connection between kinetic methods for fluid dynamic equations and macroscopic finite difference schemes the lattice boltzmann method lbm for the incompressible navier stokes ns equations and the gas kinetic scheme for the compressible ns equations are based on the kinetic theory of gases in the latter case however it is shown that the kinetic formulation is necessary only in the discontinuous reconstruction of fluid dynamic variables for shock capturing analogously we will discuss the reduction of a kinetic method for the incompressible case where the lbm scheme will be shown to shrink to an artificial compressibility type finite difference scheme we will prove first that a simple and compact lbm scheme cannot catch rarefied effects beyond navier stokes and hence that it is worth the effort to develop kinetic based fd alternatives finally we will propose two improvements to existing kinetic based fd schemes first of all a the proposed scheme is formulated purely in terms of macroscopic quantities on a compact stencil secondly b the semi implicit formulation is proposed in order to increase the stability we think that this work may be useful to others in realizing the actual possibilities of simple lbm schemes beyond navier stokes and in adopting the suggested improvements in their actual fd codes

three p value consistent procedures for multiple comparisons with a control in direction mixed families in clinical studies it is common to compare several treatments with a control in such cases the most popular statistical technique is the dunnett procedure however the dunnett procedure is designed to deal with particular families of inferences in which all hypotheses are either one sided or two sided recently based on the minimization of average simultaneous confidence interval width a single step procedure was derived to handle more general inferential families that contained a mixture of one and two sided inferences but that single step procedure is unable to guarantee the condition of p value consistency which means that when a hypothesis with a certain p value is rejected all other hypotheses with smaller p values are also rejected in this paper we present a single step procedure and two stepwise procedures which are p value consistent the two proposed stepwise procedures provide more powerful testing methods when compared with single step procedures the extent of their superiority is demonstrated with a simulation study of average power selected critical values are tabulated for the implementation of the three proposed procedures additional simulation studies provide evidence that the new stepwise procedures are robust to moderate changes in the underlying probability distributions and the proposed step up procedure is uniformly more powerful than the resampling based hochberg step up approach in all considered distribution models finally we provide a practical example with sample data extracted from a medical experiment

modified kinetic flux vector splitting schemes for compressible flows we investigate the traditional kinetic flux vector splitting kfvs and bgk schemes for the compressible euler equations first based on a careful study of the behavior of the discrete physical variables across the contact discontinuity we analyze quantitatively the mechanism of inducing spurious oscillations of the velocity and pressure in the vicinity of the contact discontinuity for the first order kfvs and bgk schemes then with the help of this analysis we propose a first order modified kfvs mkfvs scheme which is oscillation free in the vicinity of the contact discontinuity provided certain consistent conditions are satisfied moreover by using piecewise linear reconstruction and van leer s limiter the first order mkfvs scheme is extended to a second order one consequently a nonoscillatory second order mkfvs scheme is constructed finally by combing the mkfvs schemes with the model we successfully extend the mkfvs schemes to multi flows and propose therefore a first and second order mkfvs schemes for multi fluid computations which are nonoscillatory across fluid interfaces a number of numerical examples presented in this paper validate the theoretic analysis and demonstrate the good performance of the mkfvs schemes in simulation of contact discontinuities for both single and multi fluids

gas kinetic schemes for compressible flow of real gases abstract this paper extends gas kinetic schemes to the euler equations for real gases in the current scheme the maxwell boltzmann gas distribution function is modified to recover macroscopic flow equations more specifically the internal degree of freedom of the gas distribution function becomes a function of flow variables according to the general equation of state the numerical results confirm the accuracy and robustness of the gas kinetic approach

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

kinetic flux vector splitting schemes for the hyperbolic heat conduction a kinetic solver is developed for the initial and boundary value problems of the symmetric hyperbolic moment system this nonlinear system of equations is related to the heat conduction in solids at low temperatures the system consists of a conservation equation for the energy density e and a balance equation for the heat flux qi where e and qi are the four basic fields of the theory we use kinetic flux vector splitting kfvs scheme to solve these equations in one and two space dimensions the flux vectors of the equations are splitted on the basis of the local equilibrium distribution of phonons the resulting computational procedure is efficient and straightforward to implement the second order accuracy of the scheme is achieved by using muscl type reconstruction and min mod nonlinear limiters the solutions exhibit second order accuracy and satisfactory resolution of gradients with no spurious oscillations the scheme is extended to the two dimensional case in a usual dimensionally split manner in order to prescribe the boundary data we need the knowledge of the e and qi however in experiments only one of the quantities can be controlled at the boundary this problem is removed by using a continuity condition it turned out that after some short time energy and heat flux are related to each other according to rankine hugoniot jump relations to illustrate the performance of the kfvs scheme we perform several one and two dimensional test computations for the comparison of our results we use high order central schemes the present study demonstrates that this kinetic method is effective in handling such problems

