exotic one parameter semigroups of endomorphisms of a symmetric cone abstract we construct an exotic one parameter semigroup of endomorphisms of a symmetric cone c whose generator is not the sum of a lie group generator and an endomorphism of c the question is motivated by the theory of affine processes on symmetric cones which plays an important role in mathematical finance on the other hand theoretical question that we solve in this paper seems to have been implicitly open even much longer then this motivation suggests

general β jacobi corners process and the gaussian free field we prove that the two dimensional gaussian free field describes the asymptotics of global fluctuations of a multilevel extension of the general jacobi random matrix ensembles our approach is based on the connection of the jacobi ensembles to a degeneration of the macdonald processes that parallels the degeneration of the macdonald polynomials to the heckman opdam hypergeometric functions of type a we also discuss the limit 2015 wiley periodicals inc

efficient sequential designs with binary data abstract a class of sequential designs for estimating the percentiles of a quantal response curve is proposed its updating rule is based on an efficient summary of all of the data available via a parametric model the logit mle version of the proposed designs can be viewed as a natural analog of the robbins monro procedure in the case of binary data it is shown to be asymptotically consistent optimal and nonparametric via its connection with the latter procedure for certain choices of initial designs the proposed method performs very well in a simulation study for sample sizes up to 35 a nonparametric sequential design via the spearman karber estimator for estimating the median is also proposed

a new integral formula for heckman opdam hypergeometric functions abstract we provide harish chandra type formulas for the multivariate bessel functions and heckman opdam hypergeometric functions as representation valued integrals over dressing orbits our expression is the quasi classical limit of the realization of macdonald polynomials as traces of intertwiners of quantum groups given by etingof and kirillov jr in 10 integration over the liouville tori of the gelfand tsetlin integrable system and adjunction for higher calogero moser hamiltonians recovers and gives a new proof of the integral realization over gelfand tsetlin polytopes which appeared in the recent work 4 of borodin and gorin on the jacobi corners ensemble

a hybrid estimator in nonlinear and generalised linear mixed effects models summary a hybrid method that combines laplace s approximation and monte carlo simulations to evaluate integrals in the likelihood function is proposed for estimation of the parameters in nonlinear mixed effects models that assume a normal parametric family for the random effects simulations show that these parametric estimates of fixed effects are close to the nonparametric estimates even though the mixing distribution is far from the assumed normal parametric family an asymptotic theory of this hybrid method for parametric estimation without requiring the true mixing distribution to belong to the assumed parametric family is developed to explain these results this hybrid method and its asymptotic theory are also extended to generalised linear mixed effects models

moment maps at the quantum level we introduce the notion of moment maps for quantum groups acting on their module algebras when the module algebras are quantizations of poisson manifolds we prove that the construction at the quantum level is a quantization of that at the semi classical level we also prove that the corresponding smashed product algebras are quantizations of the semi direct product poisson structures

a note on the existence of the posterior distribution for a class of mixed models for binomial responses summary necessary and sufficient conditions are given for the existence of the posterior distribution of the variance components in a class of mixed models for binomial responses the implications of our results are illustrated through an example

generalized monte carlo significance tests summary simple monte carlo significance testing has many applications particularly in the preliminary analysis of spatial data the method requires the value of the test statistic to be ranked among a random sample of values generated according to the null hypothesis however there are situations in which a sample of values can only be conveniently generated using a markov chain initiated by the observed data so that independence is violated this paper describes two methods that overcome the problem of dependence and allow exact tests to be carried out the methods are applied to the rasch model to the finite lattice ising model and to the testing of association between spatial processes power is discussed in a simple case

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

a crossed random effects modeling approach for estimating diagnostic accuracy from ordinal ratings without a gold standard in diagnostic studies without a gold standard the assumption on the dependence structure of the multiple tests or raters plays an important role in model performance in case of binary disease status both conditional independence and crossed random effects structure have been proposed and their performance investigated less attention has been paid to the situation where the true disease status is ordinal in this paper we propose crossed subject specific and rater specific random effects to account for the dependence structure and assess the robustness of the proposed model to misspecification in the random effects distributions we applied the models to data from the physician reliability study which focuses on assessing the diagnostic accuracy in a population of raters for the staging of endometriosis a gynecological disorder in women using this new methodology we estimate the probability of a correct classification and show that regional experts can more easily classify the intermediate stage than resident physicians

