adaptive unstructured volume remeshing ii application to two and three dimensional level set simulations of multiphase flow in part i adaptive unstructured volume remeshing i the method j comput phys in press we presented an adaptive remeshing algorithm that automatically adjusts the size of the elements of meshes of unstructured triangles 2d and unstructured tetrahedra 3d with time and position in the computational domain in order to efficiently resolve the relevant physical scales here we illustrate the performance of an implementation of the algorithm in finite element level set simulations of deformable droplet and fluid fluid interface interactions breakup and coalescence in multiphase flows the wide range of length scales characterizing the dynamics are accurately resolved as demonstrated by comparison to experiments and to theoretical and sharp interface boundary integral numerical results the computational cost is found to be competitive even with respect to boundary integral methods for the first time using an interface capturing level set method we successfully simulate the inertia driven impact and rebound of a liquid droplet from a liquid interface and find agreement with recent experimental results

the variable selection problem abstract the problem of variable selection is one of the most pervasive model selection problems in statistical applications often referred to as the problem of subset selection it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables or predictors but there is uncertainty about which subset to use this vignette reviews some of the key developments that have led to the wide variety of approaches for this problem

modeling a no slip flow boundary with an external force field abstract a novel technique related to peskin s immersed boundary approach is used to introduce solid surfaces into a simulated flow field the navier stokes equations permit the presence of an externally imposed body force that may vary in space and time forces are chosen to lie along a desired surface and to have a magnitude and direction opposing the local flow such that the flow is brought to rest on an element of the surface for unsteady viscous flow the direct calculation of the needed force is facilitated by a feedback scheme in which the velocity is used to iteratively determine the desired value in particular we determine the surface body force from the relation f x 5 t t 0 u x 5 t dt u x 5 t for surface points x 5 velocity u time t and negative constants and examples are presented which include 2d flow around cylinders 3d turbulent channel flow where one boundary is simulated with a force field and turbulent channel flow over a riblet covered surface while the new method may be applied to complex geometries on a non cartesian mesh we have chosen to use a simple cartesian grid all simulations are done with a spectral code in a single computational domain without any mapping of the mesh

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

diagonal implicit multigrid algorithm for the euler equations a multigrid implementation of the alternating direction implicit algorithm has been developed to solve the euler equations of inviscid compressible flow the equations are approximated using a finite volume spatial approximation with added dissipation provided by an adaptive blend of second and fourth differences for computational efficiency the equations are diagonalized by a local similariity transformation so that only a decoupled system of scalar pentadiagonal systems need be solved along each line results are computed for transonic flows past airfoils and include pressure distributions to verify the accuracy of the basic scheme and convergence histories to demonstrate the efficiency of the method

predictor selection for positive autoregressive processes let observations y1 yn be generated from a first order autoregressive ar model with positive errors in both the stationary and unit root cases we derive moment bounds and limiting distributions of an extreme value estimator of the ar coefficient these results enable us to provide asymptotic expressions for the mean squared error mse of and the mean squared prediction error mspe of the corresponding predictor of yn 1 based on these expressions we compare the relative performance of and the least squares predictor estimator from the mspe mse point of view our comparison reveals that the better predictor estimator is determined not only by whether a unit root exists but also by the behavior of the underlying error distribution near the origin and hence is difficult to identify in practice to circumvent this difficulty we suggest choosing the predictor estimator with the smaller accumulated prediction error and show that the predictor estimator chosen in this way is as

stability of solutions for stochastic impulsive systems via comparison approach this note studies stability problem of solutions for stochastic impulsive systems by employing lyapunov like function method and it s formula comparison principles of existence and uniqueness and stability of solutions for stochastic impulsive systems are established based on these comparison principles the stability properties of stochastic impulsive systems are derived by the corresponding stability properties of a deterministic impulsive system as the application the stability results are used to design impulsive control for the stabilization of unstable stochastic systems finally one example is given to illustrate the obtained results

var forecasting under misspecification the paper considers multi step forecasting of a stationary vector process under a quadratic loss function with a collection of finite order vector autoregressions var under severe misspecification it is preferable to use the multi step loss function also for parameter estimation we propose a modification to shibata s ann statist 8 1980 147 final prediction error criterion to jointly choose the var lag order and one of two predictors the maximum likelihood estimator plug in predictor or the loss function estimator plug in predictor a monte carlo experiment illustrates the theoretical results and documents the empirical performance of the selection criterion