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

hybrid continuum molecular simulations of transient gas flows with rarefaction an adaptively coupled continuum molecular approach for compressible viscous flows in transient calculations is presented the continuum domain is described by the unsteady compressible navier stokes equations and the molecular domain is solved by direct simulation monte carlo a strategy is described to extend the overlapped schwarz method with dirichlet dirichlet boundary condition coupling procedure to transient simulations the method has been successfully validated against full direct simulation monte carlo results for transient simulations of a one dimensional shock tube and a two dimensional pressure driven slit flow a sensitivity analysis showed that the used overlapped schwarz coupling method with dirichlet dirichlet boundary conditions is only weakly sensitive to various parameters e g the exact position of the continuum molecular interface the size of the overlap region and the scatter in the molecular solution which is a clear advantage over the more commonly used flux based coupling technique another advantage of the chosen coupling method is that the continuum and molecular time steps can be decoupled and that in general a coupling time step can be used that is much larger than the molecular time step the study performed also highlighted a limit of the method it was found to be necessary to keep the courant number based on the coupling time step the cell size in the continuum region and the molecular most probable velocity below 1 to avoid instabilities

hypothesis testing in an errors in variables model with heteroscedastic measurement errors in many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors the main goal of this paper is to consider inference on such models with error prone observations and variances of the measurement errors changing across observations we suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed aggregate data allow the estimation of the error variances maximum likelihood estimates are computed numerically via the em algorithm consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed test statistics are proposed for testing hypotheses of interest further we implement a simple graphical device that enables an assessment of the model s goodness of fit results of simulations concerning the properties of the test statistics are reported the approach is illustrated with data from the who monica project on cardiovascular disease

generation of the chapman enskog distribution a pair of simple efficient and robust algorithms for generating random velocities sampled from the chapman enskog distribution is presented

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

simple derivation of high resolution schemes for compressible flows by kinetic approach the high resolution scheme for the compressible navier stokes equations developed in ohwada and kobayashi management of discontinuous reconstruction in kinetic schemes j comput phys 197 2004 116 138 is rederived without using any special techniques of kinetic theory the scheme is simplified and its efficiency is improved by introducing an artificial equilibrium function high performance of the new scheme is demonstrated in the problems of double mach reflection forward facing step and shock boundary layer interaction the detailed information for easy programming is also given

management of discontinuous reconstruction in kinetic schemes the present paper highlights the importance of management of the discontinuous reconstruction in the kinetic schemes for gasdynamic equation systems firstly it is revealed by the analysis of the gas kinetic bgk scheme jcp 171 2001 289 that a continuous reconstruction created from a discontinuous one is a key to the successful kinetic schemes when it is applied to a well resolved region the numerical flux that takes account of the collision effect correctly becomes lax wendroff like when it is applied to an unresolved region such as a shock layer an appreciable numerical dissipation which contributes to the suppression of spurious oscillations is produced secondly new kinetic schemes for the compressible navier stokes euler equations are developed by using the key the numerical flux of one of the schemes is computed by using the splitting algorithm where the effect of the molecular collision is directly taken into account and the undesirable error of the splitting algorithm in the case where the time step is much larger than the mean free time is avoided by a simple modification of the initial data although a discontinuous reconstruction is employed in the approximation of the initial data the continuity is automatically taken into account in the dominant part of the numerical flux the other schemes are the extensions of the lax wendroff type scheme to the case of the key reconstruction thirdly the performance of these schemes is tested it is demonstrated that they work as shock capturing schemes and yield fine boundary layer profiles with a reasonable number of cells such as 10 cells in the layer

