the stability in _ and _ of the projection onto finite element function spaces on etablit la stabilite de la l 2 projection sur quelques espaces a elements finis v h consideree comme une application dans l p et w p 1 1 p sous des hypotheses de regularite faibles

bayesian experimental design for multiple hypothesis testing abstract the problem of designing an optimal experiment for the purpose of performing one or more hypothesis tests is considered the bayesian decision theoretic approach is used to arrive at several new optimality criteria for this purpose for a single hypothesis test the resulting optimal designs are the well known optimal designs that minimize the posterior variance of the parameter being tested for multiple tests an experimental design must perform well under several competing criteria different approaches to achieving this goal are explored including constrained optimization and an additive weighted loss the resulting optimality criteria are sensitive not only to the posterior variances of the parameters under test but also to their prior means

open fuzzy cubature rule with application to nonlinear fuzzy volterra integral equations in two dimensions abstract in this paper we propose an open fuzzy cubature formula and as application we construct an iterative numerical method for solving nonlinear fuzzy volterra integral equations in two dimensions the convergence of the method is proved by providing the error estimate and it is tested on two numerical experiments

a wavelet mra based adaptive semi lagrangian method for the relativistic vlasov maxwell system in this paper we present a new method for the numerical solution of the relativistic vlasov maxwell system on a phase space grid using an adaptive semi lagrangian method the adaptivity is performed through a wavelet multiresolution analysis which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function therefore the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and cpu time we apply this numerical scheme to reduced vlasov maxwell systems arising in laser plasma physics interaction of relativistically strong laser pulses with overdense plasma slabs is investigated these vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping particle acceleration and electron plasma wavebreaking however the wavelet based adaptive method that we developed here does not yield significant improvements compared to vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation here the vlasov simulations are performed in a two dimensional phase space where the development of thin filaments strongly amplified by relativistic effects requires an important increase of the total number of points of the phase space grid as they get finer as time goes on the adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper volume which arises in higher dimensions because of the surface to volume scaling and the essentially one dimensional structure of the filaments moreover the main way to improve the efficiency of the adaptive method is to increase the local character in phase space of the numerical scheme by considering multiscale reconstruction with more compact support and by replacing the semi lagrangian method with more local in space numerical scheme as compact finite difference schemes discontinuous galerkin method or finite element residual schemes which are well suited for parallel domain decomposition techniques

conservative numerical schemes for the vlasov equation abstract a new scheme for solving the vlasov equation using a phase space grid is proposed the algorithm is based on the conservation of the flux of particles and the distribution function is reconstructed using various techniques that allow control of spurious oscillations or preservation of the positivity several numerical results are presented in two and four dimensional phase space and the scheme is compared with the semilagrangian method this method is almost as accurate as the semilagrangian one and the local reconstruction technique is well suited for parallel computation

a bayesian analysis of kriging this article is concerned with predicting for gaussian random fields in a way that appropriately deals with uncertainty in the covariance function to this end we analyze the best linear unbiased prediction procedure within a bayesian framework particular attention is paid to the treatment of parameters in the covariance structure and their effect on the quality both real and perceived of the prediction these ideas are implemented using topographical data from davis

an essay on statistical decision theory 2000 an essay on statistical decision theory journal of the american statistical association vol 95 no 452 pp 1277 1281

dispersive and dissipative behaviour of high order discontinuous galerkin finite element methods the dispersive and dissipative properties of hp version discontinuous galerkin finite element approximation are studied in three different limits for the small wave number limit hk 0 we show the discontinuous galerkin gives a higher order of accuracy than the standard galerkin procedure thereby confirming the conjectures of hu and atkins j comput phys 182 2 2002 516 if the mesh is fixed and the order p is increased it is shown that the dissipation and dispersion errors decay at a super exponential rate when the order p is much larger than hk finally if the order is chosen so that 2p 1 hk for some fixed constant 1 then it is shown that an exponential rate of decay is obtained