identifiability of models for multiple diagnostic testing in the absence of a gold standard summary we discuss the issue of identifiability of models for multiple dichotomous diagnostic tests in the absence of a gold standard gs test data arise as multinomial or product multinomial counts depending upon the number of populations sampled models are generally posited in terms of population prevalences test sensitivities and specificities and test dependence terms it is commonly believed that if the degrees of freedom in the data meet or exceed the number of parameters in a fitted model then the model is identifiable goodman 1974 biometrika 61 215 231 established that this was not the case a long time ago we discuss currently available models for multiple tests and argue in favor of an extension of a model that was developed by dendukuri and joseph 2001 biometrics 57 158 167 subsequently we further develop goodman s technique and make geometric arguments to give further insight into the nature of models that lack identifiability we present illustrations using simulated and real data

a new criterion for indecomposability of positive maps we give a criterion for a positive mapping on the space of operators on a hilbert space to be indecomposable we show that this criterion can be applied to two families of positive maps these families of maps can then be used to form separability criteria for bipartite quantum states that can detect the entanglement of bound entangled quantum states

construction of 3 3 entangled edge states with positive partial transposes we construct a class of 3 3 entangled edge states with positive partial transposes using indecomposable positive linear maps this class contains several new types of entangled edge states with respect to the range dimensions of themselves and their partial transposes

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

iterative simulation methods abstract the standard methods of generating sample from univariate distributions often become hopelessly inefficient when applied to realizations of stochastic processes iterative methods are not widely known amongst statisticians but some are standard practice in statistical physics and chemistry the methods are surveyed and compared with particular reference to their convergence properties

nonparametric estimation of roc curves in the absence of a gold standard in the evaluation of diagnostic accuracy of tests a gold standard on the disease status is required however in many complex diseases it is impossible or unethical to obtain such a gold standard if an imperfect standard is used the estimated accuracy of the tests would be biased this type of bias is called imperfect gold standard bias in this article we develop a nonparametric maximum likelihood method for estimating roc curves and their areas of ordinal scale tests in the absence of a gold standard our simulation study shows that the proposed estimators for the roc curve areas have good finite sample properties in terms of bias and mean squared error further simulation studies show that our nonparametric approach is comparable to the binormal parametric method and is easier to implement finally we illustrate the application of the proposed method in a real clinical study on assessing the accuracy of seven specific pathologists in detecting carcinoma in situ of the uterine cervix

generalized choi maps in three dimensional matrix algebra we consider a class of positive linear maps in the three dimensional matrix algebra which are generalizations of the positive linear map constructed by choi in the relation with positive semidefinite biquadratic forms we find conditions for which such maps are completely positive completely copositive decomposable and two positive

positive linear maps between matrix algebras which fix diagonals abstract we consider a class of positive linar maps from the n dimensional matrix algebra into itself which fix diagonal entries we show that they are expressed by hadamard products and study their decompositions into the sums of completely positive linear maps and completely copositive linear maps in the three dimensional case we show that every positive linear map in this type is decomposable and give an intrinsic characterization for the positivity of these maps when the involving coefficients are real numbers

a class of generalized positive linear maps on matrix algebras abstract we construct a class of positive linear maps on matrix algebras we find conditions when these maps are atomic decomposable and completely positive we obtain a large class of atomic positive linear maps as applications in quantum information theory we discuss the structural physical approximation and optimality of entanglement witness associated with these maps

gues and queues consider the process d k k 1 2 given by b i being independent standard brownian motions this process describes the limiting behavior near the edge in queues in series totally asymmetric exclusion processes or oriented percolation the problem of finding the distribution of d was posed in gw the main result of this paper is that the process d has the law of the process of the largest eigenvalues of the main minors of an infinite random matrix drawn from gaussian unitary ensemble

cones of positive maps and their duality relations the structure of cones of positive and k positive maps acting on a finite dimensional hilbert space is investigated special emphasis is given to their duality relations to the sets of superpositive and k superpositive maps we characterize k positive and k superpositive maps with regard to their properties under taking compositions a number of results obtained for maps are also rephrased for the corresponding cones of block positive k block positive separable and k entangled operators due to the jamiolkowski choi isomorphism generalizations to a situation where no such simple isomorphism is available are also made employing the idea of mapping cones as a side result to our discussion we show that extreme entanglement witnesses which are optimal should be of special interest in entanglement studies