estimation by data augmentation in regression models with continuous and discrete covariates measured with error estimation methods are considered for regression models which have both misclassified discrete covariates and continuous covariates measured with error adjusted parameter estimates are obtained using the method of data augmentation where the true values of the covariates measured with error are regarded as missing data validation data on the covariates are assumed to be available the distinction between internal and external validation data is emphasized and its effects on the analysis are examined the method is illustrated with simulated data 1997 by john wiley sons ltd

kinetic flux vector splitting for the navier stokes equations before a hybrid scheme can be developed combining the direct simulation monte carlo dsmc method and a navier stokes ns representation one must have access to compatible kinetic split fluxes from the ns portion of the hybrid scheme the kinetic theory basis is given for the development of the required fluxes from the chapman enskog velocity distribution function for a simple gas and these are then extended to a polyatomic gas by use of the eucken approximation the derived fluxes are then used to implement boundary conditions at solid surfaces that are based on concepts associated with kinetic theory and the dsmc method this approach is shown to lead to temperature slip and velocity slip as a natural outcome of the new formulation a requirement for use in the near continuum regime where dsmc and ns must be joined several different flows for which solid boundaries are not present are computed using the derived fluxes together with a second order finite volume scheme and the results are shown to agree well with several established numerical schemes for the ns equations

a bayesian semiparametric model for case control studies with errors in variables summary we develop a model and a numerical estimation scheme for a bayesian approach to inference in case control studies with errors in covariables the model proposed in this paper is based on a nonparametric model for the unknown joint distribution for the missing data the observed covariates and the proxy this nonparametric distribution defines the measurement error component of the model which relates the missing covariates x with a proxy w the oxymoron nonparametric bayes refers to a class of flexible mixture distributions for the likelihood of disease given covariates we choose a logistic regression model by using a parametric disease model and nonparametric exposure model we obtain robust interpretable results quantifying the effect of exposure

a bayesian approach to logistic regression models having measurement error following a mixture distribution to estimate the parameters in a logistic regression model when the predictors are subject to random or systematic measurement error we take a bayesian approach and average the true logistic probability over the conditional posterior distribution of the true value of the predictor given its observed value we allow this posterior distribution to consist of a mixture when the measurement error distribution changes form with observed exposure we apply the method to study the risk of alcohol consumption on breast cancer using the nurses health study data we estimate measurement error from a small subsample where we compare true with reported consumption some of the self reported non drinkers truly do not drink the resulting risk estimates differ sharply from those computed by standard logistic regression that ignores measurement error

inferences about exposure disease associations using probability of exposure information unconditional and conditional likelihood methods are proposed for modeling odds and odds ratios relating a binary disease variable and an exposure variable that is only known probabilistically e g via measurement of a surrogate exposure variable while adjusting appropriately for a vector of covariables assuming nondifferential errors a probabilistic structure is developed that permits analysis of the marginal relation between disease and the surrogate while maintaining important properties of the marginal relation between disease and true exposure in particular analyses conditioned on marginal totals in surrogate disease tables remove the same nuisance parameters as are removed in a conditional analysis of true exposure disease tables in addition a relation between the probability of exposure poe in the disease and disease free groups is derived permitting the use of information about exposure from populations with structure different from the study population examples are presented illustr

bayesian analysis of case control studies with categorical covariates in a case control study the appropriate likelihood is the retrospective likelihood i e the likelihood of exposure given disease for the classical frequentist analysis the prospective likelihood i e the likelihood of disease given exposure and the retrospective likelihood produce the same odds ratio estimators for exposure and so logistic regression may be used for both the bayesian analysis is not so simple but the bayesian framework for case control studies offers flexible possibilities for the hierarchical modelling that is needed in many contexts we review the bayesian approaches to the analysis of case control studies developed so far show how to extend these approaches to the situation of a study with any number of categorical or discretised continuous exposure variables and identifying suitable priors we then show how the resulting models may be fitted using markov chain monte carlo methods and provide an illustration based on genotype data