the numerical method of successive interpolations for two point boundary value problems with deviating argument a new numerical method for two point boundary value problems associated to differential equations with deviating argument is obtained the method uses the fixed point technique the trapezoidal quadrature rule and the cubic spline interpolation procedure the convergence of the method is proved without smoothness conditions the kernel function being lipschitzian in each argument the interpolation procedure is used only on the points where the argument is modified a practical stopping criterion of the algorithm is obtained and the accuracy of the method is illustrated on some numerical examples of the pantograph type

bayesian estimation and experimental design in linear regression models estimation and design as a bayesian decision problem choice of a prior distribution conjugate prior distributions bayes estimation of the regression parameter optimality and robustness of the bayes estimator bayesian interpretation of estimators using non bayesian prior knowledge bayes estimation in case of prior ignorance further problems the design problem for the linear bayes estimator characterization of optimal designs construction of optimal continuous designs construction of exact optimal designs

maximum entropy sampling and optimal bayesian experimental design when shannon entropy is used as a criterion in the optimal design of experiments advantage can be taken of the classical identity representing the joint entropy of parameters and observations as the sum of the marginal entropy of the observations and the preposterior conditional entropy of the parameters following previous work in which this idea was used in spatial sampling the method is applied to standard parameterized bayesian optimal experimental design under suitable conditions which include non linear as well as linear regression models it is shown in a few steps that maximizing the marginal entropy of the sample is equivalent to minimizing the preposterior entropy the usual bayesian criterion thus avoiding the use of conditional distributions it is shown using this marginal formulation that under normality assumptions every standard model which has a two point prior distribution on the parameters gives an optimal design supported on a single point other results include a new asymptotic formula which applies as the error variance is large and bounds on support size

the ordinary successive approximations method and pade approximants for solving a differential equation with variant retarded argument the aim of this paper is to present an efficient numerical procedure for solving boundary value problems for a differential equation with retarded argument x t a t x t t t f t x t f t l 0 0 0

a novel method for nonlinear boundary value problems in this paper a novel numerical method is proposed for solving nonlinear boundary value problems this method is based on a combination of the reproducing kernel and least squares methods so the accuracy of this method is improved we have proved the uniform convergence of the approximate solution u n by convergence of u n in w 3 a b numerical results obtained by using the scheme show that the numerical scheme is feasible and effective

numerical methods for discontinuous linear boundary value problems with deviation arguments abstract numerical methods for the solution of discontinuous linear boundary value problems with deviation arguments are developed

numerical solution of functional differential integral and integro differential equations this paper describes a numerical method based on lagrange interpolation and chebyshev interpolation to treat functional integral equations of volterra type and fredholm type also the method can be extended to functional differential and integro differential equations various numerical examples are treated

on a boundary value problem for a differential equation with variant retarded argument in this paper we applied two approximate methods for the solution of a boundary value problem for a differential equation with retarded argument x t a t x t t t f t x t f t l 0 t 0 x t x t where 0 t t and a t f t t t 0 0 t t and f t l 0 t 0 are known continuous functions

a finite element code for the simulation of one dimensional vlasov plasmas i theory abstract the galerkin method is used to obtain a finite element solution to the vlasov poisson equations over the two dimensional x v phase plane using bilinear element shape functions a set of linear equations for updated values of the distribution function is obtained in which time dependent and time independent coefficients are separated to reduce the computation involved the noise levels are low and the energy conservation good the finite element approach offers certain advantages over alternative methods in applications to problems in plasma physics in particular the flexibility in using elements of different size allows problems in which regions of the plasma are characterized by often widely differing scale lengths to be treated efficiently

