comparing the performance of two indices for spatial model selection application to two mortality data the statistical analysis of spatially correlated data has become an important scientific research topic lately the analysis of the mortality or morbidity rates observed at different areas may help to decide if people living in certain locations are considered at higher risk than others once the statistical model for the data of interest has been chosen further effort can be devoted to identifying the areas under higher risks many scientists including statisticians have tried the conditional autoregressive car model to describe the spatial autocorrelation among the observed data this model has greater smoothing effect than the exchangeable models such as the poisson gamma model for spatial data this paper focuses on comparing the two types of models using the index lg the ratio of local to global variability two applications taiwan asthma mortality and scotland lip cancer are considered and the use of lg is illustrated the estimated values for both data sets are small implying a poisson gamma model may be favoured over the car model we discuss the implications for the two applications respectively to evaluate the performance of the index lg we also compute the bayes factor a bayesian model selection criterion to see which model is preferred for the two applications and simulation data to derive the value of lg we estimate its posterior mode based on samples derived from the bugs program while for bayes factor we use the double laplace metropolis method schwarz criterion and a modified harmonic mean for approximations the results of lg and bayes factor are consistent we conclude that lg is fairly accurate as an index for selection between poisson gamma and car model when easy and fast computation is of concern we recommend using lg as the first and less costly index

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

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

the powers and strengths of tests for multinomials and contingency tables abstract the strength of a significance test is defined as a weighted average of the power especially if the weights are a prior density the concept is a compromise between neyman pearsonian and bayesian methods and is applied to tests for multinomial equiprobability and for no association in contingency tables the differences of the power functions of two criteria x 2 and g are illustrated for the trinomial where g arose earlier from a partially bayesian approach other methods for apprehending power functions of several variables are discussed for 2 2 contingency tables with equal row or column totals the power and strength functions of several statistics are equal

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

a taxonomy of latent structure assumptions for probability matrix decomposition models a taxonomy of latent structure assumptions lsas for probability matrix decomposition pmd models is proposed which includes the original pmd model maris de boeck van mechelen 1996 as well as a three way extension of the multiple classification latent class model maris 1999 it is shown that pmd models involving different lsas are actually restricted latent class models with latent variables that depend on some external variables for parameter estimation a combined approach is proposed that uses both a mode finding algorithm em and a sampling based approach gibbs sampling a simulation study is conducted to investigate the extent to which information criteria specific model checks and checks for global goodness of fit may help to specify the basic assumptions of the different pmd models finally an application is described with models involving different latent structure assumptions for data on hostile behavior in frustrating situations

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

the hirsch conjecture for dual transportation polyhedra an algorithm is given that joins any pair of extreme points of a dual transportation polyhedron by a path of at most m 1 n 1 extreme edges

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

the complexity of generic primal algorithms for solving general integer programs primal methods constitute a common approach to solving combinatorial optimization problems starting from a given feasible solution they successively produce new feasible solutions with increasingly better objective function value until an optimal solution is reached from an abstract point of view an augmentation problem is solved in each iteration that is given a feasible point these methods find an augmenting vector if one exists usually augmenting vectors with certain properties are sought to guarantee the polynomial running time of the overall algorithm in this paper we show that one can solve every integer programming problem in polynomial time provided one can efficiently solve the directed augmentation problem the directed augmentation problem arises from the ordinary augmentation problem by splitting each direction into its positive and its negative part and by considering linear objectives on these parts our main result states that in order to get a polynomial time algorithm for optimization it is sufficient to efficiently find for any linear objective function in the positive and negative part an arbitrary augmenting vector this result also provides a general framework for the design of polynomial time algorithms for specific combinatorial optimization problems we demonstrate its applicability by considering the min cost flow problem by giving a novel algorithm for linear programming over unimodular spaces and by providing a different proof that for 0 1 integer programming an efficient algorithm solving the ordinary augmentation problem suffices for efficient optimization our main result also implies that directed augmentation is at least as hard as optimization in other words for an np hard problem already the task of finding a directed augmenting vector in polynomial time is hopeless unless p np we illustrate this kind of consequence with the help of the knapsack problem

model based gaussian and non gaussian clustering abstract the classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms including those based on the sum of squares criterion and on the criterion of friedman and rubin 1967 however as currently implemented it does not allow the specification of which features orientation size and shape are to be common to all clusters and which may differ between clusters also it is restricted to gaussian distributions and it does not allow for noise we propose ways of overcoming these limitations a reparameterization of the covariance matrix allows us to specify that some features but not all be the same for all clusters a practical framework for non gaussian clustering is outlined and a means of incorporating noise in the form of a poisson process is described an approximate bayesian method for choosing the number of clusters is given the performance of the proposed methods is studied by simulation with encouraging results the methods are applied to the analysis of a data set arising in the study of diabetes and the results seem better than those of previous analyses rh

