive densities are considered we show that the bayesian predictive densities minimize a generalized bayes risk we also find that the asymptotic expansions of the densities are related to the coefficients of the alpha connections of a statistical manifold in addition we discuss the difference between two risk functions of the generalized bayesian predictions based on different priors finally using the non informative priors i e jeffreys and reference priors uniform prior and conjugate prior two examples are presented to illustrate the main results

conditional mean estimation via jump diffusion processes in multiple target tracking recognition a new algorithm is presented for generating the conditional mean estimates of functions of target positions orientations and type in recognition and tracking of an unknown number of targets and target types taking a bayesian approach a posterior measure is defined on the tracking target parameter space by combining a narrowband sensor array manifold model with a high resolution imaging model and a prior based on airplane dynamics the newtonian force equations governing rigid body dynamics are utilized to form the prior density on airplane motion the conditional mean estimates are generated using a random sampling algorithm based on jump diffusion processes for empirically generating mmse estimates of functions of these random target positions orientations and type under the posterior measure results are presented on target tracking and identification from an implementation of the algorithm on a networked silicon graphics workstation and decmpp maspar parallel machine

finite volume fractional moment criteria for anderson localization a technically convenient signature of localization exhibited by discrete operators with random potentials is exponential decay of the fractional moments of the green function within the appropriate energy ranges known implications include spectral localization absence of level repulsion strong form of dynamical localization and a related condition which plays a significant role in the quantization of the hall conductance in two dimensional fermi gases we present a family of finite volume criteria which under some mild restrictions on the distribution of the potential cover the regime where the fractional moment decay condition holds the constructive criteria permit to establish this condition at spectral band edges provided there are sufficient lifshitz tail estimates on the density of states they are also used here to conclude that the fractional moment condition and thus the other manifestations of localization are valid throughout the regime covered by the multiscale analysis in the converse direction the analysis rules out fast power law decay of the green functions at mobility edges

predictive fit for natural exponential families summary the paper examines predictive distributions concentrating on measuring their fit to the true distribution by average kullback leibler divergence the notion of an averaged bootstrap predictive distribution is introduced this predictive distribution is shown to be asymptotically superior to the estimative distribution in terms of average kullbackleibler divergence when the true distribution is in a natural exponential family smallsample results are presented for the poisson and binomial distributions which suggest that the bootstrap distribution performs well in these cases

information measures for object recognition accommodating signature variability this paper presents measures characterizing the information content of remote observations of ground scenes imaged via optical and infrared sensors object recognition is posed in the context of deformable templates the special euclidean group is used to accommodate geometric variation of object pose principal component analysis of object signatures is used to represent and efficiently accommodate variation in object signature due to changes in the thermal state of the object surface mutual information measures which are independent of the recognition system are calculated quantifying both the information gain due to remote observations of the scene and the information loss due to signature variability signature model mismatch is quantitatively examined using the kullback leibler divergence expressions are derived quadratically approximating the posterior conditional entropy on the orthogonal group for high signal to noise ratio it is demonstrated that quadratic modules accurately characterize the posterior entropy for broad ranges of signal to mise ratio information gain in multiple sensor scenarios is quantified and it is demonstrated that the cost of signature uncertainty for the comanche series of flir images collected by the us army night vision electronic sensors directorate is approximately 0 8 bits with an associated near doubling of mean squared error uncertainty in pose

on asymptotic properties of predictive distributions summary second order asymptotic theory of predictive distributions is investigated it is shown that estimative distributions with asymptotically efficient estimators can be improved to predictive distributions that do not belong to the model the model is assumed to be a multidimensional curved exponential family predictive distributions can be constructed by shifting estimative distributions in a direction orthogonal to the model the average kullback leibler divergence from the true distribution to a predictive distribution is represented as the sum of two components one of them depends on the choice of the estimative distribution and the other depends on the shift orthogonal to the model the optimal shift orthogonal to the model is obtained a quantity that can be regarded as the mixture mean curvature of the model in the space of all probability distributions is introduced the difference in average kullback leibler divergence between an estimative distribution and the optimal predictive distribution obtained by shifting it can be regarded as the mixture mean curvature of the model an asymptotic expression for bayesian predictive distributions is also obtained

entropy and equilibrium via games of complexity abstract it is suggested that thermodynamical equilibrium equals game theoretical equilibrium aspects of this thesis are discussed the philosophy is consistent with maximum entropy thinking of jaynes but goes one step deeper by deriving the maximum entropy principle from an underlying game theoretical principle the games introduced are based on measures of complexity entropy is viewed as minimal complexity it is demonstrated that tsallis entropy q entropy and kaniadakis entropy entropy can be obtained in this way based on suitable complexity measures a certain unifying effect is obtained by embedding these measures in a two parameter family of entropy functions