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

multi point boundary value problems for second order functional differential equations this paper is concerned with the existence of extreme solutions of multi point boundary value problem for a class of second order functional differential equations we introduce a new concept of lower and upper solutions by using the method of upper and lower solutions and monotone iterative technique we obtain the existence of extreme solutions

existence of solutions of boundary value problems for second order functional differential equations abstract in this paper we deal with the boundary value problem x f t x x t x x t x 0 x 0 c 1 c 2 c 1 c 2 r x j 0 x 1 x j 0 where f car j r c r r c r c r j 0 1 1 a j a 0 1 a j and a 0 1 are two special sets of functionals and x j is the restriction of x to j we find sufficient conditions for the existence of solutions of the above problem the proof is based on the leray schauder degree theory

eaton s markov chain its conjugate partner and mathscr p admissibility suppose that x is a random variable with density f x and that x is a proper posterior corresponding to an improper prior the prior is called p admissible if the generalized bayes estimator of every bounded function of is almost admissible under squared error loss eaton showed that recurrence of the markov chain with transition density r x f x dx is a sufficient condition for p admissibility of we show that eaton s markov chain is recurrent if and only if its conjugate partner with transition density r y x f y x d is recurrent this provides a new method of establishing p admissibility often one of these two markov chains corresponds to a standard stochastic process for which there are known results on recurrence and transience for example when x is poisson and an improper gamma prior is placed on the markov chain defined by r y x is equivalent to a branching process with immigration we use this type of argument to establish p admissibility of some priors when f is a negative binomial mass function and when f is a gamma density with known shape

a high order semi lagrangian discontinuous galerkin method for vlasov poisson simulations without operator splitting abstract in this paper we develop a high order semi lagrangian sl discontinuous galerkin dg method for nonlinear vlasov poisson vp simulations without operator splitting in particular we combine two recently developed novel techniques one is the high order non splitting sldg transport method cai et al 2017 4 and the other is the high order characteristics tracing technique proposed in qiu and russo 2017 29 the proposed method with up to third order accuracy in both space and time is locally mass conservative free of splitting error positivity preserving stable and robust for large time stepping size the sldg vp solver is applied to classic benchmark test problems such as landau damping and two stream instabilities for vp simulations efficiency and effectiveness of the proposed scheme is extensively tested tremendous cpu savings are shown by comparisons between the proposed sl dg scheme and the classical runge kutta dg method

discontinuous galerkin methods for the vlasov maxwell equations discontinuous galerkin methods are developed for solving the vlasov maxwell system methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy such properties in general are hard to achieve within other numerical method frameworks for simulating the vlasov maxwell system the proposed scheme employs discontinuous galerkin discretizations for both the vlasov and the maxwell equations resulting in a consistent description of the distribution function and electromagnetic fields it is proven up to some boundary effects that charge is conserved and the total energy can be preserved with suitable choices of the numerical flux for the maxwell equations and the underlying approximation spaces error estimates are established for several flux choices the scheme is tested on the streaming weibel instability the order of accuracy and conservation properties of the proposed method are verified

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

direct operatorial tau method for pantograph type equations abstract the lanczos tau method is applied to find chebyshev polynomial approximations for the solutions of pantograph differential equations the results are accompanied by an error analysis numerical examples calculated by our matlab package chebpack confirm the theory and prove the importance for practice of this approach

minimax adjustment technique and fuzzy information abstract in this paper the minimax adjustment technique is generalized to fuzzy information sets using a quadratic loss function and specific ellipsoidal constraints the case of fuzzy information can be reduced to the case of crisp information here the minimax adjustment technique is equivalent to a projection method furthermore a characterization of the solution is given being not far away from an explicit representation applications to statistics and to economics are presented

a subdivision approach to the construction of approximate solutions of boundary value problems with deviating arguments abstract using the ideas employed in the construction of subdivision algorithms we offer here a high accuracy algorithm to compute numerical solutions for two point boundary value problems of differential equations with deviating arguments numerical examples are included to demonstrate the fast convergence and high accuracy of the algorithm this paper is a further development to our previous works for solving various types of boundary value problems

