a note on bayes factors for log linear contingency table models with vague prior information spiegelhalter and smith 1982 hereafter ssproposed an approximate method for calculating the bayes factor for a log linear model mo for a contingency table against the saturated model m1 with vague prior information we adopt their notation and denote by ss n equation n of ss suppose x1 xk have a multinomial distribution with parameters 014 4k where xi 0 0 x4i 1 we write yt log x1 log xk 01 log 01 log dk and y diag x1 xk then if m1 is the saturated model and mo is the nested log linear model defined by setting the contrasts co1 0 where c is an s x k matrix with rank s and rows summing to zero the approximate bayes factor bo1 for mo against m1 is given by ss 32 this however is indeterminate if any of the cell frequencies in the table is zero this is because of the use by ss of a prior density proportional to h i if however we use instead the standard jeffreys prior density proportional to i1i 1 2 the problem no longer arises then by the arguments of ss and lindley 1964 the resulting bayes factor is still given by ss 32 with xi replaced by xi 2 in the definitions of y and y i 1 k and ss 33 replaced by c 1 2 s2 1 cct i 1 2 if this solution is adopted the prior is proper and so in principle the problem of assigning an arbitrary multiplicative constant for which the ss approach was primarily devised need not arise one could in theory simply apply bayes theorem directly and so obtain the bayes factor exactly however in practice this is difficult to do and i know of no general solution to the problem even for simpler more specific contingency table and related models such as those of independence or equiprobability finding the bayes factor exactly is not too easy see for example crook and good 1982 altham 1971 gunel and dickey 1974 gunel 1982 broniatowski 1981 and references therein the second purpose of this note is to point out that conditionally on mo

generic simplicity of the spectrum and stabilization for a plate equation in this work we prove the generic simplicity of the spectrum of the clamped plate equation in a bounded regular domain of mathbb r d that is given omega subset mathbb r d we show that there exists an arbitrarily small deformation of the domain u such that all the eigenvalues of the plate system in the deformed domain omega u are simple to prove this result we first prove a nonstandard unique continuation property for this system that also holds generically with respect to the perturbations of the domain both the proof of this generic uniqueness result and the generic simplicity of the spectrum use baire s lemma and shape differentiation finally we show an application of this unique continuation property to a result of generic stabilization for a plate system with one dissipative boundary condition

a bayesian approach for predicting with polynomial regression of unknown degree this article compares three methods for computing the posterior probabilities of the possible orders in polynomial regression models these posterior probabilities are used for forecasting using bayesian model averaging it is shown that bayesian model averaging provides a closer relationship between the theoretical coverage of the high density predictive interval hdpi and the observed coverage than those corresponding to selecting the best model the performance of the different procedures is illustrated with simulations and some known engineering data

gaussian wave packet transform based numerical scheme for the semi classical schrodinger equation with random inputs abstract in this work we study the semi classical limit of the schrodinger equation with random inputs and show that the semi classical schrodinger equation produces o e oscillations in the random variable space with the gaussian wave packet transform the original schrodinger equation is mapped to an ordinary differential equation ode system for the wave packet parameters coupled with a partial differential equation pde for the quantity w in rescaled variables further we show that the w equation does not produce e dependent oscillations and thus it is more amenable for numerical simulations we propose multi level sampling strategy in implementing the gaussian wave packet transform where in the most costly part i e simulating the w equation it is sufficient to use e independent samples we also provide extensive numerical tests as well as meaningful numerical experiments to justify the properties of the numerical algorithm and hopefully shed light on possible future directions

model comparison of nonlinear structural equation models with fixed covariates recently it has been recognized that the commonly used linear structural equation model is inadequate to deal with some complicated substantive theory a new nonlinear structural equation model with fixed covariates is proposed in this article a procedure which utilizes the powerful path sampling for computing the bayes factor is developed for model comparison in the implementation the required random observations are simulated via a hybrid algorithm that combines the gibbs sampler and the metropolis hastings algorithm it is shown that the proposed procedure is efficient and flexible and it produces bayesian estimates of the parameters latent variables and their highest posterior density intervals as by products empirical performances of the proposed procedure such as sensitivity to prior inputs are illustrated by a simulation study and a real example

extending a bayesian analysis of the two period crossover to accommodate missing data summary a procedure is developed for performing a bayesian analysis of a simple two period crossover design when some observations are missing in one or both treatment periods the approach requires the numerical evaluation of a single integral to be performed for each posterior marginal distribution of interest the relative efficiency of this approach to one in which patients with missing data are excluded is investigated

a wavefront based gaussian beam method for computing high frequency wave propagation problems we present a novel wavefront method based on gaussian beams for computing high frequency wave propagation problems unlike standard geometrical optics gaussian beams compute the correct solution of the wave field also at caustics the method tracks a front of two canonical beams with two particular initial values for width and curvature in a fast post processing step from the canonical solutions we recreate any other gaussian beam with arbitrary initial data on the initial front this provides a simple mechanism to include a variety of optimization processes including error minimization and beam width minimization for a posteriori selection of optimal beam initial parameters the performance of the method is illustrated with two numerical examples

