data free inference of the joint distribution of uncertain model parameters a critical problem in accurately estimating uncertainty in model predictions is the lack of details in the literature on the correlation or full joint distribution of uncertain model parameters in this paper we describe a framework and a class of algorithms for analyzing such missing data problems in the setting of bayesian statistics the analysis focuses on the family of posterior distributions consistent with given statistics e g nominal values confidence intervals the combining of consistent distributions is addressed via techniques from the opinion pooling literature the developed approach allows subsequent propagation of uncertainty in model inputs consistent with reported statistics in the absence of data

using relative entropy to find optimal approximations an application to simple fluids abstract we develop a maximum relative entropy formalism to generate optimal approximations to probability distributions the central results consist of a justifying the use of relative entropy as the uniquely natural criterion to select a preferred approximation from within a family of trial parameterized distributions and b to obtain the optimal approximation by marginalizing over parameters using the method of maximum entropy and information geometry as an illustration we apply our method to simple fluids the exact canonical distribution is approximated by that of a fluid of hard spheres the proposed method first determines the preferred value of the hard sphere diameter and then obtains an optimal hard sphere approximation by a suitably weighed average over different hard sphere diameters this leads to a considerable improvement in accounting for the soft core nature of the interatomic potential as a numerical demonstration the radial distribution function and the equation of state for a lennard jones fluid argon are compared with results from molecular dynamics simulations

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

variable selection in semiparametric linear regression with censored data summary we describe two procedures for selecting variables in the semiparametric linear regression model for censored data one procedure penalizes a vector of estimating equations and simultaneously estimates regression coefficients and selects submodels a second proce dure controls systematically the proportion of unimportant variables through forward selection and the addition of pseudorandom variables we explore both rank based statistics and buckley james statistics in the setting proposed and evaluate the performance of all methods through extensive simulation studies and one real data set

maximum entropy and bayesian data analysis entropic prior distributions the problem of assigning probability distributions which reflect the prior information available about experiments is one of the major stumbling blocks in the use of bayesian methods of data analysis in this paper the method of maximum relative entropy me is used to translate the information contained in the known form of the likelihood into a prior distribution for bayesian inference the argument is inspired and guided by intuition gained from the successful use of me methods in statistical mechanics for experiments that cannot be repeated the resulting entropic prior is formally identical with the einstein fluctuation formula for repeatable experiments however the expected value of the entropy of the likelihood turns out to be relevant information that must be included in the analysis the important case of a gaussian likelihood is treated in detail

hardness of approximating the shortest vector problem in lattices let p 1 be any fixed real we show that assuming np n rp there is no polynomial time algorithm that approximates the shortest vector problem svp in e p norm within a constant factor under the stronger assumption np n rtime 2poly log n we show that there is no polynomial time algorithm with approximation ratio 2 log n 1 2 e where n is the dimension of the lattice and e 0 is an arbitrarily small constant we first give a new randomized reduction from closest vector problem cvp to svp that achieves some constant factor hardness the reduction is based on bch codes its advantage is that the svp instances produced by the reduction behave well under the augmented tensor product a new variant of tensor product that we introduce this enables us to boost the hardness factor to 2 log n 1 2 e

gradient descent learning in and out of equilibrium relations between the off thermal equilibrium dynamical process of on line learning and the thermally equilibrated off line learning are studied for potential gradient descent learning the approach of opper to study on line bayesian algorithms is used for potential based or maximum likelihood learning we look at the on line learning algorithm that best approximates the off line algorithm in the sense of least kullback leibler information loss the closest on line algorithm works by updating the weights along the gradient of an effective potential which is different from the parent off line potential a few examples are analyzed and the origin of the potential annealing is discussed

consistent inference of probabilities for reproducible experiments the need for inducing a probability distribution from partial data and the complementary problem of the analysis of an observed distribution in terms of fewer relevant variables occur in many branches of physics for reproducible experiments consistency conditions which must be satisfied by any algorithm for inferring a discrete probability distribution with given averages are formulated the only consistent algorithm is the one leading to the distribution of maximal entropy subject to the given constraints

