nonlocality of symmetric states in this letter we study the nonlocal properties of permutation symmetric states of n qubits we show that all these states are nonlocal via an extended version of the hardy paradox and associated inequalities natural extensions of both the paradoxes and the inequalities are developed which relate different entanglement classes to different nonlocal features belonging to a given entanglement class will guarantee the violation of associated bell inequalities which see the persistence of correlations to subsets of players whereas there are states outside that class which do not violate

entanglement in the symmetric sector of n qubits we discuss the entanglement properties of symmetric states of n qubits the majorana representation maps a generic such state into a system of n points on a sphere entanglement invariants either under local unitaries lu or stochastic local operations and classical communication slocc can then be addressed in terms of the relative positions of the majorana points in the lu case an overcomplete set of invariants can be built from the inner product of the radial vectors pointing to these points this is detailed for the well documented three qubits case in the slocc case a cross ratio of related mobius transformations are shown to play a central role exemplified here for four qubits finally as a side result we also analyze the manifold of maximally entangled 3 qubit state both in the symmetric and generic case

two element by element iterative solutions for shallow water equations in this paper we apply the generalized taylor galerkin finite element model to simulate bore wave propagation in a domain of two dimensions for stability and accuracy reasons we generalize the model through the introduction of four free parameters one set of parameters is rigorously determined to obtain the high order finite element solution the other set of free parameters is determined from the underlying discrete maximum principle to obtain the monotonic solutions the resulting two models are used in combination through the flux correct transport technique of zalesak thereby constructing a finite element model which has the ability to capture hydraulic discontinuities in addition this paper highlights the implementation of two krylov subspace iterative solvers namely the bi conjugate gradient stabilized bi cgstab and the generalized minimum residual gmres methods for the sake of comparison the multifrontal direct solver is also considered the performance characteristics of the investigated solvers are assessed using results of a standard test widely used as a benchmark in hydraulic modeling based on numerical results it is shown that the present finite element method can render the technique suitable for solving shallow water equations with sharply varying solution profiles also the gmres solver is shown to have a much better convergence rate than the bi cgstab solver thereby saving much computing time compared to the multifrontal solver

algorithms for optimal discontinuous piecewise linear and constant l 2 fits to continuous functions with adjustable nodes in one and two dimensions in this paper a direct variational approach with nonstandard variations is used to generate algorithms to determine optimal discontinuous piecewise linear and piecewise constant l2 fits to a continuous function of one or two variables with adjustable nodes in the one variable case the algorithm is fast and robust the mesh cannot tangle and the resulting fits are continuous a e in the two variable case on an adjustable triangular grid the algorithm is less robust but gives good results for particular functions possessing a single steep feature the extension to higher dimensions is straightforward

on parametric density estimation summary the paper makes a critical assessment of aitchison s criterion of density estimation it seems not to satisfy certain intuitive requirements a new criterion based on decisions theoretic considerations is introduced it is shown through examples that the judgement about the choice of density estimates is seriously dependent on the criterion chosen some other density estimates are introduced which look similar to bayesian predictive density estimates without using a prior distribution

a self excited threshold autoregressive state space model for menstrual cycles forecasting menstruation and identifying within cycle stages based on basal body temperature the menstrual cycle is divided into hypothermic and hyperthermic phases based on the periodic shift in the basal body temperature bbt reflecting events occurring in the ovary in the present study we proposed a state space model that explicitly incorporates the biphasic nature of the menstrual cycle in which the probability density distributions for the advancement of the menstrual phase and that for the bbt switch depending on a latent state variable our model derives the predictive distribution of the day of the next menstruation onset that is adaptively adjusted by accommodating new observations of the bbt sequentially it also enables us to obtain conditional probabilities of the woman being in the early or late stages of the cycle which can be used to identify the duration of hypothermic and hyperthermic phases possibly as well as the day of ovulation by applying the model to real bbt and menstruation data we show that the proposed model can properly capture the biphasic characteristics of menstrual cycles providing a good prediction of the menstruation onset in a wide range of age groups the application of the proposed model to a large data set containing 25 622 cycles provided by 3533 women further highlighted the between age differences in the population characteristics of menstrual cycles suggesting its wide applicability

