the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

fixed width multiple comparison procedures using common random numbers for steady state simulations abstract suppose that there are k 2 different systems i e stochastic processes where each system has an unknown steady state mean performance we consider the problem of running a two stage simulation using common random numbers to construct fixed width confidence intervals for two multiple comparison problems under the assumptions that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem and that the asymptotic covariance matrix satisfies a condition known as sphericity we prove that our confidence intervals are asymptotically valid as the desired half width of the confidence intervals tend to zero we develop both absolute and relative width confidence intervals empirical results are presented indicating the procedures robustness to violations of the sphericity assumption

a direct finite element method study of generalized thermoelastic problems abstract by using the principle of virtual work the finite element equations corresponding to the generalized thermoelasticity with two relaxation times i e the g l theory are derived in order to improve the accuracy of integral transform method especially in two three dimension the equations are solved directly in time domain as numerical examples the developed method is used to investigate the generalized thermoelastic behavior of a slim strip and a semi infinite plate subject to thermal shock loading the results demonstrate that the developed method can faithfully predict the deformation of the structure and most importantly the delicate second sound effect of heat conduction in both one and two dimensional solids whilst it is usually difficult to model especially in two dimensional by using the transform method this method can also be used to study generalized piezothermoelastic and magnetothermoelastic problems

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

theoretical explanation of observed decreasing failure rate pooled data on the times of successive failures of the air conditioning system of a fleet of jet airplanes seemed to indicate that the life distribution had a decreasing failure rate more refined analysis showed that the failure distribution for each airplane separately was exponential but with a different failure rate using the theorem that a mixture of distributions each having a non increasing failure rate e g a mixture of exponential distributions itself has a non increasing failure rate the apparent decreasing failure rate of the pooled air conditioning life distribution was satisfactorily explained the present study has implications in other areas where an observed decreasing failure rate may well be the result of mixing exponential distributions having different parameters

the tzitzeica equation a backlund transformation interpreted as truncated painleve expansion it is shown that the overdetermined system of equations obtained by truncating the painleve expansion for the classical tzitzeica equation admits a solution which defines a backlund transformation

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

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

tests of sphericity of normal distributions and the analysis of repeated measures designs the locally best invariant test statistic for testing sphericity of normal distributions is shown to be a simple function of the box geisser greenhouse degrees of freedom correction factor in a repeated measures design because of this relationship it provides a more intuitively appealing test of the necessary and sufficient conditions for valid f tests in repeated measures analysis of variance than the likelihood ratio test the properties of the two tests are compared and tables of the critical values of the box geisser greenhouse correction factor are given

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

hyper complex four manifolds from the tzitzeica equation it is shown how solutions to the tzitzeica equation can be used to construct a family of pseudo hyper complex metrics in four dimensions

a class of 1 d gas flows soluble by the inverse scattering transform abstract we first show that the euler equations of 1 dimensional adiabatic gas dynamics with arbitrary equation of state present a symmetry s of order three i e such that s3 1 for a particular class of equations of state which may be viewed as representing the geometrical center of the symmetry a higher symmetry exists the sl 3 symmetry in agreement with the results of ref 2 for these equations of state we derive riemann invariants and are thus able to reduce the system of the euler s equations to a mere second order equation versus characteristic coordinates that equation turns out to be soluble by an inverse scattering method with a third order scattering operator as shown in ref 6 we thus provide a first instance of soliton propagation on a nondissipative gaseous background it must be noted however that these are solitons in a mathematical sense only as the space time in which they propagate uniformly does not coincide with ordinary space time

explicit integrability for hamiltonian systems and the painleve conjecture we analyze a class of hamiltonian systems in two dimensions for which we proved that a second constant of motion exists it is shown that using the two first integrals the equations of motion can be written in a form which allows their integration by quadratures an analysis of the equations of motion in this reduced form establishes the behavior of the solutions in the complex time plane it is shown explicitly that the systems belonging to this class possess the weak painleve property i e their solutions in complex time can present singularities of a specific algebraic type