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

interpretations of some parameter dependent generalizations of classical matrix ensembles two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions pdfs as the parameter is varied one interpolates between the eigenvalue pdf for the superposition of two classical ensembles with orthogonal symmetry and the eigenvalue pdf for a single classical ensemble with unitary symmetry while the other interpolates between a classical ensemble with orthogonal symmetry and a classical ensemble with symplectic symmetry we give interpretations of these pdfs in terms of probabilities associated to the continuous robinson schensted knuth correspondence between matrices with entries chosen from certain exponential distributions and non intersecting lattice paths and in the course of this probability measures on partitions and pairs of partitions are identified the latter are generalized by using macdonald polynomial theory and a particular continuum limit the jacobi limit of the resulting measures is shown to give pdfs related to those appearing in the work of anderson on the selberg integral and also in some classical work of dixon by interpreting anderson s and dixon s work as giving the pdf for the zeros of a certain rational function it is then possible to identify random matrices whose eigenvalue pdfs realize the original parameter dependent pdfs this line of theory allows sampling of the original parameter dependent pdfs their dixon anderson type generalizations and associated marginal distributions from the zeros of certain polynomials defined in terms of random three term recurrences

a series of absolutely indecomposable positive maps in matrix algebras abstract we provide examples of positive maps in m n c n 4 which cannot be decomposed into a sum of a 2 positive map and a 2 copositive map

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

on the convergence of monte carlo maximum likelihood calculations summary monte carlo maximum likelihood for normalized families of distributions can be used for an extremely broad class of models given any family he 0 e 0 of non negative integrable functions maximum likelihood estimates in the family obtained by normalizing the functions to integrate to 1 can be approximated by monte carlo simulation the only regularity conditions being a compactification of the parameter space such that the evaluation maps 0 h0 x remain continuous then with probability 1 the monte carlo approximant to the log likelihood hypoconverges to the exact log likelihood its maximizer converges to the exact maximum likelihood estimate approximations to profile likelihoods hypoconverge to the exact profile and level sets of the approximate likelihood support regions converge to the exact sets in painleve kuratowski set convergence the same results hold when there are missing data if a wald type integrability condition is satisfied asymptotic normality of the monte carlo error and convergence of the monte carlo approximation to the observed fisher information are also shown

constructing positive maps from block matrices positive maps are useful for detecting entanglement in quantum information theory any entangled state can be detected by some positive map in this paper the relation between positive block matrices and completely positive trace preserving maps is characterized consequently a new method for constructing decomposable maps from positive block matrices is derived in addition a method for constructing positive but not completely positive maps from hermitian block matrices is also obtained

a monte carlo method for high dimensional integration a new method for the numerical integration of very high dimensional functions is introduced and implemented based on the metropolis monte carlo algorithm the logarithm of the high dimensional integral is reduced to a 1 dimensional integration of a certain statistical function with respect to a scale parameter over the range of the unit interval the improvement in accuracy is found to be substantial comparing to the conventional crude monte carlo integration several numerical demonstrations are made and variability of the estimates are shown

quantum sl_2 infinite curvature and pitman s 2m x theorem the classical theorem by pitman states that a brownian motion minus twice its running infimum enjoys the markov property on the one hand biane understood that pitman s theorem is intimately related to the representation theory of the quantum group mathcal u q left mathfrak sl 2 right in the so called crystal regime q rightarrow 0 on the other hand bougerol and jeulin showed the appearance of exactly the same pitman transform in the infinite curvature limit r rightarrow infty of a brownian motion on the hyperbolic space mathbb h 3 sl 2 mathbb c su 2 this paper aims at understanding this phenomenon by giving a unifying point of view in order to do so we exhibit a presentation mathcal u q hbar left mathfrak sl 2 right of the jimbo drinfeld quantum group which isolates the role of curvature r and that of the planck constant hbar the simple relationship between parameters is q e r the semi classical limits hbar rightarrow 0 are the poisson lie groups dual to sl 2 mathbb c with varying curvatures r in mathbb r we also construct classical and quantum random walks drawing a full picture which includes biane s quantum walks and the construction of bougerol jeulin taking the curvature parameter r to infinity leads indeed to the crystal regime at the level of representation theory hbar 0 and to the bougerol jeulin construction in the classical world hbar 0 all these results are neatly in accordance with the philosophy of kirillov s orbit method

recursive construction for a class of radial functions i ordinary space a class of spherical functions is studied which can be viewed as the matrix generalization of bessel functions we derive a recursive structure for these functions we show that they are only special cases of more general radial functions which also have a properly generalized recursive structure some explicit results are worked out for the first time we identify a subclass of such radial functions which consist of a finite number of terms only