approximate random variate generation from infinitely divisible distributions with applications to bayesian inference summary stochastic processes with independent increments play a central role in bayesian nonparametric inference the distributions of the increments of these processes aside from fixed points of discontinuity are infinitely divisible and their laplace and or fourier transforms in the levy representation are usually known conventional bayesian inference in this context has been limited largely to providing point estimates of the random quantities of interest although markov chain monte carlo methods have been used to obtain a fuller analysis in the context of dirichlet process priors in this paper we propose and implement a general method for simulating infinitely divisible random variates when their fourier or laplace transforms are available in the levy representation theoretical justification is established by proving a convergence theorem that is a sampling form of a classical theorem in probability the results provide a method for implementing bayesian nonparametric inference by using a wide range of stochastic processes as priors

a wavelet or lifting scheme based imputation method summary the paper proposes a new approach to imputation using the expected sparse representation of a surface in a wavelet or lifting scheme basis our method incorporates a bayesian mixture prior for these wavelet coefficients into a gibbs sampler to generate a complete posterior distribution for the variable of interest intuitively the estimator operates by borrowing strength from those observed neighbouring values to impute at the unobserved sites we demonstrate the strong performance of our estimator in both one and two dimensional imputation problems where we also compare its application with the standard imputation techniques of kriging and thin plate splines

high resolution finite element analysis of shallow water equations in two dimensions abstract we present in this study the taylor galerkin finite element model to stimulate shallow water equations for bore wave propagation in a domain of two dimensions to provide the necessary precision for the prediction of a sharply varying solution profile the generalized taylor galerkin finite element model is constructed through introduction of four parameters this paper also presents the fundamental theory behind the choice of free parameters one set of parameters is theoretically determined to obtain the high order accurate taylor galerkin finite element model the other set of free parameters is determined using the underlying discrete maximum principle to obtain the low order monotonic taylor galerkin finite element model theoretical study reveals that the higher order scheme exhibits dispersive errors near the discontinuity while lower order scheme dissipates the discontinuity a scheme which has a high resolution shock capturing ability as a built in feature is thus needed in the present study notice that lumping of the mass matrix equations is invoked in the low order scheme to allow simulation of the hydraulic problem with discontinuities we check the prediction accuracy against suitable test problems preferably ones for which exact solutions are available based on numerical results it is concluded that the taylor galerkin flux corrected transport tg fct finite element method can render the technique suitable for solving shallow water equations with sharply varying solution profiles

nonparametric bayesian bioassay with prior constraints on the shape of the potency curve summary we consider the problem of implementing nonparametric bayesian analysis of bioassay problems when the prior constrains the form of the potency curve for example to be convex concave or ogive sampling based approaches to calculating posterior features of interest are detailed and illustrated extensions to prior constraints on hazard rates are outlined

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

bayesian nonparametric estimation via gibbs sampling for coherent systems with redundancy we consider a coherent system s consisting of m independent components for which we do not know the distributions of the components lifelengths if we know the structure function of the system then we can estimate the distribution of the system lifelength by estimating the distributions of the lifelengths of the individual components suppose that we can collect data under the autopsy model wherein a system is run until a failure occurs and then the status functioning or dead of each component is obtained this test is repeated n times the autopsy statistics consist of the age of the system at the time of breakdown and the set of parts that are dead by the time of breakdown we develop a nonparametric bayesian estimate of the distributions of the component lifelengths and then use this to obtain an estimate of the distribution of the lifelength of the system the procedure is applicable to machine test settings wherein the machines have redundant designs a parametric procedure is also given

modeling conception as an aggregated bernoulli outcome with latent variables via the em algorithm we describe a general method for analyzing aggregated bernoulli outcomes the research is motivated by an epidemiological reproductive study where the outcome was whether pregnancy was detected in a woman s particular menstrual cycle and the bernoulli trials corresponded to days with intercourse during the cycle each cycle is either viable or not i e is or is not susceptible to conception we develop an em algorithm approach to maximizing the observed data pseudo likelihood based on a set of unobservable latent outcomes linked to the specific days with intercourse this method is flexible in that it allows one to model effect of covariates on the susceptibility factor and on the latent outcomes application of the method to fertility studies enables one to investigate covariates with a long term or transient effect on the daily conception probability a complication is that most couples contribute more than one cycle in a prospective study a generalized estimating equation approach adjusts for the dependency among outcomes within individual couples the method can be applied in any setting where dependency among bernoulli trials is induced by a susceptibility factor and the trial outcomes are only observable in the aggregate