the singular boundary method for two dimensional static thermoelasticity analysis based on the singular boundary method sbm coupled with the radial basis functions rbf a meshless algorithm is proposed to solve two dimensional static thermoelasticity problems the displacements and stresses can be written as the sum of a homogeneous solution and a particular solution the rbf and sbm are used to construct the corresponding approximate particular and homogeneous parts respectively all unknowns are determined by satisfying the governing equations and the boundary conditions numerical experiments are performed for different cases and the proposed meshless method is effectively validated by comparing the results with the available analytical solutions

backlund transformation of partial differential equations from the painleve gambier classification ii tzitzeica equation from the existing methods of singularity analysis only we derive the two equations which define the backlund transformation of the tzitzeica equation this is achieved by defining a truncation in the spirit of the approach of weiss et al so as to preserve the lorentz invariance of the tzitzeica equation if one assumes a third order scattering problem this truncation admits a unique solution thus leading to a matrix lax pair and a darboux transformation in order to obtain the backlund transformation bt which is the main new result of this paper one represents the lax pair by an equivalent two component riccati pseudopotential this yields two different bts the first one is a bt for the hirota satsuma equation while the second one is a bt for the tzitzeica equation one of the two equations defining the bt is the fifth ordinary differential equation of gambier

a reference bayesian test for nested hypotheses and its relationship to the schwarz criterion abstract to compute a bayes factor for testing h 0 0 in the presence of a nuisance parameter priors under the null and alternative hypotheses must be chosen as in bayesian estimation an important problem has been to define automatic or reference methods for determining priors based only on the structure of the model in this article we apply the heuristic device of taking the amount of information in the prior on equal to the amount of information in a single observation then after transforming to be null orthogonal to we take the marginal priors on to be equal under the null and alternative hypotheses doing so and taking the prior on to be normal we find that the log of the bayes factor may be approximated by the schwarz criterion with an error of order o p n rather than the usual error of order o p 1 this result suggests the schwarz criterion should provide sensible approximate solutions to bayesian testing problems at least when the hypotheses are nested when

testing a point null hypothesis the irreconcilability of p values and evidence abstract the problem of testing a point null hypothesis or a small interval null hypothesis is considered of interest is the relationship between the p value or observed significance level and conditional and bayesian measures of evidence against the null hypothesis although one might presume that a small p value indicates the presence of strong evidence against the null such is not necessarily the case expanding on earlier work especially edwards lindman and savage 1963 and dickey 1977 it is shown that actual evidence against a null as measured say by posterior probability or comparative likelihood can differ by an order of magnitude from the p value for instance data that yield a p value of 05 when testing a normal mean result in a posterior probability of the null of at least 30 for any objective prior distribution objective here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null other definiti

maximum likelihood estimation of nonlinear structural equation models the existing maximum likelihood theory and its computer software in structural equation modeling are established based on linear relationships among manifest variables and latent variables however models with nonlinear relationships are often encountered in social and behavioral sciences in this article an em type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model to avoid computation of the complicated multiple integrals involved the e step is completed by a metropolis hastings algorithm it is shown that the m step can be completed efficiently by simple conditional maximization standard errors of the maximum likelihood estimates are obtained via louis s formula the methodology is illustrated with results from a simulation study and two real examples

a note on a class of solitary like solutions of the tzitzeica equation generated by a similarity reduction abstract in this paper new class of solutions of the tzitzeica equation are derived by using the classical lie symmetry analysis the important aspect of this paper however is the fact that the analysis results in a new class of solitary like solutions the so called cusp solitary solutions this special type of solutions are not found in the current literature and represents a necessary contribution for the whole solution manifold the studied equation was originally found in the field of geometry otherwise the tzitzeica equation takes place in many branches of non linear sciences therefore explicit class of solutions connected by a physical meaning are of great importance the analysis is restricted to the case of traveling waves represented by a similarity variable describing any wave propagation a complete characterization of the group properties is given the classical lie point symmetries are derived and algebraic properties are determined similarity solutions and transformations are given in a most general form and have been derived for the first time in terms of jacobian elliptic functions it is worth to mention that the application of known powerful algebraic methods e g special function transform methods are not appropriate to study the solution manifold hence the present paper is therefore suitable to create a deeper insight into the solution manifold with respect to the traveling wave picture