a performance comparison of semi lagrangian discontinuous galerkin and spline based vlasov solvers in four dimensions abstract the purpose of the present paper is to compare two semi lagrangian methods in the context of the four dimensional vlasov poisson equation more specifically our goal is to compare the performance of the more recently developed semi lagrangian discontinuous galerkin scheme to cubic spline interpolation which is widely used in eulerian vlasov simulation to that end we perform simulations for nonlinear landau damping and a two stream instability and provide benchmarks for the selalib and sldg codes both on a workstation and using mpi on a cluster in addition we will present results for the graphic processing unit gpu implementation contained in sldg we find that the semi lagrangian discontinuous galerkin scheme shows a moderate improvement in run time for nonlinear landau damping and a substantial improvement for the two stream instability it should be emphasized that these results are markedly different from results obtained in the asymptotic regime which favor spline interpolation thus we conclude that the traditional approach of evaluating numerical methods is misleading even for short time simulations in addition the absence of any global communication in the semi lagrangian discontinuous galerkin method gives it a decisive advantage for scaling to more than 256 cores

finite difference methods for boundary value problems of differential equations with deviating arguments abstract we propose a convergent finite difference method to construct an approximate solution of the boundary value problems with deviating arguments the method developed takes into account the continuity limitations of the solutions of these problems to demonstrate the effectiveness of the proposed method numerical evidence is also included

a predictive approach to the bayesian design problem with application to normal regression models a predictive decision theoretic approach is developed for the bayesian design problem the loss functions used are fair bayes or proper scoring rules and are quadratic measures of distance between probability measures optimal bayesian designs are those which minimise the preposterior risk for the decision problem such designs typically depend on both the prior distribution and the loss function the results are applied to certain normal regression models where explicit optimal designs are constructed

hamiltonian splitting for the vlasov maxwell equations a new splitting is proposed for solving the vlasov maxwell system this splitting is based on a decomposition of the hamiltonian of the vlasov maxwell system and allows for the construction of arbitrary high order methods by composition independent of the specific deterministic method used for the discretization of the phase space moreover we show that for a spectral method in space this scheme satisfies poisson s equation without explicitly solving it finally we present some examples in the context of the time evolution of an electromagnetic plasma instability which emphasizes the excellent behavior of the new splitting compared to methods from the literature

discontinuous galerkin algorithms for fully kinetic plasmas abstract we present a new algorithm for the discretization of the non relativistic vlasov maxwell system of equations for the study of plasmas in the kinetic regime using the discontinuous galerkin finite element method for the spatial discretization we obtain a high order accurate solution for the plasma s distribution function time stepping for the distribution function is done explicitly with a third order strong stability preserving runge kutta method since the vlasov equation in the vlasov maxwell system is a high dimensional transport equation up to six dimensions plus time we take special care to note various features we have implemented to reduce the cost while maintaining the integrity of the solution including the use of a reduced high order basis set a series of benchmarks from simple wave and shock calculations to a five dimensional turbulence simulation are presented to verify the efficacy of our set of numerical methods as well as demonstrate the power of the implemented features

numerical study of the two species vlasov ampere system in this paper we propose energy conserving eulerian solvers for the two species vlasov ampere va system and apply the methods to simulate current driven ion acoustic instability the two species va systems are of practical importance in applications and they conserve many physical quantities including the particle number of each species and the total energy that is comprised of kinetic energy for both species and the electric energy the main goal of this paper is to generalize our previous work for the single species va system 9 and vlasov maxwell vm system 8 to the two species case the methodologies proposed involve careful design of temporal discretization and the use of the discontinuous galerkin dg spatial discretizations we show that the energy conserving time discretizations for single species equations 9 8 can also work for the two species case if extended properly compared to other high order schemes we emphasize that our schemes can preserve the total particle number and total energy on the fully discrete level regardless of mesh size making them very attractive for long time simulations we benchmark our algorithms on a test example to check the one species limit and the current driven ion acoustic instability to simulate the current driven ion acoustic instability a slight modification for the implicit method is necessary to fully decouple the split equations this is achieved by a gauss seidel type iteration technique numerical results verified the conservation and performance of our methods finally we remark that the schemes in this paper can be readily extended to applications when the models take more general form such as the multi species vm equations

a new approach to numerical solution of fixed point problems and its application to delay differential equations in this paper we consider a certain approximation of fixed points of a continuous operator a mapping the metric space into itself by means of finite dimensional e h fixed points of a these finite dimensional functions are obtained from functions defined on discrete space grid points related to a parameter h 0 by applying suitably chosen extension operators p h a theorem specifying necessary and sufficient conditions for existence of fixed points of a in terms of e h fixed points of a is given a corollary which follows the theorem yields an approximate method for a fixed point problem and determines conditions for its convergence an example of application of the obtained general results to numerical solving of boundary value problems for delay differential equations is provided numerical experiments carried out on three examples of boundary value problems for second order delay differential equations show that the proposed approach produces much more accurate results than many other numerical methods when applied to the same examples

linear regression analysis using the relative squared error abstract in order to determine estimators and predictors in a generalized linear regression model we apply a suitably defined relative squared error instead of the most frequently used absolute squared error the general solution of a matrix problem is derived leading to minimax estimators and predictors furthermore we consider an important special case where an analogon to a well known relation between estimators and predictors holds and where generalized least squares estimators as well as kuks olman and ridge estimators play a prominent role

the selection of prior distributions by formal rules abstract subjectivism has become the dominant philosophical foundation for bayesian inference yet in practice most bayesian analyses are performed with so called noninformative priors that is priors constructed by some formal rule we review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used we give special emphasis to jeffreys s rules and discuss the evolution of his viewpoint about the interpretation of priors away from unique representation of ignorance toward the notion that they should be chosen by convention we conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly when sample sizes are small relative to the number of parameters being estimated it is dangerous to put faith in any default solution but when asymptotics take over jeffreys s rules and their variants remain reasonable choices we also provide an annotated b

miscellanea a note on bayesian design for the normal linear model with unknown error variance summary the bayesian theory of optimal experimental design for the normal linear model has been developed under the assumption of known variance the insensitivity of specific design criteria to prior assumptions on the variance distribution has been demonstrated in special cases but a general result showing the way in which bayesian optimal designs are affected by prior information on the variance is lacking this note proves that bayesian designs are insensitive to information about

a particle in cell method for the simulation of plasmas based on an unconditionally stable field solver abstract we propose a new particle in cell pic method for the simulation of plasmas based on a recently developed unconditionally stable solver for the wave equation this method is not subject to a cfl restriction limiting the ratio of the time step size to the spatial step size typical of explicit methods while maintaining computational cost and code complexity comparable to such explicit schemes we describe the implementation in one and two dimensions for both electrostatic and electromagnetic cases and present the results of several standard test problems showing good agreement with theory with time step sizes much larger than allowed by typical cfl restrictions

a splitting algorithm for vlasov simulation with filamentation filtration a fourier fourier transformed version of the splitting algorithm for simulating solutions of the vlasov poisson system of equations is introduced it is shown that with the inclusion of filamentation filtration in this transformed algorithm it is both faster and more stable than the standard splitting algorithm it is further shown that in a scalar computer environment this new algorithm is approximately equal in speed and far less noisy than its particle in cell counterpart it is conjectured that in a multiprocessor environment the filtered splitting algorithm would be faster while producing more precise results

a positivity preserving high order semi lagrangian discontinuous galerkin scheme for the vlasov poisson equations the vlasov poisson equations describe the evolution of a collisionless plasma represented through a probability density function pdf that self interacts via an electrostatic force one of the main difficulties in numerically solving this system is the severe time step restriction that arises from parts of the pdf associated with moderate to large velocities the dominant approach in the plasma physics community for removing these time step restrictions is the so called particle in cell pic method which discretizes the distribution function into a set of macro particles while the electric field is represented on a mesh several alternatives to this approach exist including fully lagrangian fully eulerian and so called semi lagrangian methods the focus of this work is the semi lagrangian approach which begins with a grid based eulerian representation of both the pdf and the electric field then evolves the pdf via lagrangian dynamics and finally projects this evolved field back onto the original eulerian mesh in particular we develop in this work a method that discretizes the 1 1 vlasov poisson system via a high order discontinuous galerkin dg method in phase space and an operator split semi lagrangian method in time second order accuracy in time is relatively easy to achieve via strang operator splitting with additional work using higher order splitting and a higher order method of characteristics we also demonstrate how to push this scheme to fourth order accuracy in time we show how to resolve all of the lagrangian dynamics in such a way that mass is exactly conserved positivity is maintained and high order accuracy is achieved the poisson equation is solved to high order via the smallest stencil local discontinuous galerkin ldg approach we test the proposed scheme on several standard test cases

critical phenomena for spitzer s reversible nearest particle systems motivated by several results and open problems concerning harris basic contact process we consider the relationship between the critical behavior of the finite and infinite versions of spitzer s reversible nearest particle systems we show that the critical values for the finite and infinite systems agree but that the behavior of the two systems at the common critical value can differ the nash williams recurrence criterion for reversible markov chains is an important tool used in the proofs of the main results and we give a new treatment of that theory finally we compute several critical exponents for the nearest particle systems

about a numerical method of successive interpolations for two point boundary value problems with deviating argument a new numerical method for two point boundary value problems with deviating argument is obtained the method uses the fixed point technique the trapezoidal quadrature rule and a birkhoff interpolation procedure the convergence of the method is proved without smoothness conditions the kernel function being only lipschitzian in each argument the interpolation procedure is used only on the points where the argument is modified a stopping criterion of the algorithm is obtained and the accuracy of the method is illustrated on four numerical examples of pantograph type

optimal bayesian designs for models with partially specified heteroscedastic structure we consider the problem of finding a nonsequential optimal design for estimating parameters in a generalized exponential growth model this problem is solved by first considering polynomial regression models with error variances that depend on the covariate value and unknown parameters a bayesian approach is adopted and optimal bayesian designs supported on a minimal number of support points for estimating the coefficients in the polynomial model are found analytically for some criteria the optimal bayesian designs depend only on the expectation of the prior but generally their dependence includes the derivative of the logarithm of the laplace transform of a measure induced by the prior the optimal design for the generalized exponential growth model is then determined from these optimal bayesian designs

on using explicit runge kutta nystrom methods for the treatment of retarded differential equations with periodic solutions in this work we dial with the treatment of second order retarded differential equations with periodic solutions by explicit runge kutta nystrom methods in the past such methods have not been studied for this class of problems we refer to the underline theory and study the behavior of various methods proposed in the literature when coupled with hermite interpolants among them we consider methods having the characteristic of phase lag order then we consider continuous extensions of the methods to treat the retarded part of the problem finally we construct scaled extensions and high order interpolants for rkn pairs which have better characteristics compared to analogous methods proposed in the literature in all cases numerical tests and comparisons are done over various test problems

numerical solutions of functional integral equations in this paper we give a more general definition of integral equations of the second and first kind which are called functional integral equations fredholm and volterra integral equations are special type of these equations we derive an expansion method to treat these equations finally we introduce numerical examples and conclusion

strictly proper scoring rules prediction and estimation scoring rules assess the quality of probabilistic forecasts by assigning a numerical score based on the predictive distribution and on the event or value that materializes a scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionf if he or she issues the probabilistic forecast f rather than g f it is strictly proper if the maximum is unique in prediction problems proper scoring rules encourage the forecaster to make careful assessments and to be honest in estimation problems strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand this article reviews and develops the theory of proper scoring rules on general probability spaces and proposes and discusses examples thereof proper scoring rules derive from convex functions and relate to information measures entropy functions and bregman divergences in the case of categorical variables we prove a rigorous version of the

coherent dispersion criteria for optimal experimental design we characterize those coherent design criteria which depend only on the dispersion matrix assumed proper and nonsingular of the state of nature which may be a parameter vector or a set of future observables and describe the associated decision problems connections are established with the classical approach to optimal design theory for the normal linear model based on concave functions of the information matrix implications of the theory for more general models are also considered

the equivalence of constrained and weighted designs in multiple objective design problems abstract several competing objectives may be relevant in the design of an experiment the competing objectives may not be easy to characterize in a single optimality criterion one approach to these design problems has been to weight each criterion and find the design that optimizes the weighted average of the criteria an alternative approach has been to optimize one criterion subject to constraints on the other criteria an equivalence theorem is presented for the bayesian constrained design problem equivalence theorems are essential in verifying optimality of proposed designs especially when as in most nonlinear design problems numerical optimization is required this theorem is used to show that the results of cook and wong on the equivalence of the weighted and constrained problems apply much more generally the results are applied to bayesian nonlinear design problems with several objectives

bayes optimal designs for two and three level factorial experiments abstract two and three level factorial designs are often used for exploratory experiments with many independent variables the purpose of such experiments is to estimate the effects of all active independent variables and their interactions for reasons of economy or other constraints only a fraction of the full number of experimental settings of the independent variables may be run precluding the separate data based estimation of all the effects in this situation of relatively sparse data and many unknown parameters the benefits of reliable prior information used in the estimation and experimental design can be especially significant in this article exact bayes optimal designs of two and three level fractional factorial experiments and of blocked two and three level factorial experiments are derived the optimality criteria used in this process are versions of the bayes criterion introduced by duncan and degroot it is shown that the classical fractional factorial designs for the 2k experime

evaluation of formal posterior distributions via markov chain arguments we consider evaluation of proper posterior distributions obtained from improper prior distributions our context is estimating a bounded function of a parameter when the loss is quadratic if the posterior mean of 0 is admissible for all bounded the posterior is strongly admissible we give sufficient conditions for strong admissibility these conditions involve the recurrence of a markov chain associated with the estimation problem we develop general sufficient conditions for recurrence of general state space markov chains that are also of independent interest our main example concerns the p dimensional multivariate normal distribution with mean vector 0 when the prior distribution has the form g 6 2 d on the parameter space r p conditions on g for strong admissibility of the posterior are provided

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

global weak solutions of vlasov maxwell systems we study here the vlasov maxwell system in its classical and relativistic form we prove the stability of solutions in weak topologies and deduce from this stability result the global existence of a weak solution with large initial data the main tools consist of a new regularity result for velocity averages of solutions of some general linear transport equations and the method of renormalization introduced by the authors in previous work

e optimal designs for rational models in this paper experimental designs for a rational model y p x q x e are investigated where p x o 1 x p x p and q x 1 p 1 x p q x q are polynomials and e is a random error two approaches bayesian d optimal and bayesian optimal design for extrapolation are examined the first criterion maximizes the expected increase in shannon information provided by the experiment asymptotically and the second minimizes the asymptotic variance of the maximum likelihood estimator mle of the mean response at an extrapolation point x e corresponding locally optimal designs are also discussed conditions are derived under which a p q 1 point design is a locally d optimal design the bayesian d optimal design is shown to be independent of the parameters in p x and to be equally weighted at each support point if the number of support points is the same as the number of parameters in the model the existence and uniqueness of the locally optimal design for extrapolation are proven the number of support points for the locally optimal design for extrapolation is exactly p q 1 these p q 1 design points are proved to be independent of the extrapolation point x e and the parameters in p x the corresponding weights are also independent of the parameters in p x but depend on x e and are not equal

a new collocation method for approximate solution of the pantograph functional differential equations with proportional delay the paper presents a new numerical method for solving functional differential equations with proportional delays of the first and higher orders the method consists of replacing the initial equation by an approximate equation which has an exact analytic solution with a set of free parameters these free parameters are determined by the use of the collocation procedure some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results the numerical results show that the proposed method is of a high accuracy and is efficient for solving a wide class of functional differential equations with proportional delays including equations of neutral type the method is applicable to both initial and boundary value problems

admissible estimation dirichlet principles and recurrence of birth death chains on ℤ p we establish a connection between admissible simultaneous estimation and recurrence of reversible markov chains on specifically to each generalized bayes estimator of the mean of a vector of p independent poisson variables for a weighted quadratic loss we associate a variational problem and a reversible birth and death chain on the variational problem is closely related to the dirichlet principle for reversible chains studied recently by griffeath liggett and lyons under side conditions admissibility of the estimator is equivalent to zero infimal energy in the variational problem and to recurrence of the markov chain this yields analytic and probabilistic criteria for inadmissibility which are applied to establish a broad class of results and previous conjectures