model selection for multivariate regression in small samples we develop a small sample criterion aicc for selecting multivariate regression models this criterion adjusts the akaike information criterion to be an exact unbiased estimator for the expected kullback leibler information a small sample comparison shows that aicc provides better model order choices than other available model selection methods data from an agricultural experiment are analyzed

adaptive tetrahedral meshing in free surface flow an unstructured three dimensional moving mesh algorithm is developed for free surface flows with the capability of simulating large deformation a robust edge swapping algorithm and an optimization based mesh smoothing algorithm are used to improve mesh quality as the interface deforms the edge swapping algorithm uses an optimal swap sequence to transform configurations with several tetrahedra sharing a common edge the optimization based mesh smoothing relocates vertex position so that the minimum quality of the incident cells is maximized also edge contraction and bisection are used to adjust the mesh resolution according to surface curvature these local refinements effectively maintain good mesh quality and appropriate mesh size while avoiding global re meshing this scheme s robustness and accuracy are demonstrated with deforming liquid ligaments periodic jets and colliding droplets

direct numerical simulation of flow past elliptic cylinders flow over elliptic cylinders can be considered prototypical of flow over a range of bluff bodies since the geometry allows one to study the effect of both thickness and angle of attack on the flow field therefore a careful study of this flow should provide valuable insight into the phenomenon of unsteady separation and the structure of bluff body wakes with this in mind a spectral collocation technique has been developed to simulate the full three dimensional incompressible flow over elliptic cylinders and unlike spectral element and spectral multidomain techniques here the flow is solved in a single domain the equations are discretized on a body fitted elliptic cylindrical grid and properties of the metric associated with this coordinate system are used to solve the governing equations in an efficient manner key issues including the inflow and outflow boundary conditions and time discretization are discussed in detail with the hope that this will facilitate future simulations of similar flows finally we present results of two and three dimensional simulations for a range of flow and geometric parameters the results are compared with available experimental data and it is found that important quantities like strouhal numbers and drag coefficients match well with established values

nonparametric identification of nonlinear time series selecting significant lags abstract in this article we suggest a nonparametric procedure for selecting significant lags in the model description of a general nonlinear stationary time series the procedure can be applied to both the conditional mean and the conditional variance and is valid for heteroscedastic series the procedure is illustrated by simulations and sunspot data lynx data and blowfly data are analyzed it is indicated that projectors can be used in conjunction with the procedure for selecting significant lags to check the adequacy of an additive time series model

average consensus in networks of dynamic agents with switching topologies and multiple time varying delays in this paper we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time varying communication delays by employing a linear matrix inequality method we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected particularly several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying communication delays numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results

the discrete continuity equation in primitive variable solutions of incompressible flow abstract the use of a non staggered computational grid for the numerical solutions of the incompressible flow equations has many advantages over the use of a staggered grid a penalty however is inherent in the finite difference approximations of the governing equations on non staggered grids in the primitive variable solutions the penalty is that the discrete continuity equation does not converge to machine accuracy rather it converges to a source term which is proportional to the fourth order derivative of the pressure the time increment and the square of the grid spacing an approach which minimizes the error in the discrete continuity equation is developed numerical results obtained for the driven cavity problem confirm the analytical developments

uniform moment bounds of fisher s information with applications to time series in this paper a uniform over some parameter space moment bound for the inverse of fisher s information matrix is established this result is then applied to develop moment bounds for the normalized least squares estimate in nonlinear stochastic regression models the usefulness of these results is illustrated using time series models in particular an asymptotic expression for the mean squared prediction error of the least squares predictor in autoregressive moving average models is obtained this asymptotic expression provides a solid theoretical foundation for some model selection criteria