existence of bounded solutions of a second order system with dissipation in this article we study the following second order system of ordinary differential equations with dissipationu cu dau khu pt u rn t r where c d and k are positive constants h rn rn is a locally lipschitz function and p r rn is a continuous and bounded function a is a n n matrix whose eigenvalues are positive under these conditions we prove that for some values of c d and k this system has a bounded solution which is exponentially asymptotically stable moreover if p t is almost periodic then this bounded solution is also almost periodic these results are applied to the spatial discretization of very well known second order partial differential equations

monte carlo methods for exploring sensitivity to distributional assumptions in a bayesian analysis of a series of 2 x 2 tables this paper develops monte carlo methods for a bayesian analysis of a series of 2 x 2 tables under a variety of distributional assumptions i assume that the data in each table were generated from a pair of binomial distributions and the logarithm of odds of a favourable response follows a bivariate distribution with means that are linear functions of covariates and an arbitrary covariance matrix i use gibbs and importance sampling methods to obtain various characteristics of the posterior distribution of the quantities of interest i apply the method to analyse the data from a population case control study given the size of the population at risk i also derive the posterior distribution of the risk difference defined as the difference in the probabilities of disease development in the exposed and unexposed groups

approximate bayes factors and accounting for model uncertainty in generalised linear models summary ways of obtaining approximate bayes factors for generalised linear models are described based on the laplace method for integrals we propose a new approximation which uses only the output of standard computer programs for estimating generalised linear models this appears to be quite accurate a reference set of proper priors is suggested both to represent the situation where there is not much prior information and to assess the sensitivity of the results to the prior distribution the methods can be used when the dispersion parameter is unknown when there is overdispersion to compare link functions and to compare error distributions and variance functions the methods can be used to implement the bayesian approach to accounting for model uncertainty we describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important software to implement the methods is available at no cost from statlib

sequential ordinal modeling with applications to survival data summary this paper considers the class of sequential ordinal models in relation to other models for ordinal response data markov chain monte carlo mcmc algorithms based on the approach of albert and chib 1993 journal of the american statistical association88 669 679 are developed for the fitting of these models the ideas and methods are illustrated in detail with a real data example on the length of hospital stay for patients undergoing heart surgery a notable aspect of this analysis is the comparison based on marginal likelihoods and training sample priors of several nonnested models such as the sequential model the cumulative ordinal model and weibull and log logistic models

symplectic coarse grained classical and semclassical evolution of subsystems new theoretical approach we study the classical and semiclassical time evolutions of subsystems of a hamiltonian system this is done using a generalization of heller s thawed gaussian approximation introduced by littlejohn the key tool in our study is an extension of gromov s principle of the symplectic camel obtained in collaboration with dias de gosson and prata arxiv 1911 03763v1 math sg 2019 this extension says that the orthogonal projection of a symplectic phase space ball on a phase space with a smaller dimension also contains a symplectic ball with the same radius in the quantum case the radii of these symplectic balls are taken equal to and represent the ellipsoids of minimum uncertainty which we called quantum blobs in previous work

almost periodic solutions to some semilinear non autonomous thermoelastic plate equations abstract the paper is concerned with the existence of almost periodic solutions to the so called semilinear thermoelastic plate systems for that the strategy consists of seeing these systems as a particular case of the semilinear parabolic evolution equations x t a t x t f t x t t r where a t for t r is a family of sectorial linear operators on a banach space x satisfying the so called acquistapace terreni conditions and f is a function defined on a real interpolation space x for 0 1 under some reasonable assumptions it will be shown that has a unique almost periodic solution we then make use of the previous result to obtain the existence and uniqueness of an almost periodic solution to the thermoelastic plate systems

existence stability and smoothness of a bounded solution for nonlinear time varying thermoelastic plate equations in this paper we study the existence stability and the smoothness of a bounded solution of the following nonlinear time varying thermoelastic plate equation with homogeneous dirichlet boundary conditions utt 2u f1 t u t 0 x t ut f2 t u t 0 x u u 0 t 0 x where 0 0 is a sufficiently regular bounded domain in rn n 1 and fe1 fe2 r l2 2 l2 define by fe t u x f t u x x x are continuous and locally lipschitz functions first we prove that the linear system f1 f2 0 generates an analytic strongly continuous semigroup which decays exponentially to zero second under some additional condition we prove that the nonlinear system has a bounded solution which is exponentially stable and for a large class of functions f1 f2 this bounded solution is almost periodic finally we use the analyticity of the semigroup generated by the linear system to prove the smoothness of the bounded solution

