asymptotic preserving schemes for highly oscillatory vlasov poisson equations this work is devoted to the numerical simulation of a vlasov poisson model describing a charged particle beam under the action of a rapidly oscillating external field we construct an asymptotic preserving numerical scheme for this kinetic equation in the highly oscillatory limit this scheme enables to simulate the problem without using any time step refinement technique moreover since our numerical method is not based on the derivation of the simulation of asymptotic models it works in the regime where the solution does not oscillate rapidly and in the highly oscillatory regime as well our method is based on a two scale reformulation of the initial equation with the introduction of an additional periodic variable

estimating a weighted average of stratum specific parameters this article investigates estimators of a weighted average of stratum specific univariate parameters and compares them in terms of a design based estimate of mean squared error mse the research is motivated by a stratified survey sample of florida medicaid beneficiaries in which the parameters are population stratum means and the weights are known and determined by the population sampling frame assuming heterogeneous parameters it is common to estimate the weighted average with the weighted sum of sample stratum means under homogeneity one ignores the known weights in favor of precision weighting adaptive estimators arise from random effects models for the parameters we propose adaptive estimators motivated from these random effects models but we compare their design based performance we further propose selecting the tuning parameter to minimize a design based estimate of mean squared error this differs from the model based approach of selecting the tuning parameter to accurately represent the heterogeneity of stratum means our design based approach effectively downweights strata with small weights in the assessment of homogeneity which can lead to a smaller mse we compare the standard random effects model with identically distributed parameters to a novel alternative which models the variances of the parameters as inversely proportional to the known weights we also present theoretical and computational details for estimators based on a general class of random effects models the methods are applied to estimate average satisfaction with health plan and care among florida beneficiaries just prior to medicaid reform

prediction error and its estimation for subset selected models strategies are compared for development of a linear regression model and the subsequent assessment of its predictive ability simulations were performed as a designed experiment over a range of data structures approaches using a forward selection of variables resulted in slightly smaller prediction errors and less biased estimators of predictive accuracy than all possible subsets selection but often did not improve on the full model random and balanced data splitting resulted in increased prediction errors and estimators with large mean squared error to maximize predictive accuracy while retaining a reliable estimate of that accuracy it is recommended that the entire sample usually he used for model development and assessment

uniformly accurate numerical schemes for highly oscillatory klein gordon and nonlinear schrodinger equations this work is devoted to the numerical simulation of nonlinear schrodinger and klein gordon equations we present a general strategy to construct numerical schemes which are uniformly accurate with respect to the oscillation frequency this is a stronger feature than the usual so called asymptotic preserving property the last being also satisfied by our scheme in the highly oscillatory limit our strategy enables to simulate the oscillatory problem without using any mesh or time step refinement and the orders of our schemes are preserved uniformly in all regimes in other words since our numerical method is not based on the derivation and the simulation of asymptotic models it works in the regime where the solution does not oscillate rapidly in the highly oscillatory limit regime and in the intermediate regime with the same order of accuracy in the same spirit as in crouseilles et al j comput phys 248 287 308 2013 the method is based on two main ingredients first we embed our problem in a suitable two scale reformulation with the introduction of an additional variable then a link is made with classical strategies based on chapman enskog expansions in kinetic theory despite the dispersive context of the targeted equations allowing to separate the fast time scale from the slow one uniformly accurate schemes are eventually derived from this new formulation and their properties and performances are assessed both theoretically and numerically

large sample bayesian inference on the parameters of the proportional hazard models this paper considers large sample bayesian analysis of the proportional hazards model when interest is in inference on the parameters and estimation of the log relative risk for specified covariate vectors rather than on prediction of the survival function we use a normal prior distribution for the parameters and make inferences based on the derived posterior distribution the suggested approach is much simpler than alternative bayesian analyses previously suggested for the proportional hazards models using simulated data we compare estimates obtained from the bayesian analysis with those obtained from the full proportional hazards model and the reduced model after backwards elimination we show that under a wider range of assumptions the bayesian analysis provides reduced estimation errors and improved rejection of noise variables finally we illustrate the methodology using data from a large study of prognostic markers in breast cancer

when should epidemiologic regressions use random coefficients summary regression models with random coefficients arise naturally in both frequentist and bayesian approaches to estimation problems they are becoming widely available in standard computer packages under the headings of generalized linear mixed models hierarchical models and multilevel models i here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed effects models now prevalent in epidemiology the argument invokes an antiparsimony principle attributed to l j savage which is that models should be rich enough to reflect the complexity of the relations under study it also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything often used to justify parsimony regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable selection algorithms and their attendant distortion of uncertainty assessments these points are illustrated with an analysis of data on diet nutrition and breast cancer

semi lagrangian schemes for the vlasov equation on an unstructured mesh of phase space a new scheme for solving the vlasov equation using an unstructured mesh for the phase space is proposed the algorithm is based on the semi lagrangian method which exploits the fact that the distribution function is constant along the characteristic curves we use different local interpolation operators to reconstruct the distribution function f some of which need the knowledge of the gradient of f we can use limiter coefficients to maintain the positivity and the l bound of f and optimize these coefficients to ensure the conservation of the l1 norm that is to say the mass by solving a linear programming problem several numerical results are presented in two and three axisymmetric case dimensional phase space the local interpolation technique is well suited for parallel computation

quasi steady state reduction for compartmental systems abstract we present a method to determine an asymptotic reduction in the sense of tikhonov and fenichel for singularly perturbed compartmental systems in the presence of slow transport it turns out that the reduction can be derived from the individual interaction terms alone we apply the result to spatially discretized reaction diffusion systems and obtain based on the reduced discretized systems a heuristic to reduce reaction diffusion systems in presence of slow diffusion

interval estimation for rank correlation coefficients based on the probit transformation with extension to measurement error correction of correlated ranked data the spearman rho s and kendall tau rank correlation coefficient are routinely used as measures of association between non normally distributed random variables however confidence limits for rho s are only available under the assumption of bivariate normality and for tau under the assumption of asymptotic normality of tau in this paper we introduce another approach for obtaining confidence limits for rho s or tau based on the arcsin transformation of sample probit score correlations this approach is shown to be applicable for an arbitrary bivariate distribution the arcsin based estimators for rho s and tau denoted by rho s a tau a are shown to have asymptotic relative efficiency are of 9 pi2 compared with the usual estimators rho s and tau when rho s and tau are respectively 0 in some nutritional applications the spearman rank correlation between nutrient intake as assessed by a reference instrument versus nutrient intake as assessed by a surrogate instrument is used as a measure of validity of the surrogate instrument however if only a single replicate or a few replicates are available for the reference instrument then the estimated spearman rank correlation will be downwardly biased due to measurement error in this paper we use the probit transformation as a tool for specifying an anova type model for replicate ranked data resulting in a point and interval estimate of a measurement error corrected rank correlation this extends previous work by rosner and willett for obtaining point and interval estimates of measurement error corrected pearson correlations

the performance of random coefficient regression in accounting for residual confounding greenland 2000 biometrics 56 915 921 describes the use of random coefficient regression to adjust for residual confounding in a particular setting we examine this setting further giving theoretical and empirical results concerning the frequentist and bayesian performance of random coefficient regression particularly we compare estimators based on this adjustment for residual confounding to estimators based on the assumption of no residual confounding this devolves to comparing an estimator from a nonidentified but more realistic model to an estimator from a less realistic but identified model the approach described by gustafson 2005 statistical science 20 111 140 is used to quantify the performance of a bayesian estimator arising from a nonidentified model from both theoretical calculations and simulations we find support for the idea that superior performance can be obtained by replacing unrealistic identifying constraints with priors that allow modest departures from those constraints in terms of point estimator bias this superiority arises when the extent of residual confounding is substantial but the advantage is much broader in terms of interval estimation the benefit from modeling residual confounding is maintained when the prior distributions employed only roughly correspond to reality for the standard identifying constraints are equivalent to priors that typically correspond much worse

a new asymptotic preserving scheme based on micro macro formulation for linear kinetic equations in the diffusion limit we propose a new numerical scheme for linear transport equations it is based on a decomposition of the distribution function into equilibrium and nonequilibrium parts we also use a projection technique that allows us to reformulate the kinetic equation into a coupled system of an evolution equation for the macroscopic density and a kinetic equation for the nonequilibrium part by using a suitable time semi implicit discretization our scheme is able to accurately approximate the solution in both kinetic and diffusion regimes it is asymptotic preserving in the following sense when the mean free path of the particles is small our scheme is asymptotically equivalent to a standard numerical scheme for the limit diffusion model a uniform stability property is proved for the simple telegraph model various boundary conditions are studied our method is validated in one dimensional cases by several numerical tests and comparisons with previous asymptotic preserving schemes

an asymptotic induced scheme for nonstationary transport equations in the diffusive limit an asymptotic induced scheme for nonstationary transport equations with the diffusion scaling is developed the scheme works uniformly for all ranges of mean free paths it is based on the asymptotic analysis of the diffusion limit of the transport equation a theoretical investigation of the behavior of the scheme in the diffusion limit is given and an approximation property is proven moreover numerical results for different physical situations are shown and the uniform convergence of the scheme is established numerically

analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit we present a mathematical analysis of the asymptotic preserving scheme proposed in m lemou and l mieussens siam j sci comput 31 2008 pp 334 368 for linear transport equations in kinetic and diffusive regimes we prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles this property is satisfied under an explicitly given cfl condition this condition tends to a parabolic cfl condition for small mean free paths and is close to a convection cfl condition for large mean free paths our analysis is based on very simple energy estimates

a two level implicit scheme for the numerical solution of the linearized vorticity equation a numerical scheme is developed to study the stability of the linearized vorticity equations the linear growth rates of kelvin helmholtz instabilities resulting from a velocity shear are calculated numerically the theory of neutrally stable waves in two dimensions is extended to include the cases where the stream function is zero or periodic at the boundary and is verified numerically for the case of a velocity profile having the shape of a cosine function the instability growth rates of the oscillations in the neighbourhood of the neutrally stable waves are calculated numerically and are shown to be in very good agreement with the theory the results are also of interest in relation to studies on the instabilities of a two dimensional guiding centre plasma and also in the study of the diocotron instability in electronics

uniformly accurate diffusive relaxation schemes for multiscale transport equations many transport equations such as the neutron transport radiative transfer and transport equations for waves in random media have a diffusive scaling that leads to the diffusion equations in many physical applications the scaling parameter mean free path may differ in several orders of magnitude from the rarefied regimes to the hydrodynamic diffusive regimes within one problem and it is desirable to develop a class of robust numerical schemes that can work uniformly with respect to this relaxation parameter in an earlier work jin pareschi and toscani siam j numer anal 35 1998 pp 2405 2439 we handled this numerical problem for discrete velocity kinetic models by reformulating the system into a form commonly used for a relaxation scheme for conservation laws jin and xin comm pure appl math 48 1995 pp 235 277 such a reformulation allows us to use the splitting technique for relaxation schemes to design a class of implicit yet explicitly implementable schemes that work with high resolution uniformly with respect to the relaxation parameter in this paper we show that such a numerical technique can be applied to a large class of transport equations with continuous velocities when one uses the even and odd parities of the transport equation

runge kutta methods for hyperbolic conservation laws with stiff relaxation terms underresolved numerical schemes for hyperbolic conservation laws with stiff relaxation terms may generate unphysical spurious numerical results or reduce to lower order if the small relaxation time is not temporally well resolved we design a second order runge kutta type splitting method that possesses the discrete analogue of the continuous asymptotic limit which thus is able to capture the correct physical behaviors with high order accuracy even if the initial layer and the small relaxation time are not numerically resolved

uniformly accurate particle in cell method for the long time solution of the two dimensional vlasov poisson equation with uniform strong magnetic field abstract in this work we focus on the numerical resolution of the four dimensional phase space vlasov poisson system subject to a uniform strong external magnetic field to do so we consider a particle in cell based method for which the characteristics are reformulated by means of the two scale formalism which is well adapted to handle highly oscillatory equations then a numerical scheme is derived for the two scale equations the so obtained scheme enjoys a uniform accuracy property meaning that its accuracy does not depend on the small parameter several numerical results illustrate the capabilities of the method

an asymptotic preserving automatic domain decomposition method for the vlasov poisson bgk system with applications to plasmas in this work we present an efficient strategy to deal with plasma physics simulations in which localized departures from thermodynamical equilibrium are present the method is based on the introduction of intermediate regions which allows smooth transitions between kinetic and fluid zones in this paper we extend domain decomposition techniques obtained through dynamic coupling and buffer zones to the study of plasmas and moreover we combine them with asymptotic preserving and asymptotically accurate strategies for the time integration we use a hybrid scheme in which both kinetic and fluid descriptions are considered and coupled together while the kinetic model is solved by asymptotic preserving and accurate methods in order to guarantee high efficiency and accuracy in all regimes the numerical scheme is validated and its performances are analyzed by numerical simulations

efficient asymptotic preserving ap schemes for some multiscale kinetic equations many kinetic models of the boltzmann equation have a diffusive scaling that leads to the navier stokes type parabolic equations as the small scaling parameter approaches zero in practical applications it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter from the rarefied kinetic regimes to the hydrodynamic diffusive regimes an earlier approach in s jin l pareschi and g toscani siam j numer anal 35 1998 pp 2405 2439 reformulates such systems into the common hyperbolic relaxation system by jin and xin for hyperbolic conservation laws used to construct the relaxation schemes and then uses a multistep time splitting method to solve the relaxation system here we observe that the combination of the two time split steps may yield hyperbolic parabolic systems that are more advantageous in both stability and efficiency for numerical computations we show that such an approach yields a class of asymptotic preserving ap schemes which are suitable for the computation of multiscale kinetic problems we use the goldstein taylor and carleman models to illustrate this approach

high order time discretization for backward semi lagrangian methods we introduce different high order time discretization schemes for backward semi lagrangian methods these schemes are based on multi step schemes like adams moulton and adams bashforth schemes combined with backward finite difference schemes we apply these methods to transport equations for plasma physics applications and for the numerical simulation of instabilities in fluid mechanics in the context of backward semi lagrangian methods this time discretization strategy is particularly efficient and accurate when the spatial error discretization becomes negligible and allows to use large time steps

second stage least squares versus penalized quasi likelihood for fitting hierarchical models in epidemiologic analyses hierarchical regression analysis holds much promise for epidemiologic analysis but has as yet seen limited application because of lack of easily used software and the relatively lengthy run times of preferred fitting methods such as true maximum likelihood and bayesian approaches this paper compares three relatively simple choices for estimation of the regression coefficients maximum likelihood first stage combined with a weighted least squares second stage mlls joint iteratively reweighted least squares fitting of first and second stage jils and empirically penalized quasi likelihood epql these choices can be combined with various methods for estimating the second stage variance the two contrasted here are based on first and second stage residuals jils and epql yielded indistinguishable results and had small sample performance superior to mlls in larger samples there was little practical difference among the methods use of first stage residuals to estimate the prior variance required considerably more computation than use of second stage residuals but produced no discernible improvement in regression coefficient estimates all three methods performed well for estimation of first stage parameters but were less satisfactory for estimation of second stage parameters

estimation of rank correlation for clustered data it is well known that the sample correlation coefficient rxy is the maximum likelihood estimator of the pearson correlation xy for independent and identically distributed i i d bivariate normal data however this is not true for ophthalmologic data where x e g visual acuity and y e g visual field are available for each eye and there is positive intraclass correlation for both x and y in fellow eyes in this paper we provide a regression based approach for obtaining the maximum likelihood estimator of xy for clustered data which can be implemented using standard mixed effects model software this method is also extended to allow for estimation of partial correlation by controlling both x and y for a vector u of other covariates in addition these methods can be extended to allow for estimation of rank correlation for clustered data by i converting ranks of both x and y to the probit scale ii estimating the pearson correlation between probit scores for x and y and iii using the relationship between pearson and rank correlation for bivariate normally distributed data the validity of the methods in finite sized samples is supported by simulation studies finally two examples from ophthalmology and analgesic abuse are used to illustrate the methods copyright 2017 john wiley sons ltd

asymptotically stable particle in cell methods for the vlasov poisson system with a strong external magnetic field this paper deals with the numerical resolution of the vlasov poisson system with a strong external magnetic field by particle in cell pic methods in this regime classical pic methods are subject to stability constraints on the time and space steps related to the small larmor radius and plasma frequency here we propose an asymptotic preserving pic scheme which is not subjected to these limitations our approach is based on first and higher order semi implicit numerical schemes already validated on dissipative systems s boscarino f filbet and g russo j sci comput 2016 doi 10 1007 s10915 016 0168 y additionally when the magnitude of the external magnetic field becomes large this method provides a consistent pic discretization of the guiding center equation that is an incompressible euler equation in vorticity form we propose several numerical experiments which provide a solid validation of the method and its underlying concepts

multiple imputation of industry and occupation codes in census public use samples using bayesian logistic regression abstract we describe methods used to create a new census data base that can be used to study comparability of industry and occupation classification systems this project represents the most extensive application of multiple imputation to date and the modeling effort was considerable as well hundreds of logistic regressions were estimated one goal of this article is to summarize the strategies used in the project so that researchers can better understand how the new data bases were created another goal is to show how modifications of maximum likelihood methods were made for the modeling and imputation phases of the project to multiply impute 1980 census comparable codes for industries and occupations in two 1970 census public use samples logistic regression models were estimated with flattening constants for many of the regression models considered the data were too sparse to support conventional maximum likelihood analysis so some alternative had to be employed these methods solve existence and

a new perspective on priors for generalized linear models abstract this article deals with specifications of informative prior distributions for generalized linear models our emphasis is on specifying distributions for selected points on the regression surface the prior distribution on regression coefficients is induced from this specification we believe that it is inherently easier to think about conditional means of observables given the regression variables than it is to think about model dependent regression coefficients previous use of conditional means priors seems to be restricted to logistic regression with one predictor variable and to normal theory regression we expand on the idea of conditional means priors and extend these to arbitrary generalized linear models we also consider data augmentation priors where the prior is of the same form as the likelihood we show that data augmentation priors are special cases of conditional means priors with current monte carlo methodology such as importance sampling and gibbs sampling our priors result in

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

conservative semi lagrangian schemes for vlasov equations conservative methods for the numerical solution of the vlasov equation are developed in the context of the one dimensional splitting in the case of constant advection these methods and the traditional semi lagrangian ones are proven to be equivalent but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity in the non constant advection case they present an alternative to the traditional semi lagrangian schemes which can suffer from bad mass conservation in this time splitting setting

numerical schemes for hyperbolic conservation laws with stiff relaxation terms hyperbolic systems often have relaxation terms that give them a partially conservative form and that lead to a long time behavior governed by reduced systems that are parabolic in nature in this article it is shown by asymptotic analysis and numerical examples that semidiscrete high resolution methods for hyperbolic conservation laws fail to capture this asymptotic behavior unless the small relaxation rate is resolved by a fine spatial grid we introduce a modification of higher order godunov methods that possesses the correct asymptotic behavior allowing the use of coarse grids large cell peclet numbers the idea is to build into the numerical scheme the asymptotic balances that lead to this behavior numerical experiments on 2 2 systems verify our analysis

uniform stability of a finite difference scheme for transport equations in diffusive regimes an asymptotic preserving numerical scheme with respect to diffusion scalings for a linear transport equation is investigated the scheme is adopted from a class of schemes developed in s jin l pareschi and g toscani siam j numer anal 38 2000 pp 913 936 and a klar siam j numer anal 35 1998 pp 1073 1094 stability is proven uniformly in the mean free path under a cfl type condition turning into a parabolic cfl condition in the diffusion limit

uniformly stable numerical schemes for the boltzmann equation preserving the compressible navier stokes asymptotics in this paper we develop a numerical method to solve boltzmann like equations of kinetic theory which is able to capture the compressible navier stokes dynamics at small knudsen numbers our approach is based on the micro macro decomposition technique which applies to general collision operators this decomposition is performed in all the phase space and leads to an equivalent formulation of the boltzmann or bgk equation that couples a kinetic equation with macroscopic ones this new formulation is then discretized with a semi implicit time scheme combined with a staggered grid space discretization finally several numerical tests are presented in order to illustrate the efficiency of our approach incidentally we also introduce in this paper a modification of a standard splitting method that allows to preserve the compressible navier stokes asymptotics in the case of the simplified bgk model up to our knowledge this property is not known for general collision operators

asymptotic high order mass preserving schemes for a hyperbolic model of chemotaxis we introduce a new class of finite difference schemes for approximating the solutions to an initial boundary value problem on a bounded interval for a one dimensional dissipative hyperbolic system with an external source term which arises as a simple model of chemotaxis since the solutions to this problem may converge to nonconstant asymptotic states for large times standard schemes usually fail to yield a good approximation therefore we propose a new class of schemes which use an asymptotic higher order correction second and third order in our examples to balance the effects of the source term and the influence of the asymptotic solutions special care is needed to deal with boundary conditions to avoid harmful loss of mass convergence results are proved for these new schemes and several numerical tests are presented and discussed to verify the effectiveness of their behavior

putting background information about relative risks into conjugate prior distributions in bayesian and empirical bayes analyses of epidemiologic data the most easily implemented prior specifications use a multivariate normal distribution for the log relative risks or a conjugate distribution for the discrete response vector this article describes problems in translating background information about relative risks into conjugate priors and a solution traditionally conjugate priors have been specified through flattening constants an approach that leads to conflicts with the true prior covariance structure for the log relative risks one can however derive a conjugate prior consistent with that structure by using a data augmentation approximation to the true log relative risk prior although a rescaling step is needed to ensure the accuracy of the approximation these points are illustrated with a logistic regression analysis of neonatal death risk

generalized conjugate priors for bayesian analysis of risk and survival regressions le choix pour les analyses bayesiennes portant sur les risques relatifs de distributions a priori conjuguees peut etre tres limitant du fait que la forme de cette distribution depend du parametre de valeur centrale cependant en introduisant separement ce parametre on generalise ces distributions a priori ce qui permet de modeliser une tres large palette d opinions a priori tout en conservant les proprietes de simplicite des calculs propres aux analyses conjuguees cet article illustre les resultats fournis par ces analyses avec des conjuguees generalisees a partir d exemples sur des enquetes cas x temoins dont le but etait d etudier le lien des amenagements en c bles electriques wire codes en zone residentielle et des champs magnetiques avec les cas de leucemie chez l enfant

relaxation schemes for nonlinear kinetic equations a class of numerical schemes for nonlinear kinetic equations of boltzmann type is described following wild s approach the solution is represented as a power series with parameter depending exponentially on the knudsen number this permits us to derive accurate and stable time discretizations for all ranges of the mean free path these schemes preserve the main physical properties positivity conservation of mass momentum and energy moreover for some particular models the entropy property is also shown to hold

a numerical method for kinetic semiconductor equations in the drift diffusion limit an asymptotic induced scheme for kinetic semiconductor equations with the diffusion scaling is developed the scheme is based on the asymptotic analysis of the kinetic semiconductor equation it works uniformly for all ranges of mean free paths the velocity discretization is done using quadrature points equivalent to a moment expansion method numerical results for different physical situations are presented

a combination of multiscale time integrator and two scale formulation for the nonlinear schrodinger equation with wave operator abstract in this paper we consider the nonlinear schrodinger equation with wave operator nlsw which contains a dimensionless parameter 0 e 1 as 0 e 1 the solution of the nlsw propagates fast waves in time with wavelength o e 2 and the problem becomes highly oscillatory in time the oscillations come from two parts one part is from the equation and another part is from the initial data for the ill prepared initial data case as described in bao and cai 2014 which brings inconsistency in the limit regime standard numerical methods have strong convergence order reduction in time when e becomes small we review two existing methods to solve the nlsw an exponential integrator and a two scale method we comment on their order reduction issues then we derive a multiscale decomposition two scale method for solving the nlsw by first performing a multiscale decomposition on the nlsw which decomposes it into a well behaved part and an energy unbounded part and then applying an exponential integrator for the well behaved part and a two scale approach for the energy unbounded part numerical experiments are conducted to test the proposed method which shows uniform second order accuracy without significant order reduction for all 0 e 1 comparisons are made with the existing methods

numerical passage from kinetic to fluid equations a numerical way to pass from the bhatnagar gross krook model of the boltzmann equation to compressible euler equations is presented in order to do so a stable discretization of the kinetic equati

data augmentation priors for bayesian and semi bayes analyses of conditional logistic and proportional hazards regression data augmentation priors have a long history in bayesian data analysis formulae for such priors have been derived for generalized linear models but their accuracy depends on two approximation steps this note presents a method for using offsets as well as scaling factors to improve the accuracy of the approximations in logistic regression this method produces an exceptionally simple form of data augmentation that allows it to be used with any standard package for conditional logistic or proportional hazards regression to perform bayesian and semi bayes analyses of matched and survival data the method is illustrated with an analysis of a matched case control study of diet and breast cancer

approximate bayesian inference in conditionally independent hierarchical models parametric empirical bayes models abstract we consider two stage models of the kind used in parametric empirical bayes peb methodology calling them conditionally independent hierarchical models we suppose that there are k units which may be experimental subjects cities study centers etcetera at the first stage the observation vectors yi for units i 1 k are independently distributed with densities p yi i or more generally p yi i at the second stage the unit specific parameter vectors i are iid with densities p i the peb approach proceeds by regarding the second stage distribution as a prior and noting that if were known inference about could be based on its posterior since is not known the simplest peb methods estimate the parameter by maximum likelihood or some variant and then treat as if it were known to be equal to this estimate although this procedure is sometimes satisfactory a well known defect is that it neglects the uncertainty due to the estimation of in this article w

uniformly accurate schemes for hyperbolic systems with relaxation we develop high resolution shock capturing numerical schemes for hyperbolic systems with relaxation in such systems the relaxation time may vary from order 1 to much less than unity when the relaxation time is small the relaxation term becomes very strong and highly stiff and underresolved numerical schemes may produce spurious results usually one cannot decouple the problem into separate regimes and handle different regimes with different methods thus it is important to have a scheme that works uniformly with respect to the relaxation time using the broadwell model of the nonlinear boltzmann equation we develop a second order scheme that works effectively with a fixed spatial and temporal discretization for all ranges of the mean free path formal uniform consistency proof for a first order scheme and numerical convergence proof for the second order scheme are also presented we also make numerical comparisons of the new scheme with some other schemes this study is motivated by the reentry problem in hypersonic computations

a semi bayes approach to the analysis of correlated multiple associations with an application to an occupational cancer mortality study thomas et al presented the application of empirical bayes methods to the problem of multiple inference in epidemiologic studies one limitation of their approach which they noted was the need to assume exchangeable log relative risk parameters and independent relative risk estimates numerical integration was also required here i generalize their approach to allow for non exchangeable parameters and non independent estimates the resulting method is bayesian in so far as some feature of the prior distribution are specified from prior information but is empirical bayes in so far as some explicit parameters in the prior distribution are estimated from the data estimation is based on approximations to the posterior distribution this allows one to implement the approach with standard software packages for matrix algebra the method is illustrated in an occupational mortality study of 84 exposure cancer associations

micro macro schemes for kinetic equations including boundary layers we introduce a new micro macro decomposition of collisional kinetic equations in the specific case of the diffusion limit which naturally incorporates the incoming boundary conditions the idea is to write the distribution function f in all its domain as the sum of an equilibrium adapted to the boundary which is not the usual equilibrium associated with f and a remaining kinetic part this equilibrium is defined such that its incoming velocity moments coincide with the incoming velocity moments of the distribution function a consequence of this strategy is that no artificial boundary condition is needed in the micro macro models and the exact boundary condition on f is naturally transposed to the macro part of the model this method provides an asymptotic preserving numerical scheme that generates a very good approximation of the space boundary values at the diffusive limit without any mesh refinement in the boundary layers our numerical results are in very good agreement with the exact so c

asymptotic preserving implicit explicit runge kutta methods for nonlinear kinetic equations we discuss implicit explicit imex runge kutta methods which are particularly adapted to stiff kinetic equations of boltzmann type we consider both the case of easy invertible collision operators and the challenging case of boltzmann collision operators we give sufficient conditions in order that such methods are asymptotic preserving and asymptotically accurate their monotonicity properties are also studied in the case of the boltzmann operator the methods are based on the introduction of a penalization technique for the collision integral this reformulation of the collision operator permits us to construct penalized imex schemes which work uniformly for a wide range of relaxation times avoiding the expensive implicit resolution of the collision operator finally we show some numerical results which confirm the theoretical analysis

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