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

on some criteria for estimating the order of a markov chain tong 1975 has proposed a procedure for estimating the order of a markov chain based on akaike s information criterion aic in this paper the asymptotic distribution of the aic estimator is derived and it is shown that the estimator is inconsistent as an alternative to the aic procedure the bayesian information criterion bic proposed by schwarz 1978 is shown to be consistent these two procedures yield different estimated orders when applied to specific samples of meteorological observations for parameters based on these meteorological examples the aic and bic procedures are compared by means of simulation for finite samples the results obtained have practical implications concerning whether in the routine fitting of precipitation data it is necessary to consider higher than first order markov chains

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

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

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

on the diameter of partition polytopes and vertex disjoint cycle cover we study the combinatorial diameter of partition polytopes a special class of transportation polytopes they are associated to partitions of a set x x1 xn of items into clusters c1 ck of prescribed sizes 1 k we derive upper bounds on the diameter in the form of 1 2 n 1 and lfloor frac n 2 rfloor this is a direct generalization of the diameter 2 result for the birkhoff polytope the bounds are established using a constructive graph theoretical approach where we show that special sets of vertices in graphs that decompose into cycles can be covered by a set of vertex disjoint cycles further we give exact diameters for partition polytopes with k 2 or k 3 and prove that for all k 4 and all 1 2 there are cluster sizes 3 k such that the diameter of the corresponding partition polytope is at least lceil frac 4 3 kappa 2 rceil finally we provide an o n kappa 1 kappa 2 sqrt k 1 algorithm for an edge walk connecting two given vertices of a partition polytope that also adheres to our diameter bounds

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

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

energy correlations for a random matrix model of disordered bosons linearizing the heisenberg equations of motion around the ground state of an interacting quantum many body system one gets a time evolution generator in the positive cone of a real symplectic lie algebra the presence of disorder in the physical system determines a probability measure with support on this cone the present paper analyzes a discrete family of such measures of exponential type and does so in an attempt to capture by a simple random matrix model some generic statistical features of the characteristic frequencies of disordered bosonic quasiparticle systems the level correlation functions of the said measures are shown to be those of a determinantal process and the kernel of the process is expressed as a sum of biorthogonal polynomials while the correlations in the bulk scaling limit are in accord with sine kernel or gaussian unitary ensemble universality at the low frequency end of the spectrum an unusual type of scaling behavior is found

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

large deviations for wigner s law and voiculescu s non commutative entropy we study the spectral measure of gaussian wigner s matrices and prove that it satisfies a large deviation principle we show that the good rate function which governs this principle achieves its minimum value at wigner s semicircular law which entails the convergence of the spectral measure to the semicircular law as a conclusion we give some further examples of random matrices with spectral measure satisfying a large deviation principle and argue about voiculescu s non commutative entropy

accelerated failure time regression models with a regression model of surviving fraction an application to the analysis of permanent employment in japan abstract accelerated failure time regression models with an additional regression model for the surviving fraction are proposed for the analysis of events that may never occur regardless of censoring for some people in the population risk set the models attempt to estimate simultaneously the effects of covariates on the acceleration deceleration of the timing of a given event and the surviving fraction that is the proportion of the population for which the event never occurs the extended family of the generalized gamma distribution is used for the accelerated failure time regression model the logistic function is used for the regression model of the surviving fraction the models are applied to the data of interfirm job mobility in japan to assess variability in permanent employment among white collar and blue collar employees in firms of different sizes independent from their variability in the timing of interfirm job separations

quadratic diameter bounds for dual network flow polyhedra both the combinatorial and the circuit diameter of polyhedra are of interest to the theory of linear programming for their intimate connection to a best case performance of linear programming algorithms we study the diameters of dual network flow polyhedra associated to b flows on directed graphs g v e g v e and prove quadratic upper bounds for both of them the minimum of v 1 cdot e v 1 e and frac 1 6 v 3 16 v 3 for the combinatorial diameter and frac v cdot v 1 2 v v 1 2 for the circuit diameter previously bounds on these diameters have only been known for bipartite graphs the situation is much more involved for general graphs in particular we construct a family of dual network flow polyhedra with members that violate the circuit diameter bound for bipartite graphs by an arbitrary additive constant

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

schur polynomials and biorthogonal random matrix ensembles the study of the average of schur polynomials over a stieltjes wigert ensemble has been carried out by dolivet and tierz j math phys 48 023507 2007 e print arxiv hep th 0609167 where it was shown that it is equal to quantum dimensions using the same approach we extend the result to the biorthogonal case we also study using the littlewood richardson rule some particular cases of the quantum dimension result finally we show that the notion of giambelli compatibility of schur averages introduced by borodin et al adv appl math 37 209 2006 e print arxiv math ph 0505021 also holds in the biorthogonal setting

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

random matrix models with additional interactions it has been argued that despite remarkable success existing random matrix theories are not adequate at describing disordered conductors in the metallic regime due to the presence of certain two body interactions in the effective hamiltonian for the eigenvalues in addition to the standard logarithmic interaction that arises entirely from symmetry considerations we present a new method that allows exact solution of random matrix models with such additional two body interactions this should broaden the scope of random matrix models in general