a mathematical justification for the herman kluk propagator a class of fourier integral operators which converge to the unitary group of the schrodinger equation in the semiclassical limit e 0 in the uniform operator norm is constructed the convergence allows for an error bound of order o e which can be improved to arbitrary order in e upon the introduction of corrections in the symbol on the ehrenfest timescale the result holds with a slightly weaker error bound in the chemical literature the approximation is known as the herman kluk propagator

convergence of frozen gaussian approximation for high frequency wave propagation the frozen gaussian approximation provides a highly efficient computational method for high frequency wave propagation the derivation of the method is based on asymptotic analysis in this paper for general linear strictly hyperbolic systems we establish the rigorous convergence result for frozen gaussian approximation as a byproduct higher order frozen gaussian approximation is developed 2011 wiley periodicals inc

bayesian model selection using test statistics existing bayesian model selection procedures require the specification of prior distributions on the parameters appearing in every model in the selection set in practice this requirement limits the application of bayesian model selection methodology to overcome this limitation we propose a new approach towards bayesian model selection that uses classical test statistics to compute bayes factors between possible models in several test cases our approach produces results that are similar to previously proposed bayesian model selection and model averaging techniques in which prior distributions were carefully chosen in addition to eliminating the requirement to specify complicated prior distributions this method offers important computational and algorithmic advantages over existing simulation based methods because it is easy to evaluate the operating characteristics of this procedure for a given sample size and specified number of covariates our method facilitates the selection of hyperparameter values through prior predictive simulation

on priors and bayes factors abstract by analogy to the authors measure of the influence of observations on bayes factors a new measure is proposed to determine the influence of a prior distribution on a bayes factor this is developed for linear models the method is illustrated for a consumption model using houthakker s international income and consumption data

large time behavior for convection diffusion equations in rn abstract we describe the large time behavior of solutions of the convection diffusion equation u t u a u q 1 u in 0 r n with a r n and q 1 1 n n 1 when q 1 1 n we prove that the large time behavior of solutions with initial data in l 1 r n is given by a uniparametric family of self similar solutions the relevant parameter is the mass of the solution that is conserved for all t our result extends to dimensions n 1 well known results on the large time behavior of solutions for viscous burgers equations in one space dimension the proof is based on la salle s invariance principle applied to the equation written in its self similarity variables when q 1 1 n the convection term is too weak and the large time behavior is given by the heat kernel in this case the result is easily proved applying standard estimates of the heat kernel on the integral equation related to the problem

the intrinsic bayes factor for model selection and prediction abstract in the bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions it is typically not possible to utilize standard noninformative or default prior distributions this has led bayesians to use conventional proper prior distributions or crude approximations to bayes factors in this article we introduce a new criterion called the intrinsic bayes factor which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual bayes factors the criterion can be used for nested or nonnested models and for multiple model comparison and prediction from another perspective the development suggests a general definition of a reference prior for model comparison

bayesian testing and estimation of association in a two way contingency table abstract in a two way contingency table one is interested in checking the goodness of fit of simple models such as independence quasi independence symmetry and constant association and estimating parameters that describe the association structure of the table in a large table one may be interested in detecting a few outlying cells that deviate from the main association pattern in the table bayesian tests of these hypotheses are described using a prior defined on the set of interaction terms of the log linear model these tests and associated estimation procedures have several advantages over classical fitting estimation procedures first the tests can give measures of evidence in support of simple hypotheses second the bayes factors can be used to give estimates of association parameters of the table that allow for uncertainty that the hypothesized model is true these methods are illustrated for a number of tables

a predictive approach to the analysis of designed experiments abstract viewing the analysis of designed experiments as a model selection problem we introduce the use of a predictive bayesian criterion in this context based on the predictive density of a replicate experiment pdre a calibration of the criterion is provided to assist in the model choice the relationships of the proposed criterion to other prevalent criteria such as aic bic and mallows s c p are given an information theoretic criterion based on the pdre s of two competing models is also introduced and compared with the usual f statistic for two nested models examples are given to illustrate the proposed methodology

bayesian variable selection in linear regression abstract this article is concerned with the selection of subsets of predictor variables in a linear regression model for the prediction of a dependent variable it is based on a bayesian approach intended to be as objective as possible a probability distribution is first assigned to the dependent variable through the specification of a family of prior distributions for the unknown parameters in the regression model the method is not fully bayesian however because the ultimate choice of prior distribution from this family is affected by the data it is assumed that the predictors represent distinct observables the corresponding regression coefficients are assigned independent prior distributions for each regression coefficient subject to deletion from the model the prior distribution is a mixture of a point mass at 0 and a diffuse uniform distribution elsewhere that is a spike and slab distribution the random error component is assigned a normal distribution with mean 0 and standard deviation