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

intrinsic autoregressions and related models on the two dimensional lattice summary stationary autoregressions on a two dimensional lattice are generalized to intrinsic models where only increments are assumed to be stationary prediction formulae and the asymptotic behaviour of the semivariogram are derived for parameter estimation we propose an approximate maximum likelihood estimator a generalization of whittle s estimator it is derived also for general intrinsic models

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

on a general class of models for interaction this paper develops a class of probability models for configurations of interacting points in a domain the distributions depend on a function which may be viewed as giving the potential energy of the configurations examples include models for interaction in a spatial region and on lattices and graphs new models in the general class arise naturally an example being a spatial model for points of different categories some general methods including series expansions and a simulation method known from statistical mechanics can be useful for many of these models several applications of this kind are considered and some connections between the models and with the statistical mechanics are explored

estimating the granularity coefficient of a potts markov random field within a markov chain monte carlo algorithm this paper addresses the problem of estimating the potts parameter jointly with the unknown parameters of a bayesian model within a markov chain monte carlo mcmc algorithm standard mcmc methods cannot be applied to this problem because performing inference on requires computing the intractable normalizing constant of the potts model in the proposed mcmc method the estimation of is conducted using a likelihood free metropolis hastings algorithm experimental results obtained for synthetic data show that estimating jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of on the other hand choosing an incorrect value of can degrade estimation performance significantly to illustrate the interest of this method the proposed algorithm is successfully applied to real bidimensional sar and tridimensional ultrasound images

inference for discrete markov fields the simplest nontrivial case abstract markov fields provide a general context for describing the strength and structure of spatial interactions the gibbs markov equivalence theorem preston 1974 parameterizes markov fields via their neighborhood structures yielding exponential families in canonical form likelihood inference is therefore apparently straightforward the requisite normalizing constants however are obstreperous even when asymptotic characterizations can be obtained substantial location errors arise during implementation moreover markov fields can exhibit phase transitions and long range interactions thereby creating identifiability problems these issues are illustrated in the simplest nontrivial case the classical ising model of ferromagnetism

lie poisson structure on some poisson lie groups poisson lie groups appeared in the work of drinfel d see e g drl dr2 as classical objects corresponding to quantum groups going in the other direction we may say that a poisson lie group is a group of symmetries of a phase space that are allowed to twist in a certain sense the symplectic or poisson structure the poisson structure on the group controls this twisting in a precise way quantizing both the phase space and the symmetries one may obtain a quantum group acting on a quantum phase space in recent work lu and ratiu lr used so called standard poisson structures on a compact semisimple lie group k and on its poisson dual k in order to give a new proof of the nonlinear convexity theorem of kostant ko their method is analogous to the famous symplectic proof of the linear convexity theorem given by atiyah a and guillemin and stemnberg gs the nonlinear convexity theorem like the linear one follows from a very general result on convexity of the image of the momentum map a gs however in lr it is applied not to a coadjoint orbit in t but to a symplectic leaf in k the main result of this paper is that the standard poisson structure on the poisson dual k to a compact semisimple poisson lie group k is actually isomorphic to the linear one on t this theorem seems to be related to some facts in the theory of quantum groups namely for generic q the universal enveloping algebra u t and its quantum deformation uq t are isomorphic as algebras though not as coalgebras of course since the quantum version is not cocommutative in particular there is a bijective correspondence between their representations a direct connection between our work and its quantum analogues though is still to be found the present work supplies a positive answer to question 5 1 in lr and strongly depends on that paper to simplify reading we keep the notations of lr wherever possible on one hand but give all necessary definitions on the other our work is also related to du in which the nonlinear convexity theorem is reduced to the linear one by a deformation argument not unlike the one that we use in 5 the paper is organized as follows in 2 we define poisson lie groups discuss

a class of positive atomic maps we construct a new class of positive indecomposable maps in the algebra of d d complex matrices these maps are characterized by the weakest positivity property and for this reason they are called atomic this class provides a new rich family of atomic entanglement witnesses which define an important tool for investigating quantum entanglement it turns out that they are able to detect states with the weakest quantum entanglement

a class of atomic positive linear maps in matrix algebras we find a large class of atomic positive linear maps between n dimensional matrix algebras and study their properties in connection with complete positivity 2 positivity and schwarz inequality