efficient estimation for the accelerated failure time model the accelerated failure time model provides a natural formulation of the effects of covariates on potentially censored response variable the existing semiparametric estimators are computationally intractable and statistically inefficient in this article we propose an approximate nonparametric maximum likelihood method for the accelerated failure time model with possibly time dependent covariates we estimate the regression parameters by maximizing a kernel smoothed profile likelihood function the maximization can be achieved through conventional gradient based search algorithms the resulting estimators are consistent and asymptotically normal the limiting covariance matrix attains the semiparametric efficiency bound and can be consistently estimated we also provide a consistent estimator for the error distribution extensive simulation studies demonstrate that the asymptotic approximations are accurate in practical situations and the new estimators are considerably more efficient than the existing o

solving low density subset sum problems the subset sum problem is to decide whether or not the 0 l integer programming problem s n i l a i x i m i x i 0 or 1 has a solution where the a i and m are given positive integers this problem is np complete and the difficulty of solving it is the basis of public key cryptosystems of knapsack type an algorithm is proposed that searches for a solution when given an instance of the subset sum problem this algorithm always halts in polynomial time but does not always find a solution when one exists it converts the problem to one of finding a particular short vector v in a lattice and then uses a lattice basis reduction algorithm due to a k lenstra h w lenstra jr and l lovasz to attempt to find v the performance of the proposed algorithm is analyzed let the density d of a subset sum problem be defined by d n log 2 max i a i then for almost all problems of density d d n it is proved that the lattice basis reduction algorithm locates v extensive computational tests of the algorithm suggest that it works for densities d d c n where d c n is a cutoff value that is substantially larger than 1 n this method gives a polynomial time attack on knapsack public key cryptosystems that can be expected to break them if they transmit information at rates below d c n as n

banach lie poisson spaces and reduction the category of banach lie poisson spaces is introduced and studied it is shown that the category of w algebras can be considered as one of its subcategories examples and applications of banach lie poisson spaces to quantization and integration of hamiltonian systems are given the relationship between classical and quantum reduction is discussed

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

jacobi fields on statistical manifolds of negative curvature abstract two entropic dynamical models are considered the geometric structure of the statistical manifolds underlying these models is studied it is found that in both cases the resulting metric manifolds are negatively curved moreover the geodesics on each manifold are described by hyperbolic trajectories a detailed analysis based on the jacobi equation for geodesic spread is used to show that the hyperbolicity of the manifolds leads to chaotic exponential instability a comparison between the two models leads to a relation among statistical curvature stability of geodesics and relative entropy like quantities finally the jacobi vector field intensity and the entropy like quantity are suggested as possible indicators of chaoticity in the ed models due to their similarity to the conventional chaos indicators based on the riemannian geometric approach and the zurek paz criterion of linear entropy growth respectively

on the statistical interpretation of generalized entropies abstract we present a direct generalization of the boltzmann counting method to define a generic form for a generalized entropy this form is based on the probabilities of sequences of a stochastic process usual forms of generalized entropy can be rewritten in our approach and then be reinterpreted on a statistical basis we also discuss the meaning of temperature and the zeroth law of thermodynamics renyi and tsallis entropies are used to illustrate our approach monte carlo simulations of the corresponding stochastic processes are performed and the results corroborate the approach

a general semiparametric hazards regression model efficient estimation and structure selection we consider a general semiparametric hazards regression model that encompasses the cox proportional hazards model and the accelerated failure time model for survival analysis to overcome the nonexistence of the maximum likelihood we derive a kernel smoothed profile likelihood function and prove that the resulting estimates of the regression parameters are consistent and achieve semiparametric efficiency in addition we develop penalized structure selection techniques to determine which covariates constitute the accelerated failure time model and which covariates constitute the proportional hazards model the proposed method is able to estimate the model structure consistently and model parameters efficiently furthermore variance estimation is straightforward the proposed estimation performs well in simulation studies and is applied to the analysis of a real data set