a coupling regeneration scheme for diagnosing convergence in markov chain monte carlo algorithms abstract here i propose a convergence diagnostic for markov chain monte carlo mcmc algorithms based on couplings of a markov chain with an auxiliary chain that is periodically restarted from a fixed parameter value the diagnostic provides a mechanism for estimating the specific constants governing the rate of convergence of geometrically and uniformly ergodic chains and provides a lower bound on the effective sample size of a mcmc run it also provides a simple procedure for obtaining what is with high probability an independent sample from the stationary distribution

bayesian forecasting of multinomial time series through conditionally gaussian dynamic models abstract we consider inference in the class of conditionally gaussian dynamic models for nonnormal multivariate time series in such models data are represented as drawn from nonnormal sampling distributions whose parameters are related both through time and hierarchically across several multivariate series a key example the main focus here is time series of multinomial observations a common occurrence in sociological and demographic studies involving categorical count data however we present this development in a more general setting as the resulting methods apply beyond the multinomial context we discuss inference in the proposed model class via a posterior simulation scheme based on appropriate modifications of existing markov chain monte carlo algorithms for normal dynamic linear models and including metropolis hastings components we develop an analysis of time series of flows of students in the italian secondary education system as an illustration of the models and methods

antithetic acceleration of monte carlo integration in bayesian inference abstract it is proposed to sample antithetically rather than randomly from the posterior density in bayesian inference using monte carlo integration conditions are established under which the number of replications required with antithetic sampling relative to the number required with random sampling is inversely proportional to sample size as sample size increases the result is illustrated in an experiment using a bivariate vector autoregression

a quasirandom approach to integration in bayesian statistics on passe en revue la theorie existante et on introduit de nouveaux criteres d identification de suites quasi aleatoires on suggere des extensions des regles d integration de base

outperforming the gibbs sampler empirical estimator for nearest neighbor random fields given a markov chain sampling scheme does the standard empirical estimator make best use of the data we show that this is not so and construct better estimators we restrict attention to nearest neighbor random fields and to gibbs samplers with deterministic sweep but our approach applies to any sampler that uses reversible variable at a time updating with deterministic sweep the structure of the transition distribution of the sampler is exploited to construct further empirical estimators that are combined with the standard empirical estimator to reduce asymptotic variance the extra computational cost is negligible when the random field is spatially homogeneous symmetrizations of our estimator lead to further variance reduction the performance of the estimators is evaluated in a simulation study of the ising model

potential for bias in estimating human fecundability parameters a comparison of statistical models fecundability studies where couples attempting pregnancy subject to failure conception one time in each menstrual cycle present a natural discrete failure time scenario because the biologic capacity to conceive varies among couples in the population a complication arises in choosing a method of analysis related to the fact that the maximum follow up time can vary from study to study and follow up time could potentially have different effects on parameters based on different approaches to modelling traditional development in fertility studies has been based on an implicit assumption that binary outcomes for different menstrual cycles are mutually independent we contrast traditional models to a random effects model where cycle viability is modelled as subject specific we clarify the interpretations for different parameters from different models we show that the traditional approach yields some regression parameters that depend on follow up time limiting the generalizability of inferences based on this analytic approach by contrast the subject specific model consistently estimates parameters of interest if the underlying distribution is properly specified data from a fecundability study carried out in north carolina serves to illustrate these points

natural exponential families with quadratic variance functions statistical theory the normal poisson gamma binomial negative binomial and nefghs distributions are the six univariate natural exponential families nef with quadratic variance functions qvf this sequel to morris 1982 treats certain statistical topics that can be handled within this unified nef qvf formulation including unbiased estimation bhattacharyya and cramer rao lower bounds conditional distributions and moments quadratic regression conjugate prior distributions moments of conjugate priors and posterior distributions empirical bayes and g 2 minimax marginal distributions and their moments parametric empirical bayes and characterizations

modeling human fertility in the presence of measurement error the probability of conception in a given menstrual cycle is closely related to the timing of intercourse relative to ovulation although commonly used markers of time of ovulation are known to be error prone most fertility models assume the day of ovulation is measured without error we develop a mixture model that allows the day to be misspecified we assume that the measurement errors are i i d across menstrual cycles heterogeneity among couples in the per cycle likelihood of conception is accounted for using a beta mixture model bayesian estimation is straightforward using markov chain monte carlo techniques the methods are applied to a prospective study of couples at risk of pregnancy in the absence of validation data or multiple independent markers of ovulation the identifiability of the measurement error distribution depends on the assumed model thus the results of studies relating the timing of intercourse to the probability of conception should be interpreted cautiously

econometric illustrations of novel numerical integration strategies for bayesian inference abstract recent progress with numerical techniques for implementing bayesian methods for irregular multi parameter likelihoods is reviewed and illustrated with two econometric examples the numerical integration strategies involve novel iterative adaptive uses of cartesian product and spherical rule quadrature formulae together with importance sampling techniques