precision complexity and bayesian model determination summary in this paper a new criterion for model determination is proposed an explicit decision theoretic approach to model selection is employed to derive a bayes decision rule the operational characteristics of the criterion are discussed and consistency is shown

null controllability for a semilinear parabolic equation with gradient quadratic growth abstract this article is concerned with the null controllability of a semilinear parabolic equation with the nonlinear term involving the gradient quadratic term the technique in this paper is a combination of cole hopf transformation and some methods from a y khapalov controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term a qualitative approach siam j control optim 41 2003 1886 1900

automatic bayes factors for testing equality and inequality constrained hypotheses on variances in comparing characteristics of independent populations researchers frequently expect a certain structure of the population variances these expectations can be formulated as hypotheses with equality and or inequality constraints on the variances in this article we consider the bayes factor for testing such in equality constrained hypotheses on variances application of bayes factors requires specification of a prior under every hypothesis to be tested however specifying subjective priors for variances based on prior information is a difficult task we therefore consider so called automatic or default bayes factors these methods avoid the need for the user to specify priors by using information from the sample data we present three automatic bayes factors for testing variances the first is a bayes factor with equal priors on all variances where the priors are specified automatically using a small share of the information in the sample data the second is the fractional bayes factor where a fraction of the likelihood is used for automatic prior specification the third is an adjustment of the fractional bayes factor such that the parsimony of inequality constrained hypotheses is properly taken into account the bayes factors are evaluated by investigating different properties such as information consistency and large sample consistency based on this evaluation it is concluded that the adjusted fractional bayes factor is generally recommendable for testing equality and inequality constrained hypotheses on variances

unique continuation for some evolution equations this work is concerned with unique continuation results for some evolution equations essentially of parabolic type to be more precise let l be an evolution operator acting on functions defined on some connected open set b of r r x r l is said to have the unique continuation property if every solution u of lu 0 which vanishes one some nonempty open set u i of fl vanishes in the horizontal component of o in 0 i e in x t e 0 3x x t e co the first general result of this type was established by mizohata 6 in the case where l is a second order parabolic operator with smooth coefficients however mizohata s proof is somewhat delicate it is based in particular on an extended class of calderon zygmund operators and does not lead obviously to a weakening of the smoothness of the coefficients on the other hand it is important for the applications to deal with nonsmooth coefficients since l is often obtained as the linearization of some nonlinear operator at a nonnecessarily smooth solution we refer to lions 4 and kernevez and lions 3 for applications to control theory and to 1 l for applications to transversality techniques let us now describe the content of this work in the first section we prove a unique continuation theorem when l is a second order parabolic equation our proof is simple and based on the derivation of a carleman estimate which is reminiscent of the classical carleman estimates for second order elliptic operators see 121 this carleman inequality allows the weakening of the 118 0022 0396187 3 00

an objective bayesian analysis of a crossover design via model selection and model averaging inference about the treatment effect in a crossover design has received much attention over time owing to the uncertainty in the existence of the carryover effect and its impact on the estimation of the treatment effect adding to this uncertainty is that the existence of the carryover effect and its size may depend on the presence of the treatment effect and its size we consider estimation and testing hypothesis about the treatment effect in a two period crossover design assuming normally distributed response variable and use an objective bayesian approach to test the hypothesis about the treatment effect and to estimate its size when it exists while accounting for the uncertainty about the presence of the carryover effect as well as the treatment and period effects we evaluate and compare the performance of the proposed approach with a standard frequentist approach using simulated data and real data copyright 2016 john wiley sons ltd

a matrix exponential spatial specification we introduce the matrix exponential as a way of modelling spatially dependent data the matrix exponential spatial specification mess simplifies the log likelihood allowing a closed form solution to the problem of maximum likelihood estimation and greatly simplifies the bayesian estimation of the model the mess can produce estimates and inferences similar to those from conventional spatial autoregressive models but has analytical computational and interpretive advantages we present maximum likelihood and bayesian approaches to the estimation of this spatial model specification along with methods of model comparisons over different explanatory variables and spatial specifications

bayesian inference for the common location parameter of several shifted exponential populations abstract consider k random samples which are independently drawn from k shifted exponential distributions with respective scale parameters 1 2 k and common location parameter on the basis of the given samples and in a bayesian framework we address the problem of point and interval estimation of the location parameter under the conjugate priors which are usually proper priors moreover we also address the problem of testing the equality of the location parameters we propose bayesian hypothesis testing procedures for the equality of the location parameters under the noninformative prior the noninformative prior is usually improper which yields a calibration problem that makes the bayes factor to be defined up to a multiplicative constant so we propose the default bayesian hypothesis testing procedures based on the fractional bayes factor and the intrinsic bayes factors under the reference priors our proposed bayesian procedures are compared and contrasted via a comparison study a simulation study and a real world data analysis to the existing classical exact procedures proposed by tippett tippett s method tippett 1931 fisher fisher s method fisher 1932 stouffer inverse normal method stouffer et al 1949 and george logit method george 1977 and to the generalized variable procedures proposed by tsui and weerahandi generalized p value method tsui and weerahandi 1989