computation of solid liquid phase fronts in the sharp interface limit on fixed grids a finite difference formulation is applied to track solid liquid boundaries on a fixed underlying grid the interface is not of finite thickness but is treated as a discontinuity and is explicitly tracked the imposition of boundary conditions exactly on a sharp interface that passes through the cartesian grid is performed using simple stencil readjustments in the vicinity of the interface attention is paid to formulating difference schemes that are globally second order accurate in x and t error analysis and grid refinement studies are performed for test problems involving the diffusion and convection diffusion equations and for stable solidification problems issues concerned with stability and change of phase of grid points in the evolution of solid liquid phase fronts are also addressed it is demonstrated that the field calculation is second order accurate while the position of the phase front is calculated to first order accuracy furthermore the accuracy estimates hold for the cases where there is a property jump across the interface unstable solidification phenomena are simulated and an attempt is made to compare results with previously published work the results indicate the need to begin an effort to benchmark computations of instability phenomena

twenty one ml estimators for model selection classical approaches to determine a suitable model structure from observed input output data are based on hypothesis tests and information based criteria recently the model structure has been considered as a stochastic variable and standard estimation techniques have been proposed the resulting estimators are closely related to the aforementioned methods however it turns out that there are a number of prior choices in the problem formulation which are crucial for the estimators behavior the contribution of this paper is to clarify the role of the prior choices to examine a number of possibilities and to show which estimators are consistent this is done in a linear regression framework for autoregressive models we also investigate a novel prior assumption on stability and give the estimator for the model order and the parameters themselves

consensus problem of second order multi agent systems with communication delay and input delay in this paper asynchronously coupled algorithm is used to solve the consensus problem of second order multi agent systems with both communication delay and input delay by constructing lyapunov krasovskii functional sufficient consensus conditions are obtained for second order systems under invariant input delays accompanied with time invariant and time varying communication delays respectively the conditions are all in the forms of linear matrix inequality lmi simulation illustrates the correctness of the results

alternate formulations for the pressure equation laplacian on a collocated grid for solving the unsteady incompressible navier stokes equations abstract the solution of the unsteady incompressible navier stokes on a collocated grid is investigated a consistent formulation to construct the laplacian in the pressure equation is developed it is shown that within this framework laplacians with different characteristics can be constructed which can be made to satisfy discrete continuity and considerably reduce pressure oscillations a third order forward biased approximation for the gradient operator of pressure works very well in completely eliminating pressure oscillations in a lid driven cavity flow test problem

h consensus of second order multi agent systems with asymmetric delays abstract this paper is concerned with the problem of consensus in the h sense for second order continuous time multi agent systems with multiple asymmetric time varying delays by using a model transformation approach and matrix theory we establish several conditions in terms of linear matrix inequalities such that consensus of multi agent systems can be achieved in the h sense the feasibility of the consensus conditions is also analyzed as an application we consider the case of intermittent measurement between agents numerical examples are presented to illustrate the theoretical results which can be applied to the case of negative information weights

a non staggered grid fractional step method for time dependent incompressible navier stokes equations in curvilinear coordinates a numerical method for solving three dimensional time dependent incompressible navier stokes equations in curvilinear coordinates is presented the non staggered grid method originally developed by c m rhie and w l chow aiaaj 21 1525 1983 for steady state problems is extended to compute unsteady flows in the computational space the cartesian velocity components and the pressure are defined at the center of a control volume while the volume fluxes are defined at the mid point on their corresponding cell faces the momentum equations are integrated semi implicitly by the approximate factorization technique the intermediate velocities are interpolated onto the faces of the control volume to form the source terms of the pressure poisson equation which is solved iteratively with a multigrid method the compatibility condition of the pressure poisson equation is satisfied in the same manner as in a staggered grid method mass conservation can be satisfied to machine accuracy the pressure boundary condition is derived from the momentum equations solutions of both steady and unsteady problems including the large eddy simulation of a rotating and stratified upwelling flow in an irregular container established the favorable accuracy and efficiency of the present method