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

genuinely multidimensional upwinding for the 2d shallow water equations a multidimensional upwinding technique is applied to the simulation of 2d shallow water flows it is adapted from fluctuation splitting methods recently proposed for the solution of the euler system of equations on unstructured triangular grids the basis of the numerical method is stated and the particular adaptation to the shallow water system is described numerical results of interest to hydraulic engineers are presented despite the complexities advantages related to the use of a discretisation based on triangles would seem to make the schemes competitive with those currently in use

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

parameter and state model reduction for large scale statistical inverse problems a greedy algorithm for the construction of a reduced model with reduction in both parameter and state is developed for an efficient solution of statistical inverse problems governed by partial differential equations with distributed parameters large scale models are too costly to evaluate repeatedly as is required in the statistical setting furthermore these models often have high dimensional parametric input spaces which compounds the difficulty of effectively exploring the uncertainty space we simultaneously address both challenges by constructing a projection based reduced model that accepts low dimensional parameter inputs and whose model evaluations are inexpensive the associated parameter and state bases are obtained through a greedy procedure that targets the governing equations model outputs and prior information the methodology and results are presented for groundwater inverse problems in one and two dimensions

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

screening based on the risk of cancer calculation from bayesian hierarchical changepoint and mixture models of longitudinal markers the standard approach to early detection of disease with a quantitative marker is to set a population based fixed reference level for making further individual screening or referral decisions for many types of disease including prostate and ovarian cancer additional information is contained in the subject specific temporal behavior of the marker which exhibits a characteristic alteration early in the course of the disease in this article we derive a bayesian approach to screening based on calculation of the posterior probability of disease given longitudinal marker levels the method is motivated by a randomized ovarian cancer screening trial in the united kingdom comprising 22 000 women screened over 4 years with an additional 5 years of follow up on average levels of the antigen ca125 were recorded annually in the screened arm ca125 profiles of cases and controls from the u k trial are modeled using hierarchical changepoint and mixture models posterior distributions are calculated using markov

application of conservative residual distribution schemes to the solution of the shallow water equations on unstructured meshes we consider the numerical solution of the shallow water equations on unstructured grids we focus on flows over wet areas the extension to the case of dry bed will be reported elsewhere the shallow water equations fall into the category of systems of conservation laws which can be symmetrized thanks to the existence of a mathematical entropy coinciding in this case with the total energy our aim is to show the application of a particular class of conservative residual distribution rd schemes to the discretization of the shallow water equations and to analyze their discrete accuracy and stability properties we give a review of conservative rd schemes showing relations between different approaches previously published and recall l stability and accuracy criteria characterizing the schemes in particular the accuracy of the rd method in presence of source terms is analyzed and conditions to construct rth order discretizations on irregular triangular grids are proved it is shown that the rd approach gives a natural way of obtaining high order discretizations which moreover preserves exactly the steady lake at rest solution independently on mesh topology nature of the variation of the bottom and polynomial order of interpolation used for the unknowns we also consider more general analytical solutions which are less investigated from the numerical view point on irregular grids linearity preserving rd schemes yield a truly second order approximation we also sketch a strategy to achieve discretizations which preserve exactly some of these solutions numerical results on steady and time dependent problems involving smooth and non smooth variations of the bottom topology show very promising features of the approach

conservative upwind difference schemes for the shallow water equations abstract a study of a number of current numerical schemes for the shallow water equations leads to the establishment of relationships between these schemes further analysis then suggests new formulations of the schemes as well as an alternative scheme having the same key properties

bayesian nonparametric modeling using mixtures of triangular distributions nonparametric modeling is an indispensable tool in many applications and its formulation in an hierarchical bayesian context using the entire posterior distribution rather than particular expectations increases its flexibility in this article the focus is on nonparametric estimation through a mixture of triangular distributions the optimality of this methodology is addressed and bounds on the accuracy of this approximation are derived although our approach is more widely applicable we focus for simplicity on estimation of a monotone nondecreasing regression on 0 1 with additive error effectively approximating the function of interest by a function having a piecewise linear derivative computationally accessible methods of estimation are described through an amalgamation of existing markov chain monte carlo algorithms simulations and examples illustrate the approach

the beta geometric distribution applied to comparative fecundability studies a convenient measure of fecundability is time number of menstrual cycles required to achieve pregnancy couples attempting pregnancy are heterogeneous in their per cycle probability of success if success probabilities vary among couples according to a beta distribution then cycles to pregnancy will have a beta geometric distribution the likelihood ratio test can thus be employed in studies of exposures that may impair fecundability covariates are incorporated in a natural way the model is illustrated by applying it to data on cycles to pregnancy in smokers and nonsmokers with adjustment for covariates summary in fre excerpt