approximate bayesian inference with the weighted likelihood bootstrap we introduce the weighted likelihood bootstrap wlb as a way to simulate approximately from a posterior distribution this method is often easy to implement requiring only an algorithm for calculating the maximum likelihood estimator such as iteratively reweighted least squares in the generic weighting scheme the wlb is first order correct under quite general conditions inaccuracies can be removed by using the wlb as a source of samples in the sampling importance resampling sir algorithm which also allows incorporation of particular prior information the sir adjusted wlb can be a competitive alternative to other integration methods in certain models asymptotic expansions elucidate the second order properties of the wlb which is a generalization of rubin s bayesian bootstrap the calculation of approximate bayes factors for model comparison is also considered we note that given a sample simulated from the posterior distribution the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values a modification of this estimator that avoids instability is also noted these methods provide simple ways of calculating approximate bayes factors and posterior model probabilities for a very wide class of models

bayes factors for outlier models using the device of imaginary observations abstract suppose we think that most observations in a sample have been generated from a distribution with density f x but we fear that a few outliers from a distribution with density g x may have contaminated our sample in many situations we might assume that f x is a density depending on a parameter and that g x is of the same form as f but with parameter or a number of bayesian models for this problem when f is normal have been discussed by freeman he points out that with a vague improper prior for contaminating parameters most posterior weight is put on the model allowing for the largest number of outliers he therefore confines attention to proper priors when trying to answer the question of how many outliers however in many situations we do not have very certain information on the contaminating parameters and would like to make inferences about outliers when using improper priors for the parameters of the model in this article we apply the ideas of spiegelhalter and smith to

approximate controllability for fractional semilinear parabolic equations abstract in this paper we deal with the control systems described by a large class of fractional semilinear parabolic equations firstly we reformulate the fractional parabolic equations into abstract fractional differential equations associated with a semigroup on an appropriate banach space secondly we introduce a suitable concept on a mild solution for this kind of fractional parabolic equations and present the existence and uniqueness of mild solution by utilizing the theory of semigroup of linear operator nonlinear analysis method and fixed point theorem then the approximate controllability of the fractional semilinear parabolic equations is formulated and proved at the end of the paper an example is given to illustrate our main results

objective bayesian variable selection a novel fully automatic bayesian procedure for variable selection in normal regression models is proposed the procedure uses the posterior probabilities of the models to drive a stochastic search the posterior probabilities are computed using intrinsic priors which can be considered default priors for model selection problems that is they are derived from the model structure and are free from tuning parameters thus they can be seen as objective priors for variable selection the stochastic search is based on a metropolis hastings algorithm with a stationary distribution proportional to the model posterior probabilities the procedure is illustrated on both simulated and real examples

bayesian model discrimination and bayes factors for linear gaussian state space models summary it is shown how to discriminate between different linear gaussian state space models for a given time series by means of a bayesian approach which chooses the model that minimizes the expected loss a practical implementation of this procedure requires a fully bayesian analysis for both the state vector and the unknown hyperparameters and is carried out by markov chain monte carlo methods an application to some non standard situations such as testing hypotheses on the boundary of the parameter space discriminating non nested models and discrimination of more than two models is discussed in detail

fractional bayes factors for model comparison bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves however there are difficulties with this approach when prior information about the parameters of the various models is weak partial bayes factors offer a resoiution of the problem by setting aside part of the data as a training sampie the training sampie is used to obtain an initiai informative posterior distribution of the parameters in each model model comparison is then based on a bayes factor calculated from the remaining data properties of partial bayes factors are discussed particularly in the context of weak prior information and they are found to have advantages over other proposed methods of model comparison a new variant of the partial bayes factor the fractional bayes factor is advocated on grounds of consistency simplicity robustness and coherence

approximate controllability of the semilinear heat equation this article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain when the control acts on any open and nonempty subset of or on a part of the boundary in the case of both an internal and a boundary control the approximate controllability in l p for 1 p l in the case of the interior control we also prove approximate controllability in c 0 the proof combines a variational approach to the controllability problem for linear equations and a fixed point method we also prove that the control can be taken to be of quasi bang bang form