from fixed energy localization analysis to dynamical localization an elementary path we review several techniques initiated by a remarkable work written by spencer j stat phys 51 1009 1019 1988 a quarter of century ago used and further developed in numerous subsequent researches we also describe a fairly general elementary derivation of spectral and strong dynamical anderson localization from the fixed energy analysis of the green s functions on locally finite graphs of polynomial growth obtained either by the multi scale analysis or by the fractional moment method this derivation goes in the same direction as the simon wolf method commun pure appl math 39 75 90 1986 but provides more quantitative estimates can be adapted to multi particle models and combined with a simplified variant of the germinet klein argument commun math phys 222 415 448 2001 results in an elementary proof of strong dynamical localization on arbitrary graphs of polynomial growth

reliability estimation of a n m cold standby redundancy system in a multicomponent stress strength model with generalized half logistic distribution abstract in this paper we study the estimation for the reliability of a multicomponent system named n m cold standby redundancy system based on progressive type ii censoring sample in the system there are n subsystems consisting of m statistically independent distributed strength components and only one of these subsystems works under the impact of stresses at a time and the others remain as standbys whenever the working subsystem fails one from the standbys takes its place the system fails when the entire subsystems fail it is supposed that the underlying distributions of random strength and stress both belong to the generalized half logistic distribution with different shape parameter the reliability of the system is estimated by using both classical and bayesian statistical inference uniformly minimum variance unbiased estimator and maximum likelihood estimator for the reliability of the system are derived under squared error loss function the exact expression of the bayes estimator for the reliability of the system is developed by using the gauss hypergeometric function the asymptotic confidence interval and corresponding coverage probabilities are derived based on both the fisher and the observed information matrices the approximate highest probability density credible interval is constructed by using monte carlo method monte carlo simulations are performed to compare the performances of the proposed reliability estimators a real data set is also analyzed for an illustration of the findings

quantization of multiaspect scattering data target classification and pose estimation in many sensing scenarios the observed scattered waveforms must be quantized for subsequent transmission over a communication channel rate distortion theory plays an important role in defining the bit rate required to achieve a desired distortion the distortion is typically defined in the context of signal reconstruction with the goal of achieving high fidelity synthesis of the compressed data for sensing applications however the objective is often not simply signal reconstruction but classification performance as well other related metrics include target pose estimation we consider multiaspect wave scattering in which classification and pose estimation are performed based on the quantized scattering data moreover rate distortion theory is employed to place bounds on pose estimation performance when both the target identity and pose are unknown a priori it is demonstrated that block coding with bayes vq may yield performance approaching the bound example results are presented for measured acoustic waveforms scattered from underwater elastic targets

exact minimax estimation of the predictive density in sparse gaussian models we consider estimating the predictive density under kullback leibler loss in an l0 sparse gaussian sequence model explicit expressions of the first order minimax risk along with its exact constant asymptotically least favorable priors and optimal predictive density estimates are derived compared to the sparse recovery results involving point estimation of the normal mean new decision theoretic phenomena are seen suboptimal performance of the class of plug in density estimates reflects the predictive nature of the problem and optimal strategies need diversification of the future risk we find that minimax optimal strategies lie outside the gaussian family but can be constructed with threshold predictive density estimates novel minimax techniques involving simultaneous calibration of the sparsity adjustment and the risk diversification mechanisms are used to design optimal predictive density estimates

nonproduct data dependent partitions for mutual information estimation strong consistency and applications a new framework for histogram based mutual information estimation of probability distributions equipped with density functions in rd b rd is presented in this work a general histogram based estimate is proposed considering nonproduct data dependent partitions and sufficient conditions are stipulated to guarantee a strongly consistent estimate for mutual information two emblematic families of density free strongly consistent estimates are derived from this result one based on statistically equivalent blocks the gessaman s partition and the other on a tree structured vector quantization scheme

improved minimax predictive densities under kullback leibler loss let x n p u x i and y n p v y i be independentp dimensional multivariate normal vectors with common unknown mean based on only observing x x we consider the problem of obtaining a predictive density p y x for y that is close to p y as measured by expected kullback leibler loss a natural procedure for this problem is the formal bayes predictive density p u y x under the uniform prior u 1 which is best invariant and minimax we show that any bayes predictive density will be minimax if it is obtained by a prior yielding a marginal that is superharmonic or whose square root is superharmonic this yields wide classes of minimax procedures that dominate p u y x including bayes predictive densities under superharmonic priors fundamental similarities and differences with the parallel theory of estimating a multivariate normal mean under quadratic loss are described

anderson localization and the space time characteristic of continuum states a proof of anderson localization is obtained by ruling out any continuous spectrum on the basis of the space time characteristic of its states

deformed logarithms and entropies by solving a differential functional equation inposed by the maxent principle we obtain a class of two parameter deformed logarithms and construct the corresponding two parameter generalized trace form entropies generalized distributions follow from these generalized entropies in the same fashion as the gaussian distribution follows from the shannon entropy which is a special limiting case of the family we determine the region of parameters where the deformed logarithm conserves the most important properties of the logarithm and show that important existing generalizations of the entropy are included as special cases in this two parameter class