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

measurement error instrumental variables and corrections for attenuation with applications to meta analyses macmahon et al present a meta analysis of the effect of blood pressure on coronary heart disease as well as new methods for estimation in measurement error models for the case when a replicate or second measurement is made of the fallible predictor the correction for attenuation used by these authors is compared to others already existing in the literature as well as to a new instrumental variable method the assumptions justifying the various methods are examined and their efficiencies are studied via simulation compared to the methods we discuss the method of macmahon et al may have bias in some circumstances because it does not take into account i possible correlations among the predictors within a study ii possible bias in the second measurement or iii possibly differing marginal distributions of the predictors or measurement errors across studies a unifying asymptotic theory using estimating equations is also presented

bayesian modeling of the level and duration of fertility in the menstrual cycle time to pregnancy studies that identify ovulation days and collect daily intercourse data can be used to estimate the day specific probabilities of conception given intercourse on a single day relative to ovulation in this article a bayesian semiparametric model is described for flexibly characterizing covariate effects and heterogeneity among couples in daily fecundability the proposed model is characterized by the timing of the most fertile day of the cycle relative to ovulation by the probability of conception due to intercourse on the most fertile day and by the ratios of the daily conception probabilities for other days of the cycle relative to this peak probability the ratios are assumed to be increasing in time to the peak and decreasing thereafter generalized linear mixed models are used to incorporate covariate and couple specific effects on the peak probability and on the day specific ratios a markov chain monte carlo algorithm is described for posterior estimation and the methods are illustrated through application to caffeine data from a north carolina pregnancy study

a sample reuse method for accurate parametric empirical bayes confidence intervals abstract parametric empirical bayes methods of point estimation for a vector of unknown parameters date to the landmark paper of james and stein 1961 the usual approach is to use the mean of the estimated posterior distribution of each parameter where the estimation of the prior parameters hyperparameters is accomplished through the marginal distribution of the data while point estimates computed this way usually perform well interval estimates based on the estimated posterior called naive eb intervals are not they fail to account for the variability in the estimation of the hyperparameters generally resulting in sub nominal coverage probability in the eb sense defined in morris 1983a in this paper we extend the work of carlin and gelfand 1989 who proposed a conditional bias correction method for developing eb intervals which corrects the deficiencies in the naive intervals we show how bias correction can be implemented in general via a type iii parametric bootstrap procedure a sample reuse method first employed by laird and louis 1987

unsteady free surface flow simulation over complex topography with a multidimensional upwind technique in the context of numerical techniques for solving unsteady free surface problems finite element and finite volume approximations are widely used a class of upwind methods which attempts to model the equations in a genuinely multidimensional manner has been recently introduced as an alternative multidimensional upwind schemes mus were developed initially for the approximation of steady state solutions of the two dimensional euler equations on unstructured grids although they can be applicable to any system of hyperbolic conservation laws such as the shallow water equations the formal analogy between the two systems of equations is useful for simple cases however in practical applications of interest in hydraulics complex geometries and bottom slope variation can lead to important numerical errors produced by an inadequate source term discretization this problem has been analyzed and in this work the necessity of a multidimensional upwind discretization of the source terms is justified the basis of the numerical method is stated and the particular adaptation to unsteady shallow water flows over irregular geometry is described as test cases laboratory experimental data are used together with academic tests for validation

conservative upwind difference schemes for the euler equations abstract in a recent paper 1 a number of numerical schemes for the shallow water equations based on a conservative linearization are analyzed in particular it is established that the schemes are related through the use of a source term in this paper this technique is applied to the euler equations and further analysis suggests a new formulation of an existing scheme having the same key properties