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

su 3 symmetry of the equations of unidimensional gas flow with arbitrary entropy distribution we have shown in an earlier work that assuming a particular class of equations of state the euler equations of one dimensional gas flow are invariant under an su 3 group of transformations and in fact admit of a lie group of symmetry of infinite order they therefore possess an infinite number of conservation laws we show in the present work that the su 3 symmetrical formalism still brings about tremendous simplification and analytical order in the most general case where the equation of state is arbitrary the six characteristic equations assume a vector form and relate two conjugate three dimensional vectors u and x the su 3 symmetry is only broken to a minor extent through the occurrence of a multiplicative factor in the equations the conservation laws take the form of the cauchy integrability condition for the elements of a traceless second rank tensor eij and taken all together form an su 3 octet in the most general case however there exist four conservation laws only five if the

lower bounds on bayes factors for multinomial distributions with application to chi squared tests of fit lower bounds on bayes factors in favor of the null hypothesis in multinomial tests of point null hypotheses are developed these are then applied to derive lower bounds on bayes factors in both exact and asymptotic chi squared testing situations the general conclusion is that the lower bounds tend to be substantially larger than p values raising serious questions concerning the routine use of moderately small p values to represent significant evidence against the null hypothesis

a two dimensional isogeometric boundary element method for elastostatic analysis the concept of isogeometric analysis where functions that are used to describe geometry in cad software are used to approximate the unknown fields in numerical simulations has received great attention in recent years the method has the potential to have profound impact on engineering design since the task of meshing which in some cases can add significant overhead has been circumvented much of the research effort has been focused on finite element implementations of the isogeometric concept but at present little has been seen on the application to the boundary element method the current paper proposes an isogeometric boundary element method bem which we term igabem applied to two dimensional elastostatic problems using non uniform rational b splines nurbs we find it is a natural fit with the isogeometric concept since both the nurbs approximation and bem deal with quantities entirely on the boundary the method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric bem implementation

on the choice of a model to fit data from an exponential family let x 1 cdots x n be iid observations coming from an exponential family the problem of interest is this given a finite number of models m j smoothly curved manifolds in mathbb r k choose the best model to fit the observations with some penalty for choosing models with dimensions which are too large a result of schwarz is made more specific and is extended to the case where the models are curved manifolds if s y n j is up to a constant c n independent of the model the log of the posterior probability of the j th model where the sample mean y n 1 n sum n i 1 x i has been replaced by y schwarz suggested an asymptotic expansion of s y n j whose leading terms are gamma y n j n sup psi in m j cap theta y psi b psi frac 1 2 k j log n in the case where the models are affine subspaces of mathbb r k we establish a similar asymptotic expansion including the next term with uniform bounds for y in a compact neighborhood of nabla b theta where theta is the true value of the parameter we suggest a criterion for the choice of the best model that consists of maximizing the three leading terms in the expansion s y n j we show that the criterion gives the correct model with probabilities p n theta rightarrow 1 as n rightarrow infty

common structure of several completely integrable non linear equations the author consider several non linear equations which are known to be completely integrable by the method of inverse scattering transform ranging from sine gordon and the dodd bullough equation 1976 to the axisymmetric stationary einstein maxwell equations such equations are known to be invariant under a fundamental lie group of symmetry g such as sl 2 or sl 3 in the simpler cases the author s treatment starts with the reformulation of the given equations as a system involving the scalar invariants of the lie group g only this scalar formulation is not only g invariant but also manifestly invariant under the continuous group associated with the emergence of a spectral parameter and is thus expected to be more fundamental and simpler in all the cases that the author has considered including the einstein maxwell system vector pseudopotentials of dimension not higher than three have been derived backlund transformations have been found which generate multisolitons starting from the vacuum and have the general reciprocal form x 1 x where x is a component of one of the vector or tensor pseudopotentials the author also mentions the result that kinnersley s formulation 1977 of the ernst vacuum equation 1968 is formally equivalent to the fluid dynamical problem of unidimensional ideal gas flow the dodd bullough equation is equivalent to another particular case of gas motion