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

reexamination of an information geometric construction of entropic indicators of complexity abstract information geometry and inductive inference methods can be used to model dynamical systems in terms of their probabilistic description on curved statistical manifolds in this article we present a formal conceptual reexamination of the information geometric construction of entropic indicators of complexity for statistical models specifically we present conceptual advances in the interpretation of the information geometric entropy ige a statistical indicator of temporal complexity chaoticity defined on curved statistical manifolds underlying the probabilistic dynamics of physical systems

bracket formulation of diffusion convection equations abstract an abstract diffusion convection equation is introduced it is shown that many well known and experimentally tested time evolution equations of physical systems e g the boltzmann and the enskog kinetic equations and the navier stokes fourier fluid mechanics equations are identical to or well approximated by realizations of the abstract diffusion convection equation the physical content of the abstract diffusion convection equation is compatibility with equilibrium thermodynamics it means that properties of solutions of the abstract diffusion convection equation are mathematical formulations of the experience on which equilibrium thermodynamics is based the requirement that all admissible time evolution equations are realizations of the abstract diffusion convection equation is used to find admissible closures in the bbgky and the maxwell grad hierarchies and admissible constitutive relations in generalized hydrodynamics

an improved lower bound for approximating minimum gcd multiplier in l norm gcdm in this paper we study the inapproximability of the following np complete number theoretic optimization problems introduced by rossner and seifert c rossner j p seifert the complexity of approximate optima for greatest common divisor computations in proceedings of the 2nd international algorithmic number theory symposium ants ii 1996 pp 307 322 given n numbers a 1 a n z find an minimum gcd multiplier for a 1 a n i e a vector x z n with minimum max 1 i n x i satisfying i 1 nx ia i gcd a 1 a n we show that assuming p np it is np hard to approximate the minimum gcd multiplier in norm gcdm within a factor n c l o g l o g n for some constant c 0 where n is the dimension of the given vector this improves on the best previous result the best result so far gave 2 l o g n 1 e factor hardness by rossner and seifert c rossner j p seifert the complexity of approximate optima for greatest common divisor computations in proceedings of the 2nd international algorithmic number theory symposium ants ii 1996 pp 307 322 where e 0 is an arbitrarily small constant

adaptive lasso for cox s proportional hazards model summary we investigate the variable selection problem for cox s proportional hazards model and propose a unified model selection and estimation procedure with desired theoretical properties and computational convenience the new method is based on a penalized log partial likelihood with the adaptively weighted l1 penalty on regression coefficients providing what we call the adaptive lasso estimator the method incorporates different penalties for different coefficients unimportant variables receive larger penalties than important ones so that important variables tend to be retained in the selection process whereas unimportant variables are more likely to be dropped theoretical properties such as consistency and rate of convergence of the estimator are studied we also show that with proper choice of regularization parameters the proposed estimator has the oracle properties the convex optimization nature of the method leads to an efficient algorithm both simulated and real examples show that the method performs competitively

essential equivalence of the general equation for the nonequilibrium reversible irreversible coupling generic and steepest entropy ascent models of dissipation for nonequilibrium thermodynamics by reformulating the steepest entropy ascent sea dynamical model for nonequilibrium thermodynamics in the mathematical language of differential geometry we compare it with the primitive formulation of the general equation for the nonequilibrium reversible irreversible coupling generic model and discuss the main technical differences of the two approaches in both dynamical models the description of dissipation is of the entropy gradient type sea focuses only on the dissipative i e entropy generating component of the time evolution chooses a sub riemannian metric tensor as dissipative structure and uses the local entropy density field as potential generic emphasizes the coupling between the dissipative and nondissipative components of the time evolution chooses two compatible degenerate structures poisson and degenerate co riemannian and uses the global energy and entropy functionals as potentials as an illustration we rewrite the known generic formulation of the boltzmann equation in terms of the square root of the distribution function adopted by the sea formulation we then provide a formal proof that in more general frameworks whenever all degeneracies in the generic framework are related to conservation laws the sea and generic models of the dissipative component of the dynamics are essentially interchangeable provided of course they assume the same kinematics as part of the discussion we note that equipping the dissipative structure of generic with the leibniz identity makes it automatically sea on metric leaves

quantifying the complexity of geodesic paths on curved statistical manifolds through information geometric entropies and jacobi fields abstract we characterize the complexity of geodesic paths on a curved statistical manifold m s through the asymptotic computation of the information geometric complexity v m s and the jacobi vector field intensity j m s the manifold m s is a 2 l dimensional gaussian model reproduced by an appropriate embedding in a larger 4 l dimensional gaussian manifold and endowed with a fisher rao information metric g with non trivial off diagonal terms these terms emerge due to the presence of a correlational structure embedding constraints among the statistical variables on the larger manifold and are characterized by macroscopic correlational coefficients r k first we observe a power law decay of the information geometric complexity at a rate determined by the coefficients r k and conclude that the non trivial off diagonal terms lead to the emergence of an asymptotic information geometric compression of the explored macrostates on m s finally we observe that the presence of such embedding constraints leads to an attenuation of the asymptotic exponential divergence of the jacobi vector field intensity

estimation in a linear regression model with censored data we consider the semiparametric linear regression model with censored data and with unknown error distribution we describe estimation equations of the buckley james type that admit n consistent and asymptotically normal solutions the derived estimator is efficient at a particular error distribution we show the equivalence between this type of estimator and an estimator based on a linear rank test suggested by tsiatis an extension to an estimator that is efficient everywhere is discussed

beyond boltzmann gibbs statistics maximum entropy hyperensembles out of equilibrium what is the best description that we can construct of a thermodynamic system that is not in equilibrium given only one or a few extra parameters over and above those needed for a description of the same system at equilibrium here we argue the most appropriate additional parameter is the nonequilibrium entropy of the system moreover we should not attempt to estimate the probability distribution of the system directly but rather the metaprobability or hyperensemble that the system is described by a particular probability distribution the result is an entropic distribution with two parameters one a nonequilibrium temperature and the other a measure of distance from equilibrium this dispersion parameter smoothly interpolates between certainty of a canonical distribution at equilibrium and great uncertainty as to the probability distribution as we move away from equilibrium we deduce that in general large rare fluctuations become far more common as we move away from equilibrium

penalized estimating functions and variable selection in semiparametric regression models we propose a general strategy for variable selection in semiparametric regression models by penalizing appropriate estimating functions important applications include semiparametric linear regression with censored responses and semiparametric regression with missing predictors unlike the existing penalized maximum likelihood estimators the proposed penalized estimating functions may not pertain to the derivatives of any objective functions and may be discrete in the regression coefficients we establish a general asymptotic theory for penalized estimating functions and present suitable numerical algorithms to implement the proposed estimators in addition we develop a resampling technique to estimate the variances of the estimated regression coefficients when the asymptotic variances cannot be evaluated directly simulation studies demonstrate that the proposed methods perform well in variable selection and variance estimation we illustrate our methods using data from the paul coverdell stroke registry

multigrid priors for a bayesian approach to fmri we introduce multigrid priors to construct a bayesian inspired method to asses brain activity in functional magnetic resonance imaging fmri a sequence of different scale grids is constructed over the image starting from the finest scale coarse grain data variables are sequentially defined for each scale then we move back to finer scales determining for each coarse scale a set of posterior probabilities the posterior on a coarse scale is used as the prior for activity at the next finer scale to test the method we use a linear model with a given hemodynamic response function to construct the likelihood we apply the method both to real and simulated data of a boxcar experiment to measure the number of errors we impose a decision to determine activity by setting a threshold on the posterior receiver operating characteristic roc curves are used to study the dependence on threshold and on a few hyperparameters in the relation between specificity and sensitivity we also study the deterioration of the results for real data under information loss this is done by decreasing the number of images in each period and also by decreasing the signal to noise ratio and compare the robustness to other methods