numerical hydrodynamics from gas kinetic theory a new high resolution numerical hydrodynamic scheme is developed from considerations of gas kinetic theory this boltzmann type scheme uses the particle distribution function and follows its evolution to evaluate the numerical fluxes the intrinsic multidimensional property in the evolution stage of gas distribution function distinguishes it from any other high order upwind scheme from approximate boltzmann equation the navier stokes equations can be derived and this new numerical method uses this advantage to approximate the solutions of the navier stokes equations where the advection and dissipation effects are coupled in the time dependent gas distribution function several well defined numerical test cases are presented in one and two dimensions and it is shown that the resolution in the numerical results is competitive with those of any of the current high resolution schemes without special treatment of the discontinuities for strong rarefaction waves our scheme gives better results in this thesis we try to separate clearly numerical and physical effects and we also give a concise explanation of the necessity of including numerical viscosities implicitly or explicitly in high resolution godunov type and central difference schemes even for the navier stokes equations the main part of this thesis will be published in two papers 27 and 45 in the journal of computational physics

conditional independence models for epidemiological studies with covariate measurement error we construct a unifying representation of the structure of measurement error problems with particular reference to situations commonly encountered in epidemiological studies and outline how estimation of the parameters of interest can be carried out in a bayesian framework using gibbs sampling we show how this approach can be implemented for designs involving continuous measurement errors assessed through a validation substudy and discuss our results on simulated data

some aspects of measurement error in explanatory variables for continuous and binary regression models a simple form of measurement error model for explanatory variables is studied incorporating classical and berkson cases as particular forms and allowing for either additive or multiplicative errors the work is motivated by epidemiological problems and therefore consideration is given not only to continuous response variables but also to logistic regression models the possibility that different individuals in a study have errors of different types is also considered the relatively simple estimation procedures proposed for use with cohort data and case control data are checked by simulation under the assumption of various error structures the results show that even in situations where conventional analysis yields slope estimates that are on average attenuated by a factor of approximately 50 per cent estimates obtained using the proposed amended likelihood functions are within 5 per cent of their true values the work was carried out to provide a method for the analysis of lung cancer risk following residential radon exposure but it should be applicable to a wide variety of situations

estimation and inference for logistic regression with covariate misclassification and measurement error in main study validation study designs abstract in epidemiological studies continuous covariates often are measured with error and categorical covariates often are misclassified using the logistic regression model to represent the relationship between the binary outcome and the perfectly measured and classified covariates the model for the observed main study data is derived this derivation relies on the assumption that the error in the continuous covariates is multivariate normally distributed and uses a chain of logistic regression models to describe the misclassification processes these model assumptions are empirically verified in the validation study where the misclassified and mismeasured covariates are validated using perfectly measured and classified data the full data likelihood including contributions from both the main study and the validation study is maximized to obtain the maximum likelihood estimates for the parameters of the underlying logistic regression model and of the measurement error model and reclassification mo

prospective analysis of logistic case control studies abstract in a classical case control study prentice and pyke proposed to ignore the study design and instead base estimation and inference on a random sampling i e prospective formulation we generalize this prospective formulation of case control studies to include multiplicative models stratification missing data measurement error robustness and other examples the resulting estimators which ignore the case control study aspect and instead are based on a random sampling formulation are typically consistent for nonintercept parameters and are asymptotically normally distributed we derive the resulting asymptotic covariance matrix of the parameter estimates the covariance matrix obtained by ignoring the case control sampling scheme and using prospective formulas instead is shown to be at worst asymptotically conservative and asymptotically correct in a variety of problems a simple sufficient condition guaranteeing the latter is obtained

regular article a new discrete velocity method for navier stokes equations the relation between the lattice boltzmann method which has recently become popular and the kinetic schemes which are routinely used in computational fluid dynamics is explored a new discrete velocity method for the numerical solution of navier stokes equations for incompressible fluid flow is presented by combining both the approaches the new scheme can be interpreted as a pseudo compressibility method and for a particular choice of parameters this interpretation carries over to the lattice boltzmann method

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

variance estimation for epidemiologic effect estimates under misclassification this paper presents basic methods for construction of variance estimators for epidemiologic effect estimates when adjusting for misclassification methods are described for differential and non differential misclassification and for external and internal estimates of classification rates the methods take account of sampling variability in both the observed data and the estimated classification rates the methods are illustrated in a case control analysis of the association of antibiotic use during pregnancy with sudden infant death syndrome

a runge kutta discontinuous galerkin method for viscous flow equations this paper presents a runge kutta discontinuous galerkin rkdg method for viscous flow computation the construction of the rkdg method is based on a gas kinetic formulation which not only couples the convective and dissipative terms together but also includes both discontinuous and continuous representation in the flux evaluation at a cell interface through a simple hybrid gas distribution function due to the intrinsic connection between the gas kinetic bgk model and the navier stokes equations the navier stokes flux is automatically obtained by the present method numerical examples for both one dimensional 1d and two dimensional 2d compressible viscous flows are presented to demonstrate the accuracy and shock capturing capability of the current rkdg method