using simulated annealing to optimize the feature selection problem in marketing applications the feature selection also specification problem is concerned with finding the most influential subset of predictors in predictive modeling from a much larger set of potential predictors that can contain hundreds of predictors the problem belongs to the realm of combinatorial optimization where the objective is to find the subset of variables that optimize the value of some goodness of fit function due to the dimensionality of the problem the feature selection problem belongs to the group of np hard problems most of the available predictors are noisy or redundant and add very little if any to the prediction power of the model using all the predictors in the model often results in strong over fitting and very poor predictions constructing a prediction model by checking out all possible subsets is impractical due to computational volume looking on the contribution of each predictor separately is not accurate because it ignores the inter correlations between predictors as a result no analytic solution is available for the feature selection problem requiring that one resorts to heuristics in this paper we employ the simulated annealing sa approach which is one of the leading stochastic search methods for specifying a large scale linear regression model the sa results are compared to the results of the more common stepwise regression swr approach for model specification the models are applied on realistic data sets in database marketing we also use simulated data sets to investigate what data characteristics make the swr approach equivalent to the supposedly more superior sa approach

the risk inflation criterion for multiple regression a new criterion is proposed for the evaluation of variable selection procedures in multiple regression this criterion which we call the risk inflation is based on an adjustment to the risk essentially the risk inflation is the maximum increase in risk due to selecting rather than knowing the correct predictors a new variable selection procedure is obtained which in the case of orthogonal predictors substantially improves on aic c p and bic and is close to optimal in contrast to aic c p and bic which use dimensionality penalties of 2 2 and log n respectively this new procedure uses a penalty 2 log p where p is the number of available predictors for the case of nonorthogonal predictors bounds for the optimal penalty are obtained

a cartesian grid projection method for the incompressible euler equations in complex geometries many problems in fluid dynamics require the representation of complicated internal or external boundaries of the flow here we present a method for calculating time dependent incompressible inviscid flow which combines a projection method with a cartesian grid approach for representing geometry in this approach the body is represented as an interface embedded in a regular cartesian mesh the advection step is based on a cartesian grid algorithm for compressible flow in which the discretization of the body near the flow uses a volume of fluid representation a redistribution procedure is used to eliminate time step restrictions due to small cells where the boundary intersects the mesh the projection step uses an approximate projection based on a cartesian grid method for potential flow the method incorporates knowledge of the body through volume and area fractions along with certain other integrals over the mixed cells convergence results are given for the projection itself and for the time dependent algorithm in two dimensions the method is also demonstrated on flow past a half cylinder with vortex shedding

bootstrap model selection abstract in a regression problem typically there are p explanatory variables possibly related to a response variable and we wish to select a subset of the p explanatory variables to fit a model between these variables and the response a bootstrap variable model selection procedure is to select the subset of variables by minimizing bootstrap estimates of the prediction error where the bootstrap estimates are constructed based on a data set of size n although the bootstrap estimates have good properties this bootstrap selection procedure is inconsistent in the sense that the probability of selecting the optimal subset of variables does not converge to 1 as n this inconsistency can be rectified by modifying the sampling method used in drawing bootstrap observations for bootstrapping pairs response explanatory variable it is found that instead of drawing n bootstrap observations a customary bootstrap sampling plan much less bootstrap observations should be sampled the bootstrap selection p

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

accumulated prediction errors information criteria and optimal forecasting for autoregressive time series the predictive capability of a modification of rissanen s accumulated prediction error ape criterion ape n is investigated in infinite order autoregressive ar oo models instead of accumulating squares of sequential prediction errors from the beginning ape n is obtained by summing these squared errors from stage n n where n is the sample size and 1 n n 1 1 n may depend on n under certain regularity conditions an asymptotic expression is derived for the mean squared prediction error mspe of an ar predictor with order determined by ape n this expression shows that the prediction performance of ape n can vary dramatically depending on the choice of n another interesting finding is that when n approaches 1 at a certain rate ape n can achieve asymptotic efficiency in most practical situations an asymptotic equivalence between ape n and an information criterion with a suitable penalty term is also established from the mspe point of view this offers new perspectives for understanding the information and prediction based model selection criteria finally we provide the first asymptotic efficiency result for the case when the underlying ar oo model is allowed to degenerate to a finite autoregression