maximum likelihood algorithms for generalized linear mixed models abstract maximum likelihood algorithms are described for generalized linear mixed models i show how to construct a monte carlo version of the em algorithm propose a monte carlo newton raphson algorithm and evaluate and improve the use of importance sampling ideas calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously i also use the newton raphson algorithm as a framework to compare maximum likelihood to the joint maximization or penalized quasi likelihood methods and explain why the latter can perform poorly

conditional likelihood inference under complex ascertainment using data augmentation summary in many applications particularly in genetics samples are drawn under complex ascertainment rules for example families may only be selected for study if two or more siblings have trait values exceeding some threshold the correct likelihood for inference in such situations involves the probabilities of ascertainment and these are frequently intractable a consistent but not fully efficient method of analysis of such studies is proposed the main idea is to augment the data with additional pseudo observations simulated under the ascertainment scheme and to analyse using a conditional likelihood for discrimination between true observations and pseudoobservations ascertainment probabilities cancel in this likelihood the method is illustrated with a simple example involving left truncated failure times

new examples of extremal positive linear maps abstract new families of nonnegative biquadratic forms that have 8 9 or 10 real zeros in p 2 p 2 are constructed these are the first examples with 8 9 or 10 real zeros it is known that nonnegative biquadratic forms with finitely many real zeros can have at most 10 zeros our examples show that the upper bound is obtained such biquadratic forms define positive linear maps on real symmetric 3 3 matrices that are not completely positive our constructions are explicit and moreover we are able to determine which of the examples are extremal we extend the examples to positive maps on complex matrices and find families of extreme rays in the cone of positive maps

multivariate methods in ophthalmology with application to other paired data situations methods are presented for performing multiple regression analyses and multiple logistic regression analyses on ophthalmologic data with normally and binomially distributed outcome variables while accounting for the intraclass correlation between eyes these methods are extended to more general nested data structures where a variable number of subunits are available for each primary unit of analysis as in familial data these methods can also be applied to other types of paired data as in matched studies with a variable matching ratio where one has a continuous outcome variable and wishes to control for other confounding variables while maintaining the matching examples are given of these methods with a group of over 400 patients with retinitis pigmentosa in which spherical refractive error and visual acuity are related to genetic type after the effects of age sex and the presence of cataract have been controlled

a cautionary note on the robustness of latent class models for estimating diagnostic error without a gold standard modeling diagnostic error without a gold standard has been an active area of biostatistical research in a majority of the approaches model based estimates of sensitivity specificity and prevalence are derived from a latent class model in which the latent variable represents an individual s true unobserved disease status for simplicity initial approaches assumed that the diagnostic test results on the same subject were independent given the true disease status i e the conditional independence assumption more recently various authors have proposed approaches for modeling the dependence structure between test results given true disease status this note discusses a potential problem with these approaches namely we show that when the conditional dependence between tests is misspecified estimators of sensitivity specificity and prevalence can be biased importantly we demonstrate that with small numbers of tests likelihood comparisons and other model diagnostics may not be able to distinguish between models with different dependence structures we present asymptotic results that show the generality of the problem further data analysis and simulations demonstrate the practical implications of model misspecification finally we present some guidelines about the use of these models for practitioners

on the sampling theory roundations of item response theory models item response theory it models are now in common use for the analysis of dichotomous item responses this paper examines the sampling theory foundations for statistical inference in these models the discussion includes some history on the stochastic subject versus the random sampling interpretations of the probability in irt models the relationship between three versions of maximum likelihood estimation for irt models estimating versus estimating predictors irt models and loglinear models the identifiability of irt models and the role of robustness and bayesian statistics from the sampling theory perspective

conditional logistic regression models for correlated binary data summary a class of conditional logistic regression models for clustered binary data is considered this includes the polychotomous logistic model of rosner 1984 as a special case properties such as the joint distribution and pairwise odds ratio are investigated a class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach an example on chronic obstructive pulmonary disease among sibs is presented for illustration

pseudolikelihood modeling of multivariate outcomes in developmental toxicology abstract the primary goal of this article is to determine benchmark doses based on the ethylene glycol study which comprises data from a developmental toxicity study in mice because the data involve a vector of malformation indicators a flexible model for multivariate clustered data is required an exponential family model is considered and pseudolikelihood based inferential tools are proposed hence avoiding excessive computational requirements