controls insensitizing the norm of the solution of a semilinear heat equation abstract we consider here a semilinear heat equation with partially known initial and boundary conditions the insensitizing problem consists in finding a control function such that some functional of the state is locally insensitive to the perturbations of these initial and boundary data in this paper the insensitizing control of the norm of the observation of the solution in an open subset of the domain is studied under appropriate assumptions on the nonlinearity and the observation subset it is shown that the insensitivity conditions are equivalent to a particular nonlinear exact controllability problem for parabolic equations due to the smoothing effects of this type of equation exact controllability is very hard to achieve and this is why it seems natural to introduce the idea of approximately insensitizing control and then to solve a nonlinear approximate controllability problem of a special type that is done using a linearization and fixed point method solving the linear problem leads to the proof of a nontrivial uniqueness property which is abo used to characterize a particular subset of the admissible controls this characterization is made thanks to a convex duality theorem and allows us to solve a fixed point problem and get the result for the nonlinear case various comments and conclusions are eventually given with other approximately insensitizing problems that can be solved by our methods

the selection of prior distributions by formal rules abstract subjectivism has become the dominant philosophical foundation for bayesian inference yet in practice most bayesian analyses are performed with so called noninformative priors that is priors constructed by some formal rule we review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used we give special emphasis to jeffreys s rules and discuss the evolution of his viewpoint about the interpretation of priors away from unique representation of ignorance toward the notion that they should be chosen by convention we conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly when sample sizes are small relative to the number of parameters being estimated it is dangerous to put faith in any default solution but when asymptotics take over jeffreys s rules and their variants remain reasonable choices we also provide an annotated b

propagation of quantum expectations with husimi functions we analyze the dynamics of expectation values of quantum observables for the time dependent semiclassical schrodinger equation to benefit from the positivity of husimi functions we switch between observables obtained from weyl and anti wick quantization we develop and prove a second order egorov type propagation theorem with husimi functions by establishing transition and commutator rules for weyl and anti wick operators we provide a discretized version of our theorem and present numerical experiments for schrodinger equations in dimensions two and six that validate our results

bayesian model selection analysis of a survival model with a surviving fraction we describe a methodology for model comparison in a bayesian framework as applied to survival with a surviving fraction this is illustrated using a case study of a randomized and controlled clinical trial investigating time until recurrence of depression posterior distributions are simulated using metropolis within gibbs markov chain methods models reflecting the effects of covariates on the log odds of being in the surviving fraction the log of the hazard rate as well as both and neither are compared bayes factors for comparing the models are obtained by using the bridge sampling method of calculating normalizing constants

a bayesian analysis of the two period crossover design for clinical trials statisticians have been critical of the use of the two period crossover designs for clinical trials because the estimate of the treatment difference is biased when the carryover effects of the two treatments are not equal in the standard approach if the null hypothesis of equal carryover effects is not rejected data from both periods are used to estimate and test for treatment differences if the null hypothesis is rejected data from the first period alone are used a bayesian analysis based on the bayes factor against unequal carryover effects is given although this bayesian approach avoids the all or nothing decision inherent in the standard approach it recognizes that with small trials it is difficult to provide unequivocal evidence that the carryover effects of the two treatments are equal and thus that the interpretation of the difference between treatment effects is highly dependent on a subjective assessment of the reality or not of equal carryover effects

frequentist accuracy of bayesian estimates in the absence of relevant prior experience popular bayesian estimation techniques usually begin with some form of uninformative prior distribution intended to have minimal inferential influence bayes rule will still produce nice looking estimates and credible intervals but these lack the logical force attached to experience based priors and require further justification this paper concerns the frequentist assessment of bayes estimates a simple formula is shown to give the frequentist standard deviation of a bayesian point estimate the same simulations required for the point estimate also produce the standard deviation exponential family models make the calculations particularly simple and bring in a connection to the parametric bootstrap

expected posterior prior distributions for model selection summary we consider the problem of comparing parametric models using a bayesian approach a new method of developing prior distributions for the model parameters is presented called the expected posterior prior approach the idea is to define the priors for all models from a common underlying predictive distribution in such a way that the resulting priors are amenable to modern markov chain monte carlo computational techniques the approach has subjective bayesian and default bayesian implementations and overcomes the most significant impediment to bayesian model selection that of ensuring that prior distributions for the various models are appropriately compatible

markov chain monte carlo model determination for hierarchical and graphical log linear models we use reversible jump markov chain monte carlo methods green 1995 to develop strategies for calculating posterior probabilities of hierarchical graphical or decomposable log linear models for high dimensional contingency tables even for tables of moderate size these sets of models may be very large the choice of suitable prior distributions for model parameters is also discussed in detail and two examples are presented for the first example a three way table the model probabilities calculated using our reversible jump approach are compared with model probabilities calculated exactly or by using an alternative approximation the second example is a six way contingency table for which exact methods are infeasible because of the large number of possible models we identify the most probable hierarchical graphical and decomposable models and compare the results with alternatives approaches