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

statistical inference in the multinomial multiperiod probit model abstract statistical inference in multinomial multiperiod probit models has been hindered in the past by the high dimensional numerical integrations necessary to form the likelihood functions posterior distributions or moment conditions in these models we describe three alternative estimators implemented using simulation based approaches to inference that circumvent the integration problem posterior means computed using gibbs sampling and data augmentation gibbs simulated maximum likelihood sml estimation using the ghk probability simulator and method of simulated moment msm estimation using ghk we perform a set of monte carlo experiments to compare the sampling distributions of these estimators although all three estimators perform reasonably well some important differences emerge our most important finding is that holding simulation size fixed the relative and absolute performance of the classical methods especially sml gets worse when serial correlation in disturbances is strong in data sets with an ar 1 parameter of 0 50 the rmses for sml and msm based on ghk with 20 draws exceed those of gibbs by 9 and 0 respectively but when the ar 1 parameter is 0 80 the rmses for sml and msm based on 20 draws exceed those of gibbs by 79 and 37 respectively and the number of draws needed to reduce the rmses to within 10 of gibbs are 160 and 80 respectively also the sml estimates of serial correlation parameters exhibit significant downward bias thus while conventional wisdom suggests that 20 draws of ghk is enough to render the bias and noise induced by simulation negligible our results suggest that much larger simulation sizes are needed when serial correlation in disturbances is strong

on the geometry of a class of n qubit entanglement monotones a family of n qubit entanglement monotones invariant under stochastic local operations and classical communication slocc is defined this class of entanglement monotones includes the well known examples of the concurrence the 3 tangle and some of the four five and n qubit slocc invariants introduced recently the construction of these invariants is based on bipartite partitions of the hilbert space in the form with l 2n n l 2n such partitions can be given a nice geometrical interpretation in terms of grassmannians gr l l of l planes in cl that can be realized as the zero locus of quadratic polynomials in the complex projective space of suitable dimension via the plucker embedding the invariants are neatly expressed in terms of the plucker coordinates of the grassmannians

bayes inference in the tobit censored regression model we consider the bayes estimation of the tobit censored regression model with normally distributed errors a simple condition for the existence of posterior moments is provided suitable versions of monte carlo procedures based on symmetric multivariate t distributions and laplacian approximations in a certain parametrization are developed and illustrated ideas involving data augmentation and gibbs sampling cf tanner and wong 1987 and gelfand and smith 1990 are also developed the methods are compared in two examples with diffuse priors and various combinations of sample sizes and degrees of censoring

local unitary symmetries and entanglement invariants we investigate the relation between local unitary symmetries and entanglement invariants of multi qubit systems the hilbert space of such systems can be stratified in terms of states with different types of symmetry we review the connection between this stratification and the ring of entanglement invariants and the corresponding geometric description in terms of algebraic varieties on a stratum of a non trivial symmetry group the invariants of the symmetry preserving operations gives a sufficient description of entanglement finding these invariants is often a simpler problem than finding the invariants of the local unitary group the conditions as given by the luna richardson theorem for when the ring of such invariants is isomorphic to the ring of local unitary invariants on the stratum are discussed as an example we consider symmetry groups that can be diagonalized by local unitary operations and for which the group action on each qubit is non trivial on the stratum of such a symmetry the entanglement can be described in terms of a canonical form and the invariants of the symmetry preserving operations this canonical form and the invariants are directly determined by the symmetry group further we briefly discuss how some recently proposed entanglement classification schemes capture symmetry properties

relation between optimal nonlinearity and non gaussian noise enhancing a weak signal in a nonlinear system in the study of stochastic resonance it is often mentioned that nonlinearity can enhance a weak signal embedded in noise in order to give a systematic proof of the signal enhancement in nonlinear systems we derive an optimal nonlinearity that maximizes a signal to noise ratio snr the obtained optimal nonlinearity yields the maximum unbiased signal estimation performance which is known in the context of information theory it is found that a linear system is optimal for a gaussian noise but for a non gaussian noise there exist nonlinear systems that can achieve an snr higher than that obtained from linear systems this analysis refers to a system subjected to an additive non gaussian noise with a small signal input

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

the effect of source amplitude and phase in matched field source localization traditional matched field processing is typically employed for localization of a source with unknown amplitude and phase at transmission the spectral information of the source is estimated via maximum likelihood and is used for localization with the bartlett processor maximum a posteriori estimation of the spectrum of the source is here proposed along with the estimation of source location and noise variance where the joint posterior probability distribution of all parameters is computed with gibbs sampling it is shown that the proposed method has a higher probability of correct localization than the traditional approach

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea