an implicit finite volume method for the solution of 3d low mach number viscous flows using a local preconditioning technique this paper presents a cell centered high order finite volume scheme for the solution of the three dimensional 3d navier stokes equations with low mach number the system of non linear equations is solved by means of a fully implicit pseudo transient scheme each pseudo time step is solved by a newton gmres procedure a local preconditioning technique is used to scale the speed of sound and to improve the system condition number for low mach number and low cell reynolds number this preconditioning is applied to the ausm up flux vector splitting function the method is tested on 2d and 3d low mach number laminar flows

computational study of incompressible turbulent flows with method of characteristics the current study presents numerical investigation of incompressible turbulent flow momentum and continuity equations are coupled by the artificial compressibility method acm the one equation spalart allmaras turbulence model along with rans reynolds averaged navier stokes equations is used to calculate reynolds stresses in 2 d problems for convective fluxes a characteristic based cb finite volume solution has been developed also a revised jameson averaging avr method was implemented in comparison the proposed cb upwind scheme demonstrated very accurate results high stability and faster convergence for time discretization the fifth order runge kutta scheme is used as the convergence acceleration techniques the local time stepping and implicit residual smoothing were applied considering flow behavior suitable boundary conditions have been implemented cross flow around a horizontal circular cylinder at high reynolds numbers has been studied as a benchmark the results obtained using the new proposed scheme are in good agreement with the standard available solutions in the literature

a div curl grad formulation for compressible buoyant flows solved by the least squares finite element method abstract the present paper reports the development of the least squares finite element method for simulating compressible buoyant flows at low mach numbers we propose a div curl grad formulation with unknowns including vorticity velocity heat fluxes temperature and pressure variation the formulation is proved to be elliptic such that permissible boundary conditions become self evident for a well posed flow problem in contrast to conventional approaches the present method evades the predicament of the singularity problem of low speed flows and no special treatment or artificial boundary condition is needed moreover the assembled coefficient matrix is symmetric and positive definite its inversion is implemented by an element by element jacobi conjugate gradient method as a numerical example we calculate two dimensional compressible buoyant flows inside a square enclosure at various rayleigh numbers for rayleigh number one million four secondary vortices were found embedded in the primary vortex due to significant temperature variations the fluid flows are highly compressible in the interior along the walls however the flows are incompressible the nusselt number rayleigh number correlation deduced from the numerical result compared favorably with previously reported data

adjusted score tests of homogeneity for poisson processes abstract tests of homogeneity are being increasingly used for the analysis of event time data but relatively little attention has been paid to their distributional properties in settings with small to moderate sample sizes here we consider tests of homogeneity for recurrent event data in which the null model is a poisson process and the alternative is a mixed poisson process we examine score and adjusted score statistics in the context of parametric and semiparametric regression models where the adjustments correct for the bias induced by substituting the maximum likelihood estimates of the parameters into the test statistic we report the results of simulation studies suggesting that the adjusted score statistics are superior in terms of size and power we also find that the adjusted score test in the semiparametric regression model does not perform particularly well in small samples but the adjusted score test based on a piecewise exponential model has satisfactory performance the latter thus prov

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

variance component testing in generalised linear models with random effects summary there is considerable interest in testing for overdispersion correlation and heterogeneity across groups in biomedical studies in this paper we cast the problem in the framework of generalised linear models with random effects we propose a global score test for the null hypothesis that all the variance components are zero this test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects we also propose individual score tests and their approximations for testing the variance components separately both tests can be easily implemented using existing statistical software we illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings and evaluate their performance through simulation

an asymptotic preserving all speed scheme for the euler and navier stokes equations we present an asymptotic preserving all speed scheme for the simulation of compressible flows valid at all mach numbers ranging from very small to order unity the scheme is based on a semi implicit discretization which treats the acoustic part implicitly and the convective and diffusive parts explicitly this discretization which is the key to the asymptotic preserving property provides a consistent approximation of both the hyperbolic compressible regime and the elliptic incompressible regime the divergence free condition on the velocity in the incompressible regime is respected and an the pressure is computed via an elliptic equation resulting from a suitable combination of the momentum and energy equations the implicit treatment of the acoustic part allows the time step to be independent of the mach number the scheme is conservative and applies to steady or unsteady flows and to general equations of state one and two dimensional numerical results provide a validation of the asymptotic preserving all speed properties

steady turbulent flow computations using a low mach fully compressible scheme a recently proposed modification to fully compressible schemes significantly improves the resolution of low mach number features tackling the problem of excessive numerical dissipation as the mach number reduces this paper explores the application of this modification to reynolds averaged navier stokes simulations using second and fifth order in space schemes following verification of the modeling approach four test cases are employed to highlight the scheme performance including a backward facing step a two dimensional lid driven cavity the naca 4412 airfoil incorporating a trailing edge separation and finally a mach 2 25 oblique shock wave boundary layer interaction it demonstrates first that the converged solution is grid and scheme independent as expected and that the low mach number correction provides a significant improvement in low mach number regions because this correction is easy to implement computationally inexpensive and stable the conclusion is that it should be recommend

application of time iterative schemes to incompressible flow the computation of steady incompressible flows by an euler implicit algorithm is studied using both the incompressible equations and the low mach number compressible equations the incompressible equations are handled by adding an artificial time derivative to the continuity equation this allows both the pressure and velocity to be obtained implicitly in one dimensional problems both systems converge rapidly even at low mach numbers where the eigenvalues are very stiff in two dimensions where approximate factorization is required the presence of stiff eigenvalues is highly detrimental stiffness can be avoided in the incompressible equations by selecting an appropriate pseudo mach number this insures reliable convergence and results in an efficient incompressible flow algorithm in the case of compressible equations the mach number cannot be chosen arbitrarily and the contamination introduced by approximate factorization must be removed a matrix preconditioning factor that accomplishes this is developed and demonstrated with this modification the convergence rate is the same as in the incompressible case and is independent of mach number rapid convergence is observed at mach numbers as low as 6 05

dimension reduction and semiparametric estimation of survival models in this paper we propose a new dimension reduction method by introducing a nominal regression model with the hazard function as the conditional mean which naturally retrieves information from complete data and censored data as well moreover without requiring the linearity condition the new method can estimate the entire central subspace consistently and exhaustively the method also provides an alternative approach for the analysis of censored data assuming neither the link function nor the distribution hence it exhibits superior robustness properties numerical studies show that the method can indeed be readily used to efficiently estimate survival models explore the data structures and identify important variables

reweighting to achieve elliptically contoured covariates in regression abstract we investigate a method of constructing weights to induce elliptically contoured covariates in regression analyses much recent work in regression has identified various data analytic and model robustness advantages associated with such covariates in particular new estimation methods like sir sirii save and phd have been built around the assumption of elliptically contoured covariates finite samples of regression covariates may deviate from this ideal in practice and the method developed here termed voronoi weighting can be used to induce elliptical symmetry in such samples in a number of examples we show that reweighting cases by the voronoi method can substantially enhance various procedures for covariates that deviate from elliptical symmetry we show that voronoi weighting in conjunction with some trimming via the minimum volume ellipsoid method can be effective

a high order numerical algorithm for dns of low mach number reactive flows with detailed chemistry and quasi spectral accuracy a novel and efficient algorithm is presented in this paper to deal with dns of turbulent reacting flows under the low mach number assumption with detailed chemistry and a quasi spectral accuracy the temporal integration of the equations relies on an operating split strategy where chemical reactions are solved implicitly with a stiff solver and the convection diffusion operators are solved with a runge kutta chebyshev method the spatial discretisation is performed with high order compact schemes and a fft based constant coefficient spectral solver is employed to solve a variable coefficient poisson equation the numerical implementation takes advantage of the 2decomp fft libraries developed by 1 which are based on a pencil decomposition method of the domain and are proven to be computationally very efficient an enhanced pressure correction method is proposed to speed up the achievement of machine precision accuracy it is demonstrated that a second order accuracy is reached in time while the spatial accuracy ranges from fourth order to sixth order depending on the set of imposed boundary conditions the software developed to implement the present algorithm is called holomac and its numerical efficiency opens the way to deal with dns of reacting flows to understand complex turbulent and chemical phenomena in flames

pressure based calculation procedure for viscous flows at all speeds in arbitrary configurations a calculation procedure for viscous flows at all mach numbers has been described the scheme has been developed for a nonorthogonal coordinate system in order to handle both incompressible and compressible flows pressure has been selected as a primary dependent variable in preference to density the pressure field is evaluated using the compressible form of the simpler algorithm the accuracy of the proposed scheme has been assessed by comparing the results with experimental data or other numerical results available in the literature

posterior likelihood methods for multivariate survival data this article deals with the semiparametric analysis of multivariate survival data with random block group effects survival times within the same group are correlated as a consequence of a frailty random block effect the standard approaches assume either a parametric or a completely unknown baseline hazard function this paper considers an intermediate solution that is a nonparametric function that is reasonably smooth this is accomplished by a bayesian model in which the conditional proportional hazards model is used with a correlated prior process for the baseline hazard the posterior likelihood based on data as well as the prior process is similar to the discretized penalized likelihood for the frailty model the methodology is exemplified with the recurrent kidney infections data of mcgilchrist and aisbett 1991 biometrics 47 461 466 in which the times to infections within the same patients are expected to be correlated the reanalysis of the data has shown that the estimates of the parameters of interest and the associated standard errors depend on the prior knowledge about the smoothness of the baseline hazard

implicit solution of the incompressible navier stokes equations on a non staggered grid abstract this paper presents an implicit procedure for the solution of the incompressible navier stokes equations in primitive variables the time dependent momentum equations are solved implicitly for the velocity field using the approximate factorization technique the continuity equation is satisfied at each time step through the solution of a poisson type equation for the static pressure a consistent finite difference scheme which satisfies the compatibility condition using a non staggered grid is used in the finite difference approximation of the static pressure poisson equation the results of the numerical computations in a driven cavity which are presented for the history of the residues at several reynolds numbers using different computational parameters demonstrate the excellent convergence characteristics of the solution procedure a stability analysis is conducted for the non iterative phase and numerical results are presented for a given set of compational parameters numerical results obtained for the steady state static pressure in the driven cavity are presented for the first time at re 1000 using a non staggered grid and the steady state velocity vorticity and pressure contours at re 100 400 and 1000 are compared with the computational results of other investigators additional results using a curvilinear grid are also presented for the flow in a cascade of circular airfoils at re 1000

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

approximate quasi likelihood estimation in models with surrogate predictors abstract we consider quasi likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error we review and extend four approaches to estimation in this problem all of them based on small measurement error approximations a taxonomy of the data sets likely to be available in measurement error studies is developed an asymptotic theory based on this taxonomy is obtained and includes measurement error and berkson error models as special cases

principal hessian directions for regression with measurement error summary we consider a nonlinear regression problem with predictors with measurement error we assume that the response is related to unknown linear combinations of a p dimensional predictor vector through an unknown link function instead of observing the predictors we observe a surrogate vector with the property that its expectation is linearly related to the predictor vector with constant variance we use an important linear transformation of the surrogates based on the transformed variables we develop the modified principal hessian directions method for estimating the subspace of the effective dimension reduction space we derive the asymptotic variances of the modified principal hessian directions estimators several examples are reported and comparisons are made with the sliced inverse regression method of carroll li 1992

tests for variation over groups in survival data abstract when survival data can be divided into natural groups such as in a clinical trial with patients from a number of different institutions the question arises whether effects are different for the different groups for situations where one is concerned with a random pattern of variation over groups this article proposes testing the null hypothesis of no variation using statistics based on the sums of martingale residuals over subjects within groups these tests are closely related to the locally most powerful tests of liang for testing for variation across a large number of strata the tests are applied to data from a lung cancer trial conducted by the eastern cooperative oncology group

semi implicit extension of a godunov type scheme based on low mach number asymptotics i one dimensional flow a single scale multiple space scale asymptotic analysis provides detailed insight into the low mach number limit behavior of solutions of the compressible euler equations we use the asymptotics as a guideline for developing a low mach number extension of an explicit higher order shock capturing scheme this semi implicit scheme involves multiple pressure variables large scale differencing and averaging procedures that are discretized versions of standard operations in multiple scales asymptotic analysis advection and acoustic wave propagation are discretized explicitly and upwind and only one scalar elliptic equation is to be solved implicitly at each time step this equation is a pressure correction equation for incompressible flows when the mach number is zero in the low mach number limit the time step is restricted by a courant number based essentially on the maximum flow velocity for moderate and large mach numbers the scheme reduces to the underlying explicit higher order shock capturing algorithm

a constructive approach to the estimation of dimension reduction directions in this paper we propose two new methods to estimate the dimension reduction directions of the central subspace cs by constructing a regression model such that the directions are all captured in the regression mean compared with the inverse regression estimation methods e g j amer statist assoc 86 1991 328 332 j amer statist assoc 86 1991 316 342 j amer statist assoc 87 1992 1025 1039 the new methods require no strong assumptions on the design of covariates or the functional relation between regressors and the response variable and have better performance than the inverse regression estimation methods for finite samples compared with the direct regression estimation methods e g j amer statist assoc 84 1989 986 995 ann statist 29 2001 1537 1566 j r stat soc ser b stat methodol 64 2002 363 410 which can only estimate the directions of cs in the regression mean the new methods can detect the directions of cs exhaustively consistency of the estimators and the convergence of corresponding algorithms are proved

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

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

a conservative discrete compatibility constraint low mach pressure correction algorithm for time accurate simulations of variable density flows in this paper we develop the discrete compatibility constraint pressure correction algorithm for transient simulations of variable density flows at low mach numbers the constraint for the velocity field is constructed from a combination of the discrete equations of continuity and scalar e g energy transport imposing that the newly predicted state must be compatible in agreement with the equation of state this way mass and scalar conservation are guaranteed and the equation of state is exactly fulfilled at every time step for comparison reasons two other types of well known pressure correction algorithms are also used the first class denoted as continuity constraint pressure correction is based on a constraint for the velocity field that is derived solely from the continuity equation the second class denoted as analytical compatibility constraint pressure correction constructs the constraint from an analytical combination of the material derivative of the equation of state and the continuity and scalar equations the algorithms are tested for three example fluid configurations a single fluid ideal gas a two fluid inert mixture and a two fluid reacting mixture the latter is special in the sense that the equation of state is non linear and not everywhere differentiable the continuity constraint pressure correction algorithm yields unstable solutions if density ratios are high the analytical compatibility constraint pressure correction algorithm yields stable results but the predicted states do not correspond to the equation of state the discrete compatibility constraint pressure correction algorithm performs well on all test cases the simulation results are stable and exactly match the equation of state

bayesian tests and model diagnostics in conditionally independent hierarchical models abstract consider the conditionally independent hierarchical model cihm in which observations yi are independently distributed from f yi i the parameters i are independently distributed from distributions g and the hyperparameters are distributed according to a distribution h the posterior distribution of all parameters of the cihm can be efficiently simulated by markov chain monte carlo mcmc algorithms although these simulation algorithms have facilitated the application of cihms they generally have not addressed the problem of computing quantities useful in model selection this article explores how mcmc simulation algorithms and other related computational algorithms can be used to compute bayes factors that are useful in criticizing a particular cihm in the case where the cihm models a belief that the parameters are exchangeable or lie on a regression surface the bayes factor can measure the consistency of the data with the structural prior belief bayes factors can also be u

the momentum interpolation method based on the time marching algorithm for all speed flows the time marching approach has clear physical meaning and strict mathematical nature and has been applied in computation of compressible flows widely and extended to many uniform algorithms for all speed flows remedy for its weakness in the problem of checkerboard decoupling of pressure field for incompressible flows is envisaged with the time marching momentum interpolation method mim taken into account in this paper existing preconditioning methods for suppressing decoupling and time marching mim are analyzed for this purpose and algorithms of time marching mim are proposed for steady and unsteady flows and for all speed flows asymptotic analysis shows that the supposed time marching mim has at least a third order accuracy better than the existing time marching coupling methods which only have an accuracy of the same order as the adopted scheme has effects of the time step sizes on the ability of the time marching mim to suppress the checkerboard pressure decoupling are particularly discussed in terms of the dual time stepping approach and it is revealed how the decreased sizes of either the pseudo or physical time step increases the possibility of decoupling and how choi s modification in which the history of the interface velocity is decided by itself instead of the arithmetic average of the velocities on its adjacent nodes removes the unphysical pressure oscillation with small size of the physical time step but leads to divergence with the pseudo time step as well as a remedy for the pseudo time step such methods are recommended as implicit methods and the local time step method with a proposed modification of the time marching mim preventing accuracy loss due to very large time step size numerical experiments support the theoretical analyses and show the validity of the time marching mim proposed

preconditioning method for low speed flows a well known preconditioning method for low mach number e ows is implemented in an existing numerical simulator of viscous and inviscid e ows both details concerning the numerical method and the results of the validationphasearegiven themethodisbasedonatime derivativepreconditioningofthenavier stokesequations using the so called viscous set of variables the pseudoacoustic speed introduced equalizes the eigenvalues so that the history of convergence of the preconditioned system of equations exhibits an increased rate of convergence at low mach numbers the artie cial dissipative terms have been modie ed to let them scale correctly at low speeds in theinviscidcase thevelocitydistributioncalculatedoverthecylinderwiththedescribedmethodmatchesanalytical data numericalresultsconcerningthesimulationofinviscidandturbulente owspastairfoilsarepresented inviscid e ow over the onera m6 wing is also computed it is shown that the preconditioning technique allows both an acceleration in the rate of convergence and a reduction of the wall clock time of an order of magnitude also an improved accuracy of the solution at low mach numbers has been observed

analysis of artificial pressure equations in numerical simulations of a turbulent channel flow abstract recently several methods have been proposed to simulate incompressible fluid flows using an artificial pressure evolution equation avoiding the resolution of a poisson equation these methods can be seen as various levels of approximation of the compressible navier stokes equation in the low mach number limit we study the simulation of incompressible wall bounded flows using several artificial pressure equations in order to determine the most relevant approximations the simulations are stable using a finite difference method in a staggered grid system even without diffusive term and converge to the incompressible solution both in direct numerical simulations and for coarser meshes to be used in large eddy simulations a pressure equation with a convective and a diffusive term produces a more accurate solution than a compressible solver or methods involving more approximations this suggests that it is near to an optimal level of approximation the presence of a convective term in the pressure evolution equation is in particular crucial for the accuracy of the method the rate of convergence of the solution in terms of artificial mach number is studied numerically and validates the theoretical quadratic convergence rate we demonstrate that this property can be used to accelerate the rate of convergence using an extrapolation in terms of artificial mach number since the approach is based on an explicit and local system of equations the numerical procedure is massively parallelisable and has low memory requirements

the effect of strong heat addition on the convergence of implicit schemes the effect of substantial amounts of heat addition on the convergence characteristics of implicit algorithms for flow in a converging diverging nozzle is investigated heat addition has an adverse effect on convergence because it decreases the mach number at the inlet introduces a strong energy source term and produces steep temperature gradients the nozzle convergence rate has analogous detrimental effects and is also studied comparisons of both variations show that when equivalent procedures are used beam and warming s algorithm converges for somewhat wider ranges of parameters than does maccormack s the combination of local time steps which provide uniform values of cfl throughout the grid boundary conditions based on the method of characteristics and euler implicit differencing in time provides convergence that is nearly independent of heat addition and is in close agreement with the predictions of stability theory the incorporation of real gas effects was tested and shown to have a minor effect

performance of three dimensional compressible navier stokes codes at low mach numbers the low mach number performance of two widely used three dimensional compressible navier stokes solvers is examined both of the codes employ a finite volume formulation but differ in their respective discretization and solution schemes in the first code a central difference discretization is employed and solutions are obtained using an explicit runge kutta time stepping scheme in the second code an upwind biased discretization is used and an implicit approximate factorization scheme is employed the accuracy and efficiency of the codes are assessed by comparison with results from an incompressible navier stokes solver and experimental data the test cases examined include an untwisted rectangular wing and a wing fuselage configuration the computed pressure distributions were nearly identical and agreed quite well with experimental data in addition the predicted pressure distributions were nearly identical to those predicted by the incompressible flow solver the influence of freestream mach number on the efficiency of both compressible flow solvers also is examined

analysis of an asymptotic preserving scheme for the euler poisson system in the quasineutral limit in a previous work p crispel p degond and m h vignal j comput phys 223 2007 pp 208 234 a new numerical discretization of the euler poisson system was proposed this scheme is asymptotic preserving in the quasineutral limit i e when the debye length varepsilon tends to zero which means that it becomes consistent with the limit model when varepsilon to 0 in the present work we show that the stability domain of the present scheme is independent of varepsilon this stability analysis is performed on the fourier transformed with respect to the space variable linearized system we show that the stability property is more robust when a space decentered scheme is used which brings in some numerical dissipation rather than a space centered scheme the linearization is first performed about a zero mean velocity and then about a nonzero mean velocity at the various stages of the analysis our scheme is compared with more classical schemes and its improved stability property is outlined the analysis of a fully discrete in space and time version of the scheme is also given finally some considerations about a model nonlinear problem the burgers poisson problem are also discussed

effect of grid aspect ratio on convergence the effects of high aspect ratio grids on algorithm convergence are considered by means of vector stability theory and computational experiments the results indicate that approximately factored implicit schemes experience convergence deterioration because of nonoptimum local time stepping procedures and increased need for viscous preconditioning based on this insight an enhanced algorithm is devised using improved selection of the local time step appropriate definition of the viscous preconditioning matrix and proper implementation of the boundary conditions the new algorithm provides uniformly efficient convergence at all aspect ratios for both euler and navier stokes computations for a variety of test problems

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

semiparametric bayesian analysis of multiple event time data abstract multiple event time data e g carcinogenic growths in different times and locations multiple attacks of cardiac arrest arise in various medical studies a bayesian analysis of such data based on proportional intensity model of multiple event time data is presented in this paper the bayesian structure is somewhat analogous to that used by kalbfleisch in a proportional hazard model an unobserved random frailty component is used in the proportional intensity model to take care of heterogeneity among the intensity processes in different subjects the monte carlo method of sampling from multivariate distributions the so called gibbs sampler is used to sample from the joint posterior distribution of the unknown parameters the methodology developed here is exemplified with the well known data set on rat tumors of gail santner and brown

an asymptotic preserving scheme for the two fluid euler poisson model in the quasineutral limit this paper deals with the modeling of a plasma in the quasineutral limit using the two fluid euler poisson system in this limit explicit numerical schemes suffer from severe numerical constraints related to the small debye length and large plasma frequency here we propose an implicit scheme which reduces to a scheme for the quasineutral euler model in the quasineutral limit such a property is referred to as asymptotic preservation one of the distinctive features of this scheme is that it has a comparable numerical cost to that of an explicit scheme simply the poisson equation is replaced by a different but formally equivalent elliptic problem we present numerical simulations for two different one dimensional test cases they confirm the expected stability of the scheme in the quasineutral limit they also show that this scheme has some accuracy problems in the limit of small electron to ion mass ratio in reproducing the correct electron velocity but this problem is already present in the results of the classical algorithm numerical simulations are also performed for a two dimensional problem of a plasma expansion in vacuum between two electrodes

on surrogate dimension reduction for measurement error regression an invariance law we consider a general nonlinear regression problem where the predictors contain measurement error it has been recently discovered that several well known dimension reduction methods such as ols sir and phd can be performed on the surrogate regression problem to produce consistent estimates for the original regression problem involving the unobserved true predictor in this paper we establish a general invariance law between the surrogate and the original dimension reduction spaces which implies that at least at the population level the two dimension reduction problems are in fact equivalent consequently we can apply all existing dimension reduction methods to measurement error regression problems the equivalence holds exactly for multivariate normal predictors and approximately for arbitrary predictors we also characterize the rate of convergence for the surrogate dimension reduction estimators finally we apply several dimension reduction methods to real and simulated data sets involving measurement error to compare their performances

selecting factors predictive of heterogeneity in multivariate event time data in multivariate survival analysis investigators are often interested in testing for heterogeneity among clusters both overall and within specific classes we represent different hypotheses about the heterogeneity structure using a sequence of gamma frailty models ranging from a null model with no random effects to a full model having random effects for each class following a bayesian approach we define prior distributions for the frailty variances consisting of mixtures of point masses at zero and inverse gamma densities since frailties with zero variance effectively drop out of the model this prior allocates probability to each model in the sequence including the overall null hypothesis of homogeneity using a counting process formulation the conditional posterior distributions of the frailties and proportional hazards regression coefficients have simple forms posterior computation proceeds via a data augmentation gibbs sampling algorithm a single run of which can be used to obtain model averaged estimates of the population parameters and posterior model probabilities for testing hypotheses about the heterogeneity structure the methods are illustrated using data from a lung cancer trial

on the cancellation problem in calculating compressible low mach number flows in calculating low mach number flows one faces the stiffness problem in two different facets the applicable time steps become very small the constants of the cancellation errors become very large 1 usually the first point receives attention here we want toconcentrate on the cancellation problem only to our knowledge there is no detailed investigation of this problem in the related literature in primitive variable formulations the problem can be solved by using the pressure coefficient instead of the pressure and a similar variable for the temperature or the internal energy in conservative variable formulations this is thought not to be possible and therefore is sacrificed we are able to show that a local reference state can also be introduced into a conservative scheme if carefully applied to all quantities and applied to all constituent parts of the program a detailed error analysis is given for all these parts finally we show that we can perform a very low mach number calculation atm 10 11with a seven digits arithmetic only and still maintain the set of conservative variables the governing equations are unaltered and the method depends neither on the time integration scheme nor the specific discretization the method should be used in connection with the standard strategies like preconditioning multigrid or an semi implicit method if acceleration is desired

computation of low speed flow with heat addition a perturbation expansion is used to obtain a system of conservation laws for compressible flows that is valid at arbitrarily low mach numbers these equations are rendered hyperbolic by adding an artificial time derivative to the energy equation thus introducing pseudoacoustic waves with a speed the same order as the particle velocity traditional time iterative schemes are shown to be effective in solving this system numerically stability calculations of the complete vector system indicate unconditional stability at all mach numbers in the absence of gravity but the source term introduced by buoyancy becomes destabilizing at froude numbers below about 1 this instability is amplified by approximate factorization thus precluding solutions with gravity below this mach number level computations of strong heat addition in low mach number flow both with and without gravity confirm the stability predictions convergent solutions are maintained and are used to show the effect of gravity on such flowfields

on almost linearity of low dimensional projections from high dimensional data this paper studies the shapes of low dimensional projections from high dimensional data after standardization let mathbf x be a p dimensional random variable with mean zero and identity covariance for a projection beta mathbf x beta 1 find another direction b so that the regression curve of b mathbf x against beta mathbf x is as nonlinear as possible we show that when the dimension of mathbf x is large for most directions beta even the most nonlinear regression is still nearly linear our method depends on the construction of a pair of p dimensional random variables mathbf w 1 mathbf w 2 called the rotational twin and its density function with respect to the standard normal density with this we are able to obtain closed form expressions for measuring deviation from normality and deviation from linearity in a suitable sense of average as an interesting by product from a given set of data we can find simple unbiased estimates of e f beta mathbf x t phi 1 t 1 2 and e lbrack e mathbf x mid beta beta mathbf x t 2 t 2 f 2 beta mathbf x t phi 2 1 t rbrack where phi 1 is the standard normal density f beta mathbf x is the density for beta mathbf x and the e is taken with respect to the uniformly distributed beta this is achieved without any smoothing and without resorting to any laborious projection procedures such as grand tours our result is related to the work of diaconis and freedman the impact of our result on several fronts of data analysis is discussed for example it helps establish the validity of regression analysis when the link function of the regression model may be grossly wrong a further generalization which replaces beta mathbf x by b mathbf x with b beta 1 ldots beta k for k randomly selected orthonormal vectors beta i i 1 ldots k helps broaden the scope of application of sliced inverse regression sir

a coupled implicit method for chemical non equilibrium flows at all speeds a time accurate coupled solution procedure is described for the chemical nonequilibrium navier stokes equations over a wide range of mach numbers this method employs the strong conservation form of the governing equations but uses primitive variables p g u v h y i as unknowns real gas properties and nonequilibrium chemistry are considered numerical tests include steady convergent divergent nozzle flows with air dissociation recombination chemistry dump combustor flows withn pentane air chemistry and nonreacting unsteady driven cavity flows numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for mach numbers ranging from the incompressible limit to supersonic speeds c 1993 academic press inc

principal hessian directions revisited abstract li has suggested the method of principal hessian directions for estimating plotting directions that capture curvature in regression functions this article revisits li s proposal offering a number of suggestions for improved application

a numerical method for incompressible and compressible flow problems with smooth solutions abstract a semi implicit difference method of second order in space is introduced for the numerical solution of the euler equations if the mach number e is small the solutions are second order accurate also in time in particular the solutions converge to an approximate solution of the incompressible equations as e tends to zero numerical experiments are presented for channel flow and the theoretical results given for the linearized equations are shown to be valid also for the real nonlinear problem

convergence characteristics of preconditioned euler equations the convergence characteristics of the preconditioned euler equations were studied a perturbation analysis was conducted to search for the relationships between the convergence characteristics and the flow mach numbers also the influence of cancellation errors on the convergence characteristics was investigated the governing equations were the preconditioned two dimensional euler equations flows in a two dimensional channel with a 10 circular bump in the middle of the channel were calculated at different speeds roe s fds scheme was used for spatial discretization and the lu sgs lower upper symmetric gauss seidel scheme was used for time integration it was shown that the convergence characteristics of continuity and momentum equations were maintained regardless of the mach numbers but the convergence characteristics of energy equation were strongly dependant on the mach numbers and worsened as the mach number decreased the convergence characteristics were well explained by the perturbation analysis the convergence characteristics were strongly dependant on the characteristics of the preconditioning matrix cancellation errors caused a serious convergence problem especially in the calculation of the energy equation at very low mach numbers the relative treatments and a higher precision of floating point variables alleviated cancellation problems to some extent however the convergence rate was not affected by the relative treatments or by the precision of floating point variables

a high resolution pressure based algorithm for fluid flow at all speeds abstract a new collocated finite volume based solution procedure for predicting viscous compressible and incompressible flows is presented the technique is equally applicable in the subsonic transonic and supersonic regimes pressure is selected as a dependent variable in preference to density because changes in pressure are significant at all speeds as opposed to variations in density which become very small at low mach numbers the newly developed algorithm has two new features i the use of the normalized variable and space formulation nvsf methodology to bound the convective fluxes and ii the use of a high resolution scheme in calculating interface density values to enhance the shock capturing property of the algorithm the virtues of the newly developed method are demonstrated by solving a wide range of flows spanning the subsonic transonic and supersonic spectrum results obtained indicate higher accuracy when calculating interface density values using a high resolution scheme

a unified method for computing incompressible and compressible flows in boundary fitted coordinates a unified method for computing incompressible and compressible flows with mach uniform accuracy and efficiency is described the method is equally applicable to stationary and nonstationary flows a pressure based discretisation on a staggered grid in general boundary fitted coordinates is used for the euler equations extension to navier stokes is straightforward dimensionless variables that remain finite for all mach numbers are used mach number independent accuracy and efficiency is shown by numerical experiments

a projection method for low speed flows we propose a decomposition applicable to low speed inviscid flows of all mach numbers less than 1 by using the hodge decomposition we may write the velocity field as the sum of a divergence free vector field and a gradient of a scalar function evolution equations for these parts are presented a numerical procedure based on this decomposition is designed using projection methods for solving the incompressible variables and a backward euler method for solving the potential variables numerical experiments are included to illustrate various aspects of our algorithm

generalized score test of homogeneity based on correlated random effects models summary we present a family of tests based on correlated random effects models which provides a synthesis and a generalization of recent work on homogeneity testing in these models each subject has a particular random effect but the random effects between subjects are correlated we derive the general form of the score statistic for testing that the random effects have a variance equal to 0 we apply this result to both parametric and semiparametric models in both cases we show that under certain conditions the score statistic has an asymptotic normal distribution we consider several applications of this theory including overdispersion heterogeneity between groups spatial correlations and genetic linkage

a general framework for random effects survival analysis in the cox proportional hazards setting summary the use of random effects modeling in statistics has increased greatly in recent years the introduction of such modeling into event time analysis has proceeded more slowly however previously random effects models for survival data have either required assumptions regarding the form of the baseline hazard function or restrictions on the classes of models that can be fit in this paper we develop a method of random effect analysis of survival data the hierarchical cox model that is an extension of cox s original formulation in that the baseline hazard function remains unspecified this method also allows an arbitrary distribution for the random effects we accomplish this using markov chain monte carlo methods in a bayesian setting the method is illustrated with three models for a dataset with times to multiple occurrences of mammory tumors for 48 rats treated with a carcinogen and then randomized to either treatment or control this analysis is more satisfying than standard approaches such as studying the first event for each subject which does not fully use the data or assuming independence which in this case would overestimate the precision

the second order projection method for the backward facing step flow abstract in an effort to demonstrate the validity of the second order projection method for incompressible and viscous flows inside irregular domains we use the method to study the flow in the two dimensional channel with a backward facing step the emphasis of our study is on the flow separation and reattachment phenomena calculations are performed over a wide range of reynolds numbers including the laminar transitional and turbulent regimes defined by experiments in the laminar regime we find excellent agreement with experiments in terms of the dependence of the reattachment length on the reynolds number and streamwise velocity profiles for reynolds numbers beyond the laminar regime where there are no two dimensional experimental data available for comparison we find characteristic flow structures similar to those observed in three dimensional experiments for such physically unstable flows we are able to show certain numerical convergence in the statistical behavior of the solution comparison with the random vortex method is also made and similar flow behavior is found in both solutions

a goodness of fit test for cox s proportional hazards model based on martingale residuals a goodness of fit test for cox s proportional hazards model is proposed on the basis of martingale residuals the test is derived as the score test for the presence of an extra random effect in the exponential part of the hazard function assumptions about the distribution of the random effects are not made only the correlation matrix must be specified this can be done on the basis of an existing division of individuals into groups such as families or on the basis of the distance between observed covariates the variance of the test statistic is derived using a counting process approach corrections for the estimation of parameters are available the test is demonstrated in a simulated data set as well as in a real data set on ovarian cancer

covariance analysis in generalized linear measurement error models we summarize some of the recent work on the errors in variables problem in generalized linear models the focus is on covariance analysis and in particular testing for and estimation of treatment effects there is a considerable difference between the randomized and non randomized models when testing for an effect in randomized studies simple techniques exist for testing for a treatment effect in some instances such as linear and multiplicative regression simple methods exist for estimating the treatment effect in other examples such as logistic regression estimating a treatment effect requires careful attention to measurement error in non randomized studies there is no recourse to understanding and modelling measurement error in particular ignoring measurement error can lead to the wrong conclusions for example the true but unobserved data may indicate a positive effect for treatment while the observed data indicate the opposite some of the possible methods are outlined and compared

prediction of the flowfield in laser propulsion devices the difficulties encountered in modeling laser heating in a propulsive nozzle are discussed two basic formulations an approximate low mach number analysis or the complete navier stokes equations can be used the former reduces to a single ordinary differential equation for which the mass flow is an eigenvalue this representation has been considered by several researchers but the precision with which the eigenvalue must be determined makes it impractical to obtain solutions for some values of the parameters the present paper contains the first reported solutions to the complete navier stokes equations for this problem these results which were obtained with an implicit time marching method no longer contain an eigenvalue but the complex rapidly developing physics in the flowfield prevent convergence in some regimes solutions for laser absorption in hydrogen seedant mixtures demonstrate that the position of the heat absorption region is controlled by the incoming beam intensity while the mass flux is determined by the nozzle throat area these two methods are related to each other by showing that the eigenvalue analysis is a rational approximation to the navier stokes equations

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

performance of compressible flow codes at low mach numbers the accuracy and the performance of three two dimensional compressible flow codes at freestream mach numbers as low as 0 001 are examined two of the codes employ a finite volume discretization scheme along with a multistage time stepping algorithm to solve the euler equations the two codes differ in their respective use of cell centered and node centered differencing schemes the third code uses an implicit finite difference procedure to solve the unsteady navier stokes equations computational test cases are the inviscid steady flow over a circular cylinder and the impulsively started viscous flow over a cylinder

three measures of explained variation for correlated survival data under the proportional hazards mixed effects model measures of explained variation are useful in scientific research as they quantify the amount of variation in an outcome variable of interest that is explained by one or more other variables we develop such measures for correlated survival data under the proportional hazards mixed effects model because different approaches have been studied in the literature outside the classical linear regression model we investigate three measures r 2 rres2 and 2 that quantify three different population coefficients we show that although the three population measures are not the same they reflect similar amounts of variation explained by the predictors among the three measures we show that r 2 which is the simplest to compute is also consistent for the first population measure under the usual asymptotic scenario when the number of clusters tends to infinity the other two measures on the other hand all require that in addition the cluster sizes be large we study the properties of the measures both analytically and through simulation studies we illustrate their different usage on a multi center clinical trial and a recurrent events data set copyright 2016 john wiley sons ltd

a systematic approach to the analysis of complex interaction patterns in two level factorial designs analysis of data from two level full factorial designs often ends up with a final prediction equation that gives only the significant main effect and interaction terms when the number of interactions is small simple and useful interpretation of the equation can then be drawn immediately this article addresses a different situation in which the number of significant interactions may be large so that additional efforts are needed to sort out the pattern and the relationship between them in particular we bring out a class of models in which most interactions can be attributed to just one or two or very few factors and conditional on these factors the models become essentially linear we offer a strategy for uncovering this structure by linear domain splitting whereby a complicated global model is replaced by a series of local domain specific linear models we present a recommended methodology phd principal hessian direction for systematically proceeding from the global equation to local split dom

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

an all speed roe type scheme and its asymptotic analysis of low mach number behaviour a new scheme all speed roe scheme was proposed for all speed flows compared with traditional preconditioned roe scheme all speed roe scheme changes non linear eigenvalues in the numerical dissipation terms of roe type schemes with an asymptotic analysis the low mach number behaviour of the scheme is studied theoretically in two ways in one way all speed roe scheme is regarded as finite magnification of low speed roe scheme in the low mach number limit in the other way a general form of all speed roe scheme is analyzed both ways demonstrate that all speed roe scheme has the same low mach number behaviour as the original governing equation in the continuous case which includes three important features pressure variation scales with the square of the mach number the zero order velocity field is subject to a divergence constraint and the second order pressure satisfies a poisson type equation in the case of constant entropy the analysis also leads to an unexpected conclusion that the velocity filed computed by traditional preconditioned roe scheme does not satisfy the divergence constraint as the mach number vanishes moreover the analysis explains the reason of checkerboard decoupling and shows that momentum interpolation method provides a similar mechanism as traditional preconditioned roe scheme inherently possesses to suppress checkerboard decoupling in the end general rulers for modifying non linear eigenvalues are obtained finally several numerical experiments are provided to support the theoretical analysis all speed roe scheme has a sound foundation and is expected to be widely studied and applied to all speed flow calculations

the incompressible limit of the non isentropic euler equations we study the euler equations for slightly compressible fluids that is after rescaling the limits of the euler equations of fluid dynamics as the mach number tends to zero in this paper we consider the general non isentropic equations and general data we first prove the existence of classical solutions for a time independent of the small parameter then on the whole space d we prove that the solution converges to the solution of the incompressible euler equations

mach uniformity through the coupled pressure and temperature correction algorithm we present a new type of algorithm the coupled pressure and temperature correction algorithm it is situated in between the fully coupled and the fully segregated approach and is constructed such that mach uniform accuracy and efficiency are obtained the essential idea is the separation of the convective and the acoustic thermodynamic phenomena a convective predictor is followed by an acoustic thermodynamic corrector for a general case the corrector consists of a coupled solution of the energy and the continuity equations for both pressure and temperature corrections for the special case of an adiabatic perfect gas flow the algorithm reduces to a fully segregated method with a pressure correction equation based on the energy equation various test cases are considered which confirm that mach uniformity is obtained

numerical approximations of pressureless and isothermal gas dynamics we study several schemes of first or second order accuracy based on kinetic approximations to solve pressureless and isothermal gas dynamics equations the pressureless gas system is weakly hyperbolic giving rise to the formation of density concentrations known as delta shocks for the isothermal gas system the infinite speed of expansion into vacuum leads to zero timestep in the godunov method based on exact riemann solver the schemes we consider are able to bypass these difficulties they are proved to satisfy positiveness of density and discrete entropy inequalities to capture the delta shocks and to treat data with vacuum

a superlinearly convergent mach uniform finite volume method for the euler equations on staggered unstructured grids a mach uniform finite volume scheme for solving the unsteady euler equations on staggered unstructured triangular grids that uses linear reconstruction is described the scheme is applied to three benchmark problems and is found to be considerably more accurate than a similar scheme based on piecewise constant reconstruction

upwind finite volume method with a triangular mesh for conservation laws a new upwind scheme has been developed and analyzed for a finite volume solution of the conservation laws on triangular meshes the scheme is an upwind second order extrapolation with simple local limiters and it is weakly second order accurate and satisfies maximum principles in one dimension the scheme reduces to a fully upwind second order scheme with a simple local limiter preliminary numerical results demonstrating the performance of the scheme on a variety of initial boundary value problems are presented the order of convergence of the scheme is found to vary from 1 6 to 1 9 in l1

euler equations implicit schemes and boundary conditions implicit boundary condition procedures are presented for use with implicit finite difference schemes for the unsteady euler equations this new boundary point treatment is based on the mathematical theory of characteristics for hyperbolic systems of equations along with the theoretical background the practical application of the method to several types of boundaries is also explained using several examples the specific boundary conditions covered include subsonic inflow and outflow surface tangency and shock waves the example problems include one dimensional laval nozzle flow dual throat rocket engine nozzle flow and supersonic flow past a sphere the implicit boundary treatment permits the use of large time steps allowing the finite difference algorithm to converge to the asymptotic steady state much faster than schemes that use explicitly applied boundary conditions at least an order of magnitude increase in computational speed is demonstrated in the examples shown background t he growing popularity of solutions to the euler equations in transonics and their continued application in supersonics have increased the need for quicker solutions the potential of implicit schemes in this direction has not been fully exploited for want of correct implicit application of boundary conditions the predominant use of implicit algorithms for the navier stokes equations has partly been responsible for the neglect of implicit boundary point treatment for the euler equations thus there is a need for correct and stable procedures for the easy implicit application of boundary conditions such methods will serve the two purposes of 1 reaching time asymptotic steady state faster and 2 permitting a time step for truly unsteady flow that is not necessarily restricted by the cfl stability criterion but is based upon the magnitude of the transients for clues and information on how to construct such boundary condition procedures one must turn to the mathematical theory of characteristi cs for hyperbolic systems of equations the unsteady euler equations belong to this category the theory for hyperbolic systems is rich with information on signal propagation directions the characteristics theory clearly points to the number of boundary conditions that may and need be prescribed without overdetermining the solution boundary condition procedures based on this theory have been known and applied for several years by kentzer 1 porter and coakley 2 de neef 3 and others in earlier work by this author 4 5 easily understood and implementable methods for boundary point treatment were presented however all of the above techniques were developed for explicit finite difference schemes it seems that it must be easy to extend such methodologies based on mathematical theory for hyperbolic systems to implicit finite difference schemes and indeed it is simple enough the rest of this paper describes such implicit boundary condition procedures the given examples illustrate in detail the application of the proposed methodology to specific types of boundaries and demonstrate the merits of the new scheme

estimation of multivariate frailty models using penalized partial likelihood summary there exists a growing literature on the estimation of gamma distributed multiplicative shared frailty models there is however often a need to model more complicated frailty structures but attempts to extend gamma frailties run into complications motivated by hip replacement data with a more complicated dependence structure we propose a model based on multiplicative frailties with a multivariate log normal joint distribution we give a justification and an estimation procedure for this generally structured frailty model which is a generalization of the one presented by mcgilchrist 1993 biometrics49 221 225 the estimation is based on laplace approximation of the likelihood function this leads to estimating equations based on a penalized fixed effects partial likelihood where the marginal distribution of the frailty terms determines the penalty term the tuning parameters of the penalty function i e the frailty variances are estimated by maximizing an approximate profile likelihood the performance of the approximation is evaluated by simulation and the frailty model is fitted to the hip replacement data

slicing regression a link free regression method slicing regression a link free regression m e t h o d author s naihua duan and k e r c h a u l i s o u r c e the annals of statistics v o l 19 n o 2 t u n 1991 p p 5 0 5 5 3 0 p u b l i s h e d b y institute of mathematical statistics s t a b l e u r l http www jstor org stable 2242072 accessed 16 05 2011 your use of the jstor archive indicates your acceptance of jstor s terms and conditions of use available at http www jstor org page info about policies terms jsp jstor s terms and conditions of use provides in part that unless you have obtained prior permission you may not download an entire issue of a journal or multiple copies of articles and you may use content in the jstor archive only for your personal non commercial use please contact the publisher regarding any further use of this work publisher contact information may be obtained at http www jstor org action showpublisher publishercode ims each copy of any part of a jstor transmission must contain the same copyright notice that appears on the screen or printed page of such transmission jstor is a not for profit service that helps scholars researchers and students discover use and build upon a wide range of content in a trusted digital archive we use information technology and tools to increase productivity and facilitate new forms of scholarship for more information about jstor please contact support jstor org http www jstor org

bayesian semiparametric dynamic frailty models for multiple event time data many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly such as infection hospitalization recurrence of disease or tumor onset to analyze such data it is necessary to account for within subject dependency in the multiple event times motivated by data from studies of palpable tumors this article proposes a dynamic frailty model and bayesian semiparametric approach to inference the widely used shared frailty proportional hazards model is generalized to allow subject specific frailties to change dynamically with age while also accommodating nonproportional hazards parametric assumptions on the frailty distribution are avoided by using dirichlet process priors for a shared frailty and for multiplicative innovations on this frailty by centering the semiparametric model on a conditionally conjugate dynamic gamma model we facilitate posterior computation and lack of fit assessments of the parametric model our proposed method is demonstrated using data from a cancer chemoprevention study

random effects selection in linear mixed models nous presentons le probleme pratique important de la selection des effets aleatoires dans un modele lineaire mixte un modele bayesien hierarchique est utilise pour identifier tout effet aleatoire devariance nulle l approche proposee reparametrise le modele mixte de telle sorte que les fonctions des parametres de covariance de la distribution des effets aleatoires soient incorporees comme des coefficients de regression pour des variables latentes normales nous permettons aux effets aleatoires de sortir du modele en choisissant des melanges d a priori avec des masses ponctuelles en zero pour les variances des effets aleatoires du fait de la reparametrisation le modele prend une structure lineaire conditionnelle qui facilite l utilisation de lois a priori conjuguees et normales nous demontrons que les calculs a posteriori peuvent etre effectues via un algorithme simple et efficace de monte carlo par chaine de markov les methodes sont illustrees par des donnees simulees et par des donnees reelles d exposition prenatale au polychlorobiphenile et des donnees sur le developpement psychomoteur des enfants

proportional hazards model with random effects we propose a general proportional hazards model with random effects for handling clustered survival data this generalizes the usual frailty model by allowing a multivariate random effect with arbitrary design matrix in the log relative risk in a way similar to the modelling of random effects in linear generalized linear and non linear mixed models the distribution of the random effects is generally assumed to be multivariate normal but other preferably symmetrical distributions are also possible maximum likelihood estimates of the regression parameters the variance components and the baseline hazard function are obtained via the em algorithm the e step of the algorithm involves computation of the conditional expectations of functions of the random effects for which we use markov chain monte carlo mcmc methods approximate variances of the estimates are computed by louis formula and posterior expectations and variances of the individual random effects can be obtained as a by product of the estimation the inference procedure is exemplified on two data sets

momentum variable procedure for solving compressible and incompressible flows navier stokes equations are solved for both compressible and incompressible flows using momentum component variables instead of the usual velocity variables as the dependent variables the numerical procedure is developed in a control volume based finite element context the procedure is determined in a pressure based algorithm rather than the density based algorithms which compressible methods normally use the proper selection of the connections between the variables on control volume surfaces and the main nodal values allow the use of a collocated grid arrangement the compressible and incompressible results of this algorithm are investigated by testing a number of test cases including the driven cavity an entrance region flow and a converging diverging nozzle flow the results indicate that the momentum component procedure is quite successful for solving compressible and incompressible flows within a single algorithm

on principal hessian directions for data visualization and dimension reduction another application of stein s lemma abstract modern graphical tools have enhanced our ability to learn many things from data directly with much user friendly graphical software available we are encouraged to plot a lot more often than before the benefits from direct interaction with graphics have been enormous but trailing behind these high tech advances is the issue of appropriate guidance on what to plot there are too many directions to project a high dimensional data set and unguided plotting can be time consuming and fruitless in a recent article li set up a statistical framework for study on this issue based on a notion of effective dimension reduction edr directions they are the directions to project a high dimensional input variable for the purpose of effectively viewing and studying its relationship with an output variable a methodology sliced inverse regression was introduced and shown to be useful in finding edr directions this article introduces another method for finding edr directions it begins with the observat