approximating svp to within almost polynomial factors is np hard abstract we show svp and cvp to be np hard to approximate to within n c log log n for some constant c 0 we show a direct reduction from sat to these problems that combines ideas from arora et al proc 34th ieee symp on foundations of computer science 1993 p 724 and dinur et al approximating cvp to within almost polynomial factors is np hard manuscript 1999 along with some modifications our result is obtained without relying on the pcp characterization of np although some of our techniques are derived from the proof of the pcp characterization itself stoc acm symposium on theory of computing stoc 1999

variable selection for proportional odds model in this paper we study the problem of variable selection for the proportional odds model which is a useful alternative to the proportional hazards model and might be appropriate when the proportional hazards assumption is not satisfied we propose to fit the proportional odds model by maximizing the marginal likelihood subject to a shrinkage type penalty which encourages sparse solutions and hence facilitates the process of variable selection two types of shrinkage penalties are considered the lasso and the adaptive lasso alasso penalty in the alasso penalty different weights are imposed on different coefficients such that important variables are more protectively retained in the final model while unimportant ones are more likely to be shrunk to zeros we further provide an efficient computation algorithm to implement the proposed methods and demonstrate their performance through simulation studies and an application to real data numerical results indicate that both methods can produce accurate and interpretable models and the alasso tends to work better than the usual lasso

on a general class of semiparametric hazards regression models a general class of semiparametric hazards regression models for survival data is proposed and studied this general class includes some popular classes of models as subclasses such as cox s proportional hazards model the accelerated failure time model and a recently proposed class of models called the accelerated hazards model in the general class of models a covariate s effect is identified as having two separate components namely a time scale change on hazard progression and a relative hazards ratio the new model is flexible in modelling survival data and may yield more accurate prediction of an individual s survival process by way of the nested structure that includes the proportional hazards model the accelerated failure time model and the accelerated hazards model the general class of models may provide a numerical tool for determining which of them is more appropriate for a given dataset

tuning parameter selectors for the smoothly clipped absolute deviation method summary the penalized least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method it not only automatically and consistently selects the important variables but also produces estimators which are as efficient as the oracle estimator however these attractive features depend on appropriate choice of the tuning parameter we show that the commonly used generalized crossvalidation cannot select the tuning parameter satisfactorily with a nonignorable overfitting effect in the resulting model in addition we propose a bic tuning parameter selector which is shown to be able to identify the true model consistently simulation studies are presented to support theoretical findings and an empirical example is given to illustrate its use in the female labor supply data

spatial extended hazard model with application to prostate cancer survival summary this article develops a bayesian semiparametric approach to the extended hazard model with generalization to high dimensional spatially grouped data county level spatial correlation is accommodated marginally through the normal transformation model of li and lin 2006 journal of the american statistical association 101 591 603 using a correlation structure implied by an intrinsic conditionally autoregressive prior efficient markov chain monte carlo algorithms are developed especially applicable to fitting very large highly censored areal survival data sets per variable tests for proportional hazards accelerated failure time and accelerated hazards are efficiently carried out with and without spatial correlation through bayes factors the resulting reduced interpretable spatial models can fit significantly better than a standard additive cox model with spatial frailties

generalization of the dynamical lack of fit reduction from generic to generic the lack of fit statistical reduction developed and formulated first by bruce turkington is a general method taking liouville equation for probability density detailed level and transforming it to reduced dynamics of projected quantities less detailed level in this paper the method is generalized the hamiltonian liouville equation is replaced by an arbitrary hamiltonian evolution combined with gradient dynamics generic the boltzmann entropy is replaced by an arbitrary entropy and the kinetic energy by an arbitrary energy the gradient part is a generalized gradient dynamics generated by a dissipation potential the reduced evolution of the projected state variables is shown to preserve the generic structure of the original detailed level evolution the dissipation potential is obtained by solving a hamilton jacobi equation in summary the lack of fit reduction can start with generic and obtain generic for the reduced state variables