discontinuous galerkin method for navier stokes equations using kinetic flux vector splitting kinetic schemes for compressible flow of gases are constructed by exploiting the connection between boltzmann equation and the navier stokes equations this connection allows us to construct a flux splitting for the navier stokes equations based on the direction of molecular motion from which a numerical flux can be obtained the naive use of such a numerical flux function in a discontinuous galerkin dg discretization leads to an unstable scheme in the viscous dominated case stable schemes are constructed by adding additional terms either in a symmetric or non symmetric manner which are motivated by the dg schemes for elliptic equations the novelty of the present scheme is the use of kinetic fluxes to construct the stabilization terms in the symmetric case interior penalty terms have to be added for stability and the resulting schemes give optimal convergence rates in numerical experiments the non symmetric schemes lead to a cell energy entropy inequality but exhibit sub optimal convergence rates these properties are studied by applying the schemes to a scalar convection diffusion equation and the 1 d compressible navier stokes equations in the case of navier stokes equations entropy variables are used to construct stable schemes

bayesian analysis of errors in variables regression models summary use of errors in variables models is appropriate in many practical experimental problems however inference based on such models is by no means straightforward in previous analyses simplifying assumptions have been made in order to ease this intractability but assumptions of this nature are unfortunate and restrictive in this paper we analyse errors in variables models in full generality under a bayesian formulation in order to compute the necessary posterior distributions we utilize various computational techniques two specific non linear errors in variables regression examples are considered the first is a re analysed berkson type model and the second is a classical errors in variables model our analyses are compared and contrasted with those presented elsewhere in the literature

design of validation studies for estimating the odds ratio of exposure disease relationships when exposure is misclassified summary we compared several validation study designs for estimating the odds ratio of disease with misclassified exposure we assumed that the outcome and misclassified binary covariate are available and that the error free binary covariate is measured in a subsample the validation sample we considered designs in which the total size of the validation sample is fixed and the probability of selection into the validation sample may depend on outcome and misclassified covariate values design comparisons were conducted for rare and common disease scenarios where the optimal design is the one that minimizes the variance of the maximum likelihood estimator of the true log odds ratio relating the outcome to the exposure of interest misclassification rates were assumed to be independent of the outcome we used a sensitivity analysis to assess the effect of misspecifying the misclassification rates under the scenarios considered our results suggested that a balanced design which allocates equal numbers of validation subjects into each of the four outcome mismeasured covariate categories is preferable for its simplicity and good performance a user friendly fortran program is available from the second author which calculates the optimal sampling fractions for all designs considered and the efficiencies of these designs relative to the optimal hybrid design for any scenario of interest

matrix methods for estimating odds ratios with misclassified exposure data extensions and comparisons misclassification of exposure variables is a common problem in epidemiologic studies this paper compares the matrix method barron 1977 biometrics 33 414 418 greenland 1988a statistics in medicine 7 745 757 and the inverse matrix method marshall 1990 journal of clinical epidemiology 43 941 947 to the maximum likelihood estimator mle that corrects the odds ratio for bias due to a misclassified binary covariate under the assumption of differential misclassification the inverse matrix method is always more efficient than the matrix method however the efficiency depends strongly on the values of the sensitivity specificity baseline probability of exposure the odds ratio case control ratio and validation sampling fraction in a study on sudden infant death syndrome sids an estimate of the asymptotic relative efficiency are of the inverse matrix estimate was 0 99 while the matrix method s are was 0 19 under nondifferential misclassification neither the matrix nor the inverse matrix estimator is uniformly more efficient than the other the efficiencies again depend on the underlying parameters in the sids data the mle was more efficient than the matrix method are 0 39 in a study investigating the effect of vitamin a intake on the incidence of breast cancer the mle was more efficient than the matrix method are 0 75

extension of a multiscale particle scheme to near equilibrium viscous flows a recently proposed low diffusion ld equilibrium particle method based on the direct simulation monte carlo dsmc method is modified for use with near equilibrium viscous flows a finite volume discretization of the viscous terms in the compressible navier stokes equations is used to incorporate diffusive transport effects into the ld particle method and a velocity and temperature slip wall boundary condition is employed for improved accuracy in the slip flow knudsen number regime the modified method is compared with both dsmc and theory for a series of unsteady boundary layer problems and excellent agreement is observed the computational cost of the modified ld particle method is shown for a representative near equilibrium case to be roughly four orders of magnitude lower than that of dsmc due to reduced scatter as well as less stringent cell size and time step requirements in the ld method simulation procedures are outlined for a strongly coupled hybrid algorithm where the ld particle method is used in continuum flowfield regions and dsmc is employed in nonequilibrium regions the hybrid scheme is evaluated through a comparison with numerical and experimental data for a flow of n2 through a small convergent divergent nozzle into a near vacuum and hybrid simulation results are generally found to agree very well with other available data i introduction as flows involving a wide range of characteristic length scales appear in a number of different engineering applications including those related to atmospheric flow around reentry or hypersonic vehicles high altitude rocket plumes flows within and around micro electro mechanical systems and any supersonic flow where internal shock structures are of interest in these types of flows a near equilibrium gas velocity distribution may exist through much of the flowfield as the equilibrating effect of intermolecular collisions dominates over other processes such as inhomogeneous diffusive transport or gas surface interaction which tend to pull the velocity distribution away from equilibrium however some flowfield regions may have characteristic length scales comparable to or smaller than the local mean free path so that the influence of collisions does not dominate and the velocity distribution diverges considerably from the equilibrium limit while simulation of near equilibrium flowfield regions may be efficiently performed using computational fluid dynamics cfd techniques based on the navier stokes equations nonequilibrium regions must be simulated using more expensive techniques based on the boltzmann equation the boltzmann equation is the governing equation for dilute gas flows at arbitrary knudsen numbers and its derivation follows from assumptions of molecular chaos and binary intermolecular collisions with no approximations regarding the shape of the velocity distribution the most mature and commonly used simulation method for the boltzmann equation is the direct simulation monte carlo dsmc method first introduced by bird 1 in a dsmc simulation a large number of representative particles are tracked through a computational grid and move and collide in a manner consistent with physical arguments underlying the boltzmann equation while this method may be applied to both nonequilibrium and continuum flowfield regions cell size and time step limitations often make it prohibitively expensive for simulating continuum flows where global characteristic length scales are far larger than the mean free path in practice such multiscale flows are usually simulated using both dsmc and cfd methods by applying cfd techniques in near equilibrium regions where the navier stokes equations are valid and using dsmc elsewhere in the flow in the simplest type of hybrid cfd dsmc approach a cfd simulation is performed on a domain which 1

some comments on misspecification of priors in bayesian modelling of measurement error problems in this paper we discuss some aspects of misspecification of prior distributions in the context of bayesian modelling of measurement error problems a bayesian approach to the treatment of common measurement error situations encountered in epidemiology has been recently proposed its implementation involves first the structural specification through conditional independence relationships of three submodels a measurement model an exposure model and a disease model and secondly the choice of functional forms for the distributions involved in the submodels we present some results indicating how the estimation of the regression parameters of interest which is carried out using gibbs sampling can be influenced by a misspecification of the parametric shape of the prior distribution of exposure 1997 by john wiley sons ltd

on the construction of kinetic schemes a general method for the construction of kinetic schemes of evolutionary equations is illustrated with the simple example of the linear advection equation where the role of the collision effect is clarified theoretically and numerically the application to the compressible euler equation and navier stokes equation is explained the theoretical backgrounds of the existing kinetic schemes such as the pullin scheme for the euler equation and chou baganoff scheme and modified prendergast xu scheme for the navier stokes equation are unified and their intrinsic errors are revealed

bayesian model choice via markov chain monte carlo methods summary markov chain monte carlo mcmc integration methods enable the fitting of models of virtually unlimited complexity and as such have revolutionized the practice of bayesian data analysis however comparison across models may not proceed in a completely analogous fashion owing to violations of the conditions sufficient to ensure convergence of the markov chain in this paper we present a framework for bayesian model choice along with an mcmc algorithm that does not suffer from convergence difficulties our algorithm applies equally well to problems where only one model is contemplated but its proper size is not known at the outset such as problems involving integer valued parameters multiple changepoints or finite mixture distributions we illustrate our approach with two published examples

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