boundary controllability of thermoelastic plates via the free boundary conditions controllability properties of a partial differential equation pde model describing a thermoelastic plate are studied the pde is composed of a kirchoff plate equation coupled to a heat equation on a bounded domain with the coupling taking place on the interior and boundary of the domain the coupling in this pde is parameterized by alpha 0 boundary control is exerted through the two free boundary conditions of the plate equation and through the robin boundary condition of the temperature these controls have the physical interpretation of inserted forces and moments and prescribed temperature respectively all of which act on the edges of the plate the main result here is that under such boundary control and with initial data in the basic space of well posedness one can simultaneously control the displacement of the plate exactly and the temperature approximately moreover the thermal control may be taken to be arbitrarily smooth in time and space and the thermal control region may be any nonempty subset of the boundary this controllability holds for arbitrary values of the coupling parameter alpha with the optimal controllability time in line with that seen for uncoupled kirchoff plates

extending conventional priors for testing general hypotheses in linear models summary we consider that observations come from a general normal linear model and that it is desirable to test a simplifying null hypothesis about the parameters we approach this problem from an objective bayesian model selection perspective crucial ingredients for this approach are proper objective priors to be used for deriving the bayes factors jeffreys zellner siow priors have good properties for testing null hypotheses defined by specific values of the parameters in full rank linear models we extend these priors to deal with general hypotheses in general linear models not necessarily of full rank the resulting priors which we call conventional priors are expressed as a generalization of recently introduced partially informative distributions the corresponding bayes factors are fully automatic easily computed and very reasonable the methodology is illustrated for the change point problem and the equality of treatments effects problem we compare the conventional priors derived for these problems with other objective bayesian proposals like the intrinsic priors it is concluded that both priors behave similarly although interesting subtle differences arise we adapt the conventional priors to deal with nonnested model selection as well as multiple model comparison finally we briefly address a generalization of conventional priors to nonnormal scenarios

frozen gaussian approximation based domain decomposition methods for the linear schrodinger equation beyond the semi classical regime the paper is devoted to develop efficient domain decomposition methods for the linear schrodinger equation beyond the semiclassical regime which does not carry a small enough rescaled planck constant for asymptotic methods e g geometric optics to produce a good accuracy but which is too computationally expensive if direct methods e g finite difference are applied this belongs to the category of computing middle frequency wave propagation where neither asymptotic nor direct methods can be directly used with both efficiency and accuracy motivated by recent works of the authors on absorbing boundary conditions antoine et al 2014 13 and yang and zhang 2014 43 we introduce semiclassical schwarz waveform relaxation methods sswr which are seamless integrations of semiclassical approximation to schwarz waveform relaxation methods two versions are proposed respectively based on herman kluk propagation and geometric optics and we prove the convergence and provide numerical evidence of efficiency and accuracy of these methods

approximate controllability of a semilinear heat equation in bbb r n we prove the approximate controllability of the semilinear heat equation in bbb r n we introduce the weighted sobolev spaces of escobedo and kavian and in that functional setting we adapt the technique introduced by fabre puel and zuazua for the problem in bounded domains that is we first prove the approximate controllability of the linear equation and by a fixed point method obtain the main result

extending a bayesian analysis of the two period crossover to allow for baseline measurements in the context of a two period crossover study with baseline measurements a graphical method is developed for displaying the dependence of posterior inferences concerning the treatment effect on unavoidable prior beliefs about the correct model the method is a generalization of the approach developed by grieve for the corresponding case without baselines

bayesian analysis of a poisson process with a change point summary a bayesian approach to estimation and hypothesis testing for a poisson process with a change point is developed and an example given

an intrinsic limiting procedure for model selection and hypotheses testing abstract improper priors typically arise in default bayesian estimation problems in the bayesian approach to model selection or hypothesis testing the main tool is the bayes factor when improper priors for the parameters appearing in the models are used the bayes factor is not well defined the intrinsic bayes factor introduced by berger and pericchi is an interesting method for overcoming that difficulty that method is of particular interest as a means for generating proper prior distributions intrinsic priors for model comparison from the improper priors typically used in estimation the goal of this article is to develop a limiting procedure that provides a solid justification for the use of bayes factor with intrinsic priors the procedure is formalized and discussed for nested and nonnested models illustrations and comparisons with other approximations to bayes factors such as the bayesian information criterion of schwarz and the fractional bayes factor of o hagan are provided

model choice in generalised linear models a bayesian approach via kullback leibler projections summary we propose a general bayesian method of comparing models the approach is based on the kullback leibler distance between two families of models one nested within the other for each parameter value of a full model we compute the projection of the model to the restricted parameter space and the corresponding minimum distance from the posterior distribution of the minimum distance we can judge whether or not a more parsimonious model is appropriate we show how the projection method can be implemented for generalised linear model selection and we propose some markov chain monte carlo algorithms for its practical implementation in less tractable cases we illustrate the method with examples

time optimal control of semilinear parabolic equations via bilinear controls abstract we establish the existence of the time optimal control for semilinear parabolic equations with gradient quadratic growth via bilinear controls it is worth pointing out that there is no restriction on the growth of the nonlinearity f s with respect to the variable s in the equation which is a remarkable difference compared to the semilinear parabolic system with locally distributed controls the technique used in this paper is the combination of the hopf cole transformation the a prior estimates on solutions of parabolic equations and the strategy of the stepwise control