analysis of variance why it is more important than ever analysis of variance anova is an extremely important method in exploratory and confirmatory data analysis unfortunately in complex problems e g split plot designs it is not always easy to set up an appropriate anova we propose a hierarchical analysis that automatically gives the correct anova comparisons even in complex scenarios the inferences for all means and variances are performed under a model with a separate batch of effects for each row of the anova table we connect to classical anova by working with finite sample variance components fixed and random effects models are characterized by inferences about existing levels of a factor and new levels respectively we also introduce a new graphical display showing inferences about the standard deviations of each batch of effects we illustrate with two examples from our applied data analysis first illustrating the usefulness of our hierarchical computations and displays and second showing how the ideas of anova are helpful in understanding a previously fit hierarchical model

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

assessment and propagation of model uncertainty in most examples of inference and prediction the expression of uncertainty about unknown quantities y on the basis of known quantities x is based on a model m that formalizes assumptions about how x and y are related m will typically have two parts structural assumptions s such as the form of the link function and the choice of error distribution in a generalized linear model and parameters whose meaning is specific to a given choice of s it is common in statistical theory and practice to acknowledge parametric uncertainty about given a particular assumed structure s it is less common to acknowledge structural uncertainty about s itself a widely used approach involves enlisting the aid of x to specify a plausible single best choice s for s and then proceeding as if s were known to be correct in general this approach fails to assess and propagate structural uncertainty fully and may lead to miscalibrated uncertainty assessments about y given x when miscalibration occurs it will often result in understatement of inferential or predictive uncertainty about y leading to inaccurate scientific summaries and overconfident decisions that do not incorporate sufficient hedging against uncertainty in this paper i discuss a bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible by virtue of recent computational advances and examine its implementation in examples that involve forecasting the price of oil and estimating the chance of catastrophic failure of the us space shuttle

singular boundary method for heat conduction problems with certain spatially varying conductivity the singular boundary method sbm is a recent boundary type meshless collocation method in which the solution of a given problem is expanded as a linear combination of the fundamental solutions in terms of the source points the method circumvents the fictitious boundary long perplexing the method of fundamental solution mfs by the introduction of the concept of origin intensity factors oifs this paper documents the first attempt to extend the method to heat conduction problems in nonhomogeneous materials we derive the fundamental solutions of heat conduction problems with the thermal conductivity of the quadratic exponential and trigonometric material variations in three directions furthermore we firstly theoretically derive the value of the oif for the natural logarithm function which is later extended to the oifs for a group of fundamental solutions the feasibility accuracy and stability of the presented sbm formulation are confirmed for both two 2d and three dimensional 3d examples

tzitzeica transformation is a dressing action we classify the simplest rational elements in a twisted loop group and prove that dressing actions of them on proper indefinite affine spheres give the classical tzitzeica transformation and its dual we also give the group point of view of the permutability theorem construct complex tzitzeica transformations and discuss the group structure for these transformations

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

using common random numbers for indifference zone selection and multiple comparisons in simulation we present a general recipe for constructing experiment design and analysis procedures that simultaneously provide indifference zone selection and multiple comparison inference for choosing the best among k simulated systems we then exhibit two such procedures that exploit the variance reduction technique of common random numbers to reduce the sample size required to attain a fixed precision one procedure is based on the bonferroni inequality and is guaranteed to be statistically conservative the other procedure is exact under a specific dependence structure but may be slightly liberal otherwise both are easy to apply requiring only simple calculations and tabled constants we illustrate the procedures with a numerical example