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

order selection for same realization predictions in autoregressive processes assume that observations are generated from an infinite order autoregressive ar process shibata ann statist 8 1980 147 164 considered the problem of choosing a finite order ar model allowing the order to become infinite as the number of observations does in order to obtain a better approximation he showed that for the purpose of predicting the future of an independent replicate akaike s information criterion aic and its variants are asymptotically efficient although shibata s concept of asymptotic efficiency has been widely accepted in the literature it is not a natural property for time series analysis this is because when new observations of a time series become available they are not independent of the previous data to overcome this difficulty in this paper we focus on order selection for forecasting the future of an observed time series referred to as same realization prediction we present the first theoretical verification that aic and its variants are still asymptotically elficient in the sense defined in section 4 for same realization predictions to obtain this result a technical condition easily met in common practice is introduced to simplify the complicated dependent structures among the selected orders estimated parameters and future observations in addition a simulation study is conducted to illustrate the practical implications of aic this study shows that aic also yields a satisfactory saute realization prediction in finite samples on the other hand a limitation of aic in same realization settings is pointed out it is interesting to note that this limitation of aic does not exist for corresponding independent cases

brief paper some necessary and sufficient conditions for second order consensus in multi agent dynamical systems this paper studies some necessary and sufficient conditions for second order consensus in multi agent dynamical systems first basic theoretical analysis is carried out for the case where for each agent the second order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant a necessary and sufficient condition is given to ensure second order consensus and it is found that both the real and imaginary parts of the eigenvalues of the laplacian matrix of the corresponding network play key roles in reaching consensus based on this result a second order consensus algorithm is derived for the multi agent system facing communication delays a necessary and sufficient condition is provided which shows that consensus can be achieved in a multi agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value finally simulation examples are given to verify the theoretical analysis

multiphase dynamics in arbitrary geometries on fixed cartesian grids in this work a mixed eulerian lagrangian algorithm calledelafint eulerian lagrangian algorithm for interface tracking is developed further and applied to compute flows with solid fluid and fluid fluid interfaces the method is capable of handling fluid flows in the presence of both irregularly shaped solid boundaries and moving boundaries on a fixed cartesian grid the field equations are solved on the underlying fixed grid using a collocated variable pressure based formulation the moving boundary is tracked explicitly by the lagrangian translation of marker particles the moving boundary passes through the grid and the immersed boundary technique is used to handle its interaction with the underlying grid the internal solid boundaries are dealt with by using a cut cell technique particular attention is directed toward conservation and consistency in the vicinity of both phase boundaries the complex geometry feature has been tested for a variety of flow problems the performance of the immersed boundary representation is demonstrated in the simulation of newtonian liquid drops the combination of the two features is then employed in the simulation of motion of drops through constricted tubes the capabilities developed here can be useful for solving flow problems involving moving and stationary complex boundaries

the minimum description length principle in coding and modeling we review the principles of minimum description length and stochastic complexity as used in data compression and statistical modeling stochastic complexity is formulated as the solution to optimum universal coding problems extending shannon s basic source coding theorem the normalized maximized likelihood mixture and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms we assess the performance of the minimum description length criterion both from the vantage point of quality of data compression and accuracy of statistical inference context tree modeling density estimation and model selection in gaussian linear regression serve as examples

an auxiliary grid method for computations of multiphase flows in complex geometries a method is developed for computations of interfacial flows in complex geometries the method combines a front tracking method with a newly developed finite volume fv scheme and utilizes an auxiliary grid for computationally efficient tracking of interfaces in body fitted curvilinear grids the tracking algorithm reduces particle tracking in a curvilinear grid to tracking on a uniform cartesian grid with a look up table the algorithm is general and can be used for other applications where lagrangian particles have to be tracked in curvilinear or unstructured grids the spatial and temporal errors are examined and it is shown that the method is globally second order accurate both in time and space the method is implemented to solve two dimensional planar or axisymmetric interfacial flows and is validated for a buoyancy driven drops in a straight tube and the motion of buoyancy driven drops in a periodically constricted channel