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

a scaling algorithm for optimizing arbitrary functions over vertices of polytopes in this paper we present a scaling algorithm for minimizing arbitrary functions over vertices of polytopes in an oracle model of computation which includes an augmentation oracle for the binary case when the vertices are 0 1 vectors we show that the oracle time is polynomial also this algorithm allows us to generalize some concepts of combinatorial optimization concerning performance bounds of greedy algorithms and leads to new bounds for the complexity of the simplex method

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

the hirsch conjecture for the fractional stable set polytope the edge formulation of the stable set problem is defined by two variable constraints one for each edge of a graph g g expressing the simple condition that two adjacent nodes cannot belong to a stable set we study the fractional stable set polytope i e the polytope defined by the linear relaxation of the edge formulation even if this polytope is a weak approximation of the stable set polytope its simple geometrical structure provides deep theoretical insight as well as interesting algorithmic opportunities exploiting a graphic characterization of the bases we first redefine pivots in terms of simple graphic operations that turn a given basis into an adjacent one these results lead us to prove that the combinatorial diameter of the fractional stable set polytope is at most the number of nodes of the given graph as a corollary the hirsch bound holds for this class of polytopes

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

the diameters of network flow polytopes satisfy the hirsch conjecture we solve a problem in the combinatorics of polyhedra motivated by the network simplex method we show that the hirsch conjecture holds for the diameter of the graphs of all network flow polytopes in particular the diameter of a network flow polytope for a network with n nodes and m arcs is never more than m n 1 a key step to prove this is to show the same result for classical transportation polytopes

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

random walks totally unimodular matrices and a randomised dual simplex algorithm we discuss the application of random walks to generating a random basis of a totally unimodular matrix and to solving a linear program with such a constraint matrix we also derive polynomial upper bounds on the combinatorial diameter of an associated polyhedron

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

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

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

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

the d step conjecture and its relatives the d step conjecture arose from an attempt to understand the computational complexity of edge following algorithms for linear programming such as the simplex algorithm it can be stated in terms of diameters of graphs of convex polytopes in terms of the existence of nonrevisiting paths in such graphs in terms of an exchange process for simplicial bases of a vector space and in terms of matrix pivot operations first formulated by w m hirsch in 1957 the conjecture remains unsettled though it has been proved in many special cases and counterexamples have been found for slightly stronger conjectures if the conjecture is false as we believe to be the case then finding a counterexample will be merely a small first step in the line of investigation related to the conjecture this report summarizes what is known about the d step conjecture and its relatives a considerable amount of new material is included but it does not seem to come close to settling the conjecture of special interest is the first example of a polytope that is not vertex decomposable showing that a certain natural approach to the conjecture will not work also significant are the quantitative relations among the lengths of paths associated with various forms of the conjecture

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

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

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

large deviations for disordered bosons and multiple orthogonal polynomial ensembles we prove a large deviations principle for the empirical measures of a class of biorthogonal and multiple orthogonal polynomial ensembles that includes biorthogonal laguerre jacobi and hermite ensembles the matrix model of lueck sommers and zirnbauer for disordered bosons the stieltjes wigert matrix model of chern simons theory and angelesco ensembles

on wright s generalized bessel kernel abstract in this paper we consider the wright s generalized bessel kernel k x y defined by x 0 1 j 1 1 u x j 1 u y u d u 1 0 where j a b x j 0 x j j a b j a c b 1 is wright s generalization of the bessel function this non symmetric kernel which generalizes the classical bessel kernel corresponding to 1 in random matrix theory is the hard edge scaling limit of the correlation kernel for certain muttalib borodin ensembles we show that if is rational i e m n with m n n g c d m n 1 and m 1 m n the wright s generalized bessel kernel is integrable in the sense of its izergin korepin slavnov we then come to the fredholm determinant of this kernel over the union of several scaled intervals which can also be interpreted as the gap probability the probability of finding no particles on these intervals the integrable structure allows us to obtain a system of coupled partial differential equations associated with the corresponding fredholm determinant as well as a hamiltonian interpretation as a consequence we are able to represent the gap probability over a single interval 0 s in terms of a solution of a system of nonlinear ordinary differential equations

a counterexample to the hirsch conjecture the hirsch conjecture 1957 stated that the graph of a d dimensional polytope with n facets cannot have combinatorial diameter greater than n d that is any two vertices of the polytope can be connected by a path of at most n d edges this paper presents the rst counterexample to the conjecture our polytope has dimension 43 and 86 facets it is obtained from a 5 dimensional polytope with 48 facets that violates a certain generalization of the d step conjecture of klee and walkup

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

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

the many facets of linear programming we examine the history of linear programming from computational geometric and complexity points of view looking at simplex ellipsoid interior point and other methods

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