geometry of the q exponential distribution with dependent competing risks and accelerated life testing abstract in the information geometry suggested by amari 1985 and amari et al 1987 a parametric statistical model can be regarded as a differentiable manifold with the parameter space as a coordinate system note that the q exponential distribution plays an important role in tsallis statistics see tsallis 2009 this paper investigates the geometry of the q exponential distribution with dependent competing risks and accelerated life testing alt a copula function based on the q exponential function which can be considered as the generalized gumbel copula is discussed to illustrate the structure of the dependent random variable employing two iterative algorithms simulation results are given to compare the performance of estimations and levels of association under different hybrid progressively censoring schemes hpcss

a note on modified estimative prediction limits and distributions in this paper a modification of the estimative prediction limit is derived for which the coverage probability equals the target value to third order accuracy under ordinary repeated sampling it provides an explicit approximate solution to the equation given by barndorff nielsen cox 1996 which determines an upper prediction limit for an unobserved random variable the corresponding predictive density is specified in a simple closed form and its main properties are emphasised

face recognition the problem of compensating for changes in illumination direction a face recognition system must recognize a face from a novel image despite the variations between images of the same face a common approach to overcoming image variations because of changes in the illumination conditions is to use image representations that are relatively insensitive to these variations examples of such representations are edge maps image intensity derivatives and images convolved with 2d gabor like filters here we present an empirical study that evaluates the sensitivity of these representations to changes in illumination as well as viewpoint and facial expression our findings indicated that none of the representations considered is sufficient by itself to overcome image variations because of a change in the direction of illumination similar results were obtained for changes due to viewpoint and expression image representations that emphasized the horizontal features were found to be less sensitive to changes in the direction of illumination however systems based only on such representations failed to recognize up to 20 percent of the faces in our database humans performed considerably better under the same conditions we discuss possible reasons for this superiority and alternative methods for overcoming illumination effects in recognition

new lower bounds on the self avoiding walk connective constant we give an elementary new method for obtaining rigorous lower bounds on the connective constant for self avoiding walks on the hypercubic lattice d the method is based on loop erasure and restoration and does not require exact enumeration data our bounds are best for highd and in fact agree with the first four terms of the 1 d expansion for the connective constant the bounds are the best to date for dimensionsd 3 but do not produce good results in two dimensions ford 3 4 5 and 6 respectively our lower bound is within 2 4 0 43 0 12 and 0 044 of the value estimated by series extrapolation

on signal representations within the bayes decision framework this work presents new results in the context of minimum probability of error signal representation mpe sr within the bayes decision framework these results justify addressing the mpe sr criterion as a complexity regularized optimization problem demonstrating the empirically well understood trade off between signal representation quality and learning complexity contributions are presented in three folds first the stipulation of conditions that guarantee a formal tradeoff between approximation and estimation errors under sequence of embedded transformations are provided second the use of this tradeoff to formulate the mpe sr as a complexity regularized optimization problem and an approach to address this oracle criterion in practice is given finally formal connections are provided between the mpe sr criterion and two emblematic feature transformation techniques used in pattern recognition the optimal quantization problem of classification trees cart tree pruning algorithms and some versions of fisher linear discriminant analysis lda

a simple predictive density based on the p formula the predictive density proposed by harris 1989 is based on integrating the density for a new observation with respect to the estimated sampling distribution of the maximum likelihood estimator of the unknown parameter this has good properties but is rather complicated to compute even for simple models an approximation to the harris proposal is considered which consists of approximating the sampling distribution of the maximum likelihood estimator of the unknown parameter by barndorff nielsen s 1983 p formula and then using a laplace approximation with o n 1 correction terms for integrating out the parameter the result can generally be expressed in terms of standard likelihood derivatives and takes a quite simple form for exponential families and for location models

nonsubjective priors via predictive relative entropy regret we explore the construction of nonsubjective prior distributions in bayesian statistics via a posterior predictive relative entropy regret criterion we carry out a minimax analysis based on a derived asymptotic predictive loss function and show that this approach to prior construction has a number of attractive features the approach here differs from previous work that uses either prior or posterior relative entropy regret in that we consider predictive performance in relation to alternative nondegenerate prior distributions the theory is illustrated with an analysis of some specific examples

information theory and superefficiency the asymptotic risk of efficient estimators with kullback leibler loss in smoothly parametrized statistical models is k 2n where k is the parameter dimension and n is the sample size under fairly general conditions we given a simple information theoretic proof that the set of parameter values where any arbitrary estimator is superefficient is negligible the proof is based on a result of rissanen that codes have asymptotic redundancy not smaller than k 2 log n except in a set of measure 0

estimability and likelihood inference for generalized linear mixed models using data cloning maximum likelihood estimation for generalized linear mixed models glmm an important class of statistical models with substantial applications in epidemiology medical statistics and many other fields poses significant computational difficulties in this article we use data cloning a simple computational method that exploits advances in bayesian computation in particular the markov chain monte carlo method to obtain maximum likelihood estimators of the parameters in these models this method also leads to a simple estimator of the asymptotic variance of the maximum likelihood estimators determining estimability of the parameters in a mixed model is in general a very difficult problem data cloning provides a simple graphical test to not only check if the full set of parameters is estimable but also and perhaps more importantly if a specified function of the parameters is estimable one of the goals of mixed models is to predict random effects we suggest a frequentist method to obtain predict

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