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

on residual empirical processes of stochastic regression models with applications to time series motivated by gaussian tests for a time series we are led to investigate the asymptotic behavior of the residual empirical processes of stochastic regression models these models cover the fixed design regression models as well as general ar q models since the number of the regression coefficients is allowed to grow as the sample size increases the obtained results are also applicable to nonlinear regression and stationary ar models in this paper we first derive an oscillation like result for the residual empirical process then we apply this result to autoregressive time series in particular for a stationary ar process we are able to determine the order of the number of coefficients of a fitted ar q n model and obtain the limiting gaussian processes for an unstable ar q process we show that if the characteristic polynomial has a unit root 1 then the limiting process is no longer gaussian for the explosive case one of our side results also provides a short proof for the brownian bridge results given by koul and levental

a front tracking method for the computations of multiphase flow direct numerical simulations of multiphase flows using a front tracking method are presented the method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties interfacial terms are accounted for by adding the appropriate sources as functions at the boundary separating the phases the unsteady navier stokes equations are solved by a conventional finite volume method on a fixed structured grid and the interface or front is tracked explicitly by connected marker points interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid advection of fluid properties such as density is done by following the motion of the front the method has been implemented for fully three dimensional flows as well as for two dimensional and axisymmetric ones first the method is described for the flow of two or more isothermal phases the representation of the moving interface and its dynamic restructuring as well as the transfer of information between the moving front and the fixed grid are discussed applications and extensions of the method to homogeneous bubbly flows atomization flows with variable surface tension solidification and boiling are then presented

the focused information criterion a variety of model selection criteria have been developed of general and specific types most of these aim at selecting a single model with good overall properties for example formulated via average prediction quality or shortest estimated overall distance to the true model the akaike the bayesian and the deviance information criteria along with many suitable variations are examples of such methods these methods are not concerned however with the actual use of the selected model which varies with context and application the present article takes the view that the model selector should instead focus on the parameter singled out for interest in particular a model that gives good precision for one estimand may be worse when used for inference for another estimand we develop a method that for a given focus parameter estimates the precision of any submodel based estimator the framework is that of large sample likelihood inference using an unbiased estimate of limiting risk we propose a foc

selecting optimal multistep predictors for autoregressive processes of unknown order we consider the problem of choosing the optimal in the sense of mean squared prediction error multistep predictor for an autoregressive ar process of finite but unknown order if a working ar model which is possibly misspecified is adopted for multistep predictions then two competing types of multistep predictors i e plug in and direct predictors can be obtained from this model we provide some interesting examples to show that when both plug in and direct predictors are considered the optimal multistep prediction results cannot be guaranteed by correctly identifying the underlying model s order this finding challenges the traditional model order selection criteria which usually aim to choose the order of the true model a new prediction selection criterion which attempts to seek the best combination of the prediction order and the prediction method is proposed to rectify this difficulty when the underlying model is stationary the validity of the proposed criterion is justified theoretically to obtain this result asymptotic properties of accumulated squares of multistep prediction errors are investigated in addition to overcoming the above difficulty some other advantages of the proposed criterion are also mentioned

regular article a consistent hybrid finite volume particle method for the pdf equations of turbulent reactive flows the paper describes a new hybrid finite volume fv particle method developed for the solution of the pdf equations for statistically stationary turbulent reactive flows in this approach the conservation equations for mean mass momentum and energy conservation are solved by a fv method while a particle algorithm is employed to solve the fluctuating velocity turbulence frequency compositions joint pdf transport equation the mean velocity and pressure are supplied to the particle code by the fv code which in turn obtains all the reynolds stresses the scalar fluxes and the reaction terms needed in the fv code an important feature of the method is the complete consistency between the set of equations solved by the fv and particle methods the algorithmic and numerical issues arising in the development of the hybrid method are studied in the simple setting of the stochastic ideal flow equations numerical results are obtained for 1d reactive stochastic ideal flow to demonstrate numerical properties of the method the total numerical error is identified as statistical error bias spatial truncation error and temporal truncation error in contrast to the self contained particle method the bias is found to be negligibly small it is shown that all the numerical errors converge at the expected rates finally the global convergence of the hybrid method is demonstrated and the optimal strategy for time averaging that gives the best global convergence rate is investigated

nonparametric maximum entropy the standard maximum entropy method developed by j p burg 1967 and the resulting autoregressive model have been widely applied to spectrum estimation and prediction a generalization of the maximum entropy formalism in a nonparametric setting is presented and the class of the resulting solutions is identified to be a class of markov processes the proof is based on a string of information theoretic arguments developed in a derivation of burg s maximum entropy spectrum by b s choi and t m cover 1984 a framework for the practical implementation of the proposed method is presented in the context of both continuous and discrete data