monte carlo state space likelihoods by weighted posterior kernel density estimation maximum likelihood estimation and likelihood ratio tests for nonlinear non gaussian state space models require numerical integration for likelihood calculations several methods including monte carlo mc expectation maximization mc likelihood ratios direct mc integration and particle filter likelihoods are inefficient for the motivating problem of stage structured population dynamics models in experimental settings an mc kernel likelihood mckl method is presented that estimates classical likelihoods up to a constant by weighted kernel density estimates of bayesian posteriors mckl is derived by using bayesian posteriors as importance sampling densities for unnormalized kernel smoothing integrals mc error and mode bias due to kernel smoothing are discussed and two methods for reducing mode bias are proposed zooming in on the maximum likelihood parameters using a focused prior based on an initial estimate and using a posterior cumulant based approximation of mode bias a simulated example show

indecomposable positive maps in low dimensional matrix algebras abstract we classify a series of positive maps in low dimensional matrix algebras with respect to the degree of indecomposability and provide stronger indecomposable maps in m n we also present a basic result about the atomic property

combining monte carlo and mean field like methods for inference in hidden markov random fields issues involving missing data are typical settings where exact inference is not tractable as soon as nontrivial interactions occur between the missing variables approximations are required and most of them are based either on simulation methods or on deterministic variational methods while variational methods provide fast and reasonable approximate estimates in many scenarios simulation methods offer more consideration of important theoretical issues such as accuracy of the approximation and convergence of the algorithms but at a much higher computational cost in this work we propose a new class of algorithms that combine the main features and advantages of both simulation and deterministic methods and consider applications to inference in hidden markov random fields hmrfs these algorithms can be viewed as stochastic perturbations of variational expectation maximization vem algorithms which are not tractable for hmrf we focus more specifically on one of these perturbations and we prove their almost sure convergence to the same limit set as the limit set of vem in addition experiments on synthetic and real world images show that the algorithm performance is very close and sometimes better than that of other existing simulation based and variational em like algorithms

constrained monte carlo maximum likelihood for dependent data maximum likelihood estimates mles in autologistic models and other exponential family models for dependent data can be calculated with markov chain monte carlo methods the metropolis algorithm or the gibbs sampler which simulate ergodic markov chains having equilibrium distributions in the model from one realization of such a markov chain a monte carlo approximant to the whole likelihood function can be constructed the parameter value if any maximizing this function approximates the mle

sequential monte carlo p values summary the assessment of statistical significance by monte carlo simulation may be costly in computer time this paper looks at a number of ways of calculating exact monte carlo p values by sequential sampling such p values are shown to have properties similar to those obtained by sampling with a fixed sample size both standard and generalized monte carlo procedures are discussed and in particular a sequential method is proposed for dealing with situations in which values can only be conveniently generated using a markov chain conditioned to pass through the observed data

spatial statistics and bayesian computation on wednesday may 6th 1992 professor b w silverman in the chair summary markov chain monte carlo mcmc algorithms such as the gibbs sampler have provided a bayesian inference machine in image analysis and in other areas of spatial statistics for several years founded on the pioneering ideas of ulf grenander more recently the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a markov random field has opened the way to the use of mcmc in general bayesian computation in this paper we trace the early development of mcmc in bayesian inference review some recent computational progress in statistical physics based on the introduction of auxiliary variables and discuss its current and future relevance in bayesian applications we briefly describe a simple mcmc implementation for the bayesian analysis of agricultural field experiments with which we have some practical experience

ginzburg weinstein via gelfand zeitlin let u n be the unitary group and u n the dual of its lie al gebra equipped with the kirillov poisson structure in their 1983 paper guillemin sternberg introduced a densely defined hamil tonian action of a torus of dimension n 1 n 2 on u n with mo ment map given by the gelfand zeitlin coordinates a few years later flaschka ratiu described a similar multiplicative gelfand zeitlin system for the poisson lie group u n by the ginzburg weinstein theorem u n is isomorphic to u n as a poisson manifold flaschka ratiu conjectured that one can choose the ginzburg weinstein diffeomorphism in such a way that it intertwines the linear and nonlinear gelfand zeitlin systems our main result gives a proof of this conjecture and produces a canonical ginzburg weinstein diffeomorphism

likelihood analysis of spatial point patterns summary the likelihood procedure for estimating the pairwise interaction potential function is developed for statistical analysis of homogeneous spatial point patterns approximation methods of the normalizing factor of gibbs canonical distribution are discussed both to estimate a scale parameter and to measure the softness or hardness of repulsive interactions the approximations are useful up to a considerably high density the validity of our procedure is demonstrated by some computer experi ments some real data are analysed