bayes factors for nonlinear hypotheses and likelihood distributions summary new methods are proposed which allow bayes factors to be computed for hypotheses which impose nonlinear restrictions on the parameters projection methods are used to induce the prior distribution over the restricted parameter space which is required for computation of the bayes factor various distance metrics are introduced to define the projection including a utility based metric which gives kullback leibler divergence as a special case draws from the restricted and unrestricted prior distributions are used to construct marginal distributions of the likelihood which is shown to have additional diagnostic value over and above the bayes factor these methods are applied to hypotheses statisticians are frequently asked to entertain hypotheses which are nonlinear in the model parameters nonlinear hypotheses arise both from subject matter theory as well as from the process of model selection to address nonlinear hypotheses researchers use frequentist methods which are usually implemented using asymptotic approximations berger 1987 zellner 1971 1978 1984 and others have discussed the weaknesses of the classical significance testing approach and suggest bayesian alternatives such as odds ratios the odds ratio is the ratio of posterior probabilities of two competing hypotheses and is the product of the prior odds ratio and the bayes factor the odds ratio has the conceptual advantages of providing a natural probability metric for assessing the strength of data and prior beliefs because of the difficulties of assessing priors under the nonlinear restrictions and the computation of the required integrals few bayes factors have been computed for nonlinear hypotheses see lindley 1988 for an exception in the present paper we outline a general method for computing bayes factors which is flexible conceptually appealing and computationally tractable the literature on bayes factors starts with the work of jeffreys 1961 other references include berger delampady 1987 dickey 1971 good 1985 kass vaidyanathan 1992 smith spiegelhalter 1980 and zellner 1971 1978 1984 these papers deal with the testing of linear restrictions on the parameter space often in the context of linear models even the widely used schwarz 1978 model selection criterion considers only linear restrictions in models of the exponential family form the key difficulty which has kept researchers from developing bayes factors for nonlinear hypotheses is the

singular boundary method for solving plane strain elastostatic problems this study documents the first attempt to apply the singular boundary method sbm a novel boundary only collocation method to two dimensional 2d elasticity problems unlike the method of fundamental solutions mfs the source points coincide with the collocation points on the physical boundary by using an inverse interpolation technique to regularize the singularity of the fundamental solution of the equation governing the problems of interest three benchmark elasticity problems are tested to demonstrate the feasibility and accuracy of the proposed method through detailed comparisons with the mfs boundary element method bem and finite element method fem

statistical tests with accurate size and power for balanced linear mixed models the convenience of linear mixed models for gaussian data has led to their widespread use unfortunately standard mixed model tests often have greatly inflated test size in small samples many applications with correlated outcomes in medical imaging and other fields have simple properties which do not require the generality of a mixed model alternately stating the special cases as a general linear multivariate model allows analysing them with either the univariate or multivariate approach to repeated measures unirep multirep even in small samples an appropriate unirep or multirep test always controls test size and has a good power approximation in sharp contrast to mixed model tests hence mixed model tests should never be used when one of the unirep tests uncorrected huynh feldt geisser greenhouse box conservative or multirep tests wilks hotelling lawley roy s pillai bartlett apply convenient methods give exact power for the uncorrected and box conservative tests simulations demonstrate that new power approximations for all four unirep tests eliminate most inaccuracy in existing methods in turn free software implements the approximations to give a better choice of sample size two repeated measures power analyses illustrate the methods the examples highlight the advantages of examining the entire response surface of power as a function of sample size mean differences and variability

spectrum sensing in the presence of multiple primary users we consider multi antenna cooperative spectrum sensing in cognitive radio networks when there may be multiple primary users a detector based on the spherical test is analyzed in such a scenario based on the moments of the distributions involved simple and accurate analytical formulae for the key performance metrics of the detector are derived the false alarm and the detection probabilities as well as the detection threshold and receiver operation characteristics are available in closed form simulations are provided to verify the accuracy of the derived results and to compare with other detectors in realistic sensing scenarios

a priori tests in repeated measures designs effects of nonsphericity the validity conditions for univariate repeated measures designs are described attention is focused on the sphericity requirement for av degree of freedom family of comparisons among the repeated measures sphericity exists when all contrasts contained in thev dimensional space have equal variances under nonsphericity upper and lower bounds on test size and power of a priori repeated measures f tests are derived the effects of nonsphericity are illustrated by means of a set of charts the charts reveal that small departures from sphericity 97 1 00 can seriously affect test size and power it is recommended that separate rather than pooled error term procedures be routinely used to test a priori hypotheses

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

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

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

the analysis of profile data revisited we revisit a former problem that led to much commentary regarding a proposed use of testing whether profiles for several groups in a repeated measurement scenario were parallel here we review previous approaches and propose bayesian model selection to indicate whether the profiles can be considered parallel and if so support an estimation procedure for the profile differences