inference and prediction for a general order statistic model with unknown population size abstract suppose that the first n order statistics from a random sample of n positive random variables are observed where n is unknown this the general order statistic model has been applied to the study of market penetration capture recapture burn in in repairable systems software reliability growth the estimation of the number of individuals exposed to radiation and the estimation of the number of unseen species inference is to be made about the unknown parameters especially n and future observations are to be predicted a bayes empirical bayes approach to inference is presented this permits the comparison of competing perhaps nonnested models for the distribution of the random variables in a natural way it also provides easily implemented inference and prediction procedures that avoid the difficulties of non bayesian methods one such difficulty is that the maximum likelihood estimator of n may be infinite results are given for the case in which vague prior information about the model

variational problems related to self similar solutions of the heat equation on demontre la compacite de certains plongements de sobolev sous de bonnes conditions sur les poids k x exp x c 2 r n r on considere des methodes variationnelles pour la resolution d equations elliptiques

measuring the effect of observations on bayes factors summary in this paper we consider a measure of the effect of single observations on a logarithmic bayes factor defined via the difference in the logarithms of the bayes factors conditional first on all the data and then omitting an observation the measure is related to the conditional predictive ordinate the form of the measure and examples of its use are presented for a variety of situations normal samples linear models log linear models and the checking of distributional assumptions

model selection and accounting for model uncertainty in graphical models using occam s window abstract we consider the problem of model selection and accounting for model uncertainty in high dimensional contingency tables motivated by expert system applications the approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic p values leading to the selection of a single model inference is then conditional on the selected model the sampling properties of such a strategy are complex and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest in principle a panacea is provided by the standard bayesian formalism that averages the posterior distributions of the quantity of interest under each of the models weighted by their posterior model probabilities furthermore this approach is optimal in the sense of maximizing predictive ability but this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large often greater than 1

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

bayesian model choice asymptotics and exact calculations abstract model determination is a fundamental data analytic task here we consider the problem of choosing amongst a finite with loss of generality we assume two set of models after briefly reviewing classical and bayesian model choice strategies we present a general predictive density which includes all proposed bayesian approaches we are aware of using laplace approximations we can conveniently assess and compare asymptotic behavior of these approaches concern regarding the accuracy of these approximation for small to moderate sample sizes encourages the use of monte carlo techniques to carry out exact calculations a data set fit with nested non linear models enables comparison between proposals and between exact and asymptotic values

an alternative to the standard bayesian procedure for discrimination between normal linear models summary we consider the standard bayesian procedure for discrimination focusing on its tendency to give low posterior probabilities to some correct models even in conditions of moderate to large sampling sizes furthermore in some situations that could well occur in practice the standard procedure is even asymptotically inconsistent we claim that the explanation is that the standard procedure inflates the posterior probability of the model that has the smallest expected increase in information about its parameters we then propose to modify it by an amount related to the expected gain in information and show that the lindley paradox does not occur finally we obtain the limiting alternative criterion that results by letting the prior densities become noninformative which enables us to measure how sensitive the discrimation is to the informative prior densities used

almost periodic solutions of first and second order cauchy problems abstract almost periodicity of solutions of first and second order cauchy problems on the real line is proved under the assumption that the imaginary resp real spectrum of the underlying operator is countable related results have been obtained by ruess v and basit our proof uses a new idea it is based on a factorisation method which also gives a short proof of the vector valued version of loomis classical theorem saying that a bounded uniformly continuous function from r into a banach spacexwith countable spectrum is almost periodic ifc0 x our method can also be used for solutions on the half line this is done in a separate paper

a bayesian approach to prospective binary outcome studies with misclassification in a binary risk factor misclassification in a binary exposure variable within an unmatched prospective study may lead to a biased estimate of the disease exposure relationship it usually gives falsely small credible intervals because uncertainty in the recorded exposure is not taken into account when there are several other perfectly measured covariates interrelationships may introduce further potential for bias bayesian methods are proposed for analysing binary outcome studies in which an exposure variable is sometimes misclassified but its correct values have been validated for a random subsample of the subjects this bayesian approach can model relationships between explanatory variables and between exploratory variables and the probabilities of misclassification three logistic regressions are used to relate disease to true exposure misclassified exposure to true exposure and true exposure to other covariates credible intervals may be used to make decisions about whether certain parameters are unnecessary and hence whether the model can be reduced in complexity in the disease exposure model for parameters representing coefficients related to perfectly measured covariates the precision of posterior estimates is only slightly lower than would be found from data with no misclassification for the risk factor which has misclassification the estimates of model coefficients obtained are much less biased than those with misclassification ignored