some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

a new algebraic geometry algorithm for integer programming we propose a new algorithm for solving integer programming ip problems that is based on ideas from algebraic geometry the method provides a natural generalization of the farkas lemma for ip leads to a way of performing sensitivity analysis offers a systematic enumeration of all feasible solutions and gives structural information of the feasible set of a given ip we provide several examples that offer insights on the algorithm and its properties

local existence of the strong solutions for the full navier stokes poisson equations abstract we study the full navier stokes poisson equations for viscous polytropic fluids we prove the existence and uniqueness of local strong solutions for all initial values satisfying some compatibility conditions it is important that we allow the initial density to be vacuum

approximate bayes factors and accounting for model uncertainty in generalised linear models summary ways of obtaining approximate bayes factors for generalised linear models are described based on the laplace method for integrals we propose a new approximation which uses only the output of standard computer programs for estimating generalised linear models this appears to be quite accurate a reference set of proper priors is suggested both to represent the situation where there is not much prior information and to assess the sensitivity of the results to the prior distribution the methods can be used when the dispersion parameter is unknown when there is overdispersion to compare link functions and to compare error distributions and variance functions the methods can be used to implement the bayesian approach to accounting for model uncertainty we describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important software to implement the methods is available at no cost from statlib

marginal likelihood from the metropolis hastings output this article provides a framework for estimating the marginal likelihood for the purpose of bayesian model comparisons the approach extends and completes the method presented in chib 1995 by overcoming the problems associated with the presence of intractable full conditional densities the proposed method is developed in the context of mcmc chains produced by the metropolis hastings algorithm whose building blocks are used both for sampling and marginal likelihood estimation thus economizing on prerun tuning effort and programming experiments involving the logit model for binary data hierarchical random effects model for clustered gaussian data poisson regression model for clustered count data and the multivariate probit model for correlated binary data are used to illustrate the performance and implementation of the method these examples demonstrate that the method is practical and widely applicable

on the use of panel data in stochastic frontier models with improper priors abstract we consider a bayesian analysis of the stochastic frontier model with composed error under a commonly used class of partly noninformative prior distributions the existence of the posterior distribution and of posterior moments is examined viewing this model as a normal linear regression model with regression parameters corresponding to both the frontier and the inefficiency terms generates the insights used to derived results in a very wide framework it is found that in pure cross section models posterior inference is precluded under this usual class of priors existence of a well defined posterior distribution then crucially hinges upon the structure imposed on the inefficiency terms exploiting panel data naturally suggests the use of more structured models where bayesian inference can be conducted

neighborhood systems for production sets with indivisibilities a production set with indivisibilities is described by an activity analysis matrix with activity levels which can assume arbitrary integral values a neighborhood system is an association with each integral vector of activity levels of a finite set of neighboring vectors the neighborhood relation is assumed to be symmetric and translation invariant each such neighborhood system can be used to define a local maximum for the associated integer programs obtained by selecting a single commodity whose level is to be maximized subject to specified factor endowments of the remaining commodities it is shown that each technology matrix subject to mild regularity assumptions has a unique minimal neighborhood system for which a local maximum is global the complexity of such minimal neighborhood systems is examined for several examples

on spherically symmetric solutions of the compressible isentropic navier stokes equations we prove the global existence of weak solutions to the cauchy problem for the compressible isentropic navier stokes equations in n n 2 3 when the cauchy data are spherically symmetric the proof is based on the exploitation of the one dimensional feature of symmetric solutions and use of a new multidimensional property induced by the viscous flux the present paper extends lions existence theorem 15 to the case 1 n for spherically symmetric initial data where is the specific heat ratio in the pressure n 3 2 for n 2 and n 9 5 for n 3 dedicated to professor rolf leis on the occasion of his 70th birthday

hyper markov laws in the statistical analysis of decomposable graphical models this paper introduces and investigates the notion of a hyper markov law which is a probability distribution over the set of probability measures on a multivariate space that i is concentrated on the set of markov probabilities over some decomposable graph and ii satisfies certain conditional independence restrictions related to that graph a stronger version of this hyper markov property is also studied our analysis starts by reconsidering the properties of markov probabilities using an abstract approach which thereafter proves equally applicable to the hyper markov case next it is shown constructively that hyper markov laws exist that they appear as sampling distributions of maximum likelihood estimators in decomposable graphical models and also that they form natural conjugate prior distributions for a bayesian analysis of these models as examples we construct a range of specific hyper markov laws including the hyper multinomial hyper dirichlet and the hyper wishart and inverse wishart laws these laws occur naturally in connection with the analysis of decomposable log linear and covariance selection models

global existence of strong solutions of navier stokes equations with non newtonian potential for one dimensional isentropic compressible fluids abstract the aim of this paper is to discuss the global existence and uniqueness of strong solution for a class of the isentropic compressible navier stokes equations with non newtonian in one dimensional bounded intervals we prove two global existence results on strong solutions of the isentropic compressible navier stokes equations the first result shows only the existence and the second one shows the existence and uniqueness result based on the first result but the uniqueness requires some compatibility condition

strong solutions of the navier stokes equations for isentropic compressible fluids we study strong solutions of the isentropic compressible navier stokes equations in a domain r3 we first prove the local existence of unique strong solutions provided that the initial data 0 and u0 satisfy a natural compatibility condition the important point in this paper is that we allow the initial vacuum the initial density may vanish in an open subset of we then prove a new uniqueness result and stability result our results are valid for unbounded domains as well as bounded ones

variation of cost functions in integer programming we study the problem of minimizingc x subject toa x b x 0 andx integral for a fixed matrixa two cost functionsc andc are considered equivalent if they give the same optimal solutions for eachb we construct a polytopest a whose normal cones are the equivalence classes explicit inequality presentations of these cones are given by the reduced grobner bases associated witha the union of the reduced grobner bases asc varies called the universal grobner basis consists precisely of the edge directions ofst a we present geometric algorithms for computingst a the graver basis and the universal grobner basis

a flexible approach to parametric inference in nonlinear and time varying time series models many structural break and regime switching models have been used with macroeconomic and financial data in this paper we develop an extremely flexible modeling approach which can accommodate virtually any of these specifications we build on earlier work showing the relationship between flexible functional forms and random variation in parameters our contribution is based around the use of priors on the time variation that is developed from considering a hypothetical reordering of the data and distance between neighboring reordered observations the range of priors produced in this way can accommodate a wide variety of nonlinear time series models including those with regime switching and structural breaks by allowing the amount of random variation in parameters to depend on the distance between reordered observations the parameters can evolve in a wide variety of ways allowing for everything from models exhibiting abrupt change e g threshold autoregressive models or standard structural break models to those which allow for a gradual evolution of parameters e g smooth transition autoregressive models or time varying parameter models bayesian econometric methods for inference are developed for estimating the distance function and types of hypothetical reordering conditional on a hypothetical reordering and distance function a simple reordering of the actual data allows us to estimate our models with standard state space methods by a simple adjustment to the measurement equation we use artificial data to show the advantages of our approach before providing two empirical illustrations involving the modeling of real gdp growth

posterior predictive p values extending work of rubin this paper explores a bayesian counterpart of the classical p value namely a tail area probability of a test statistic under a null hypothesis the bayesian formulation using posterior predictive replications of the data allows a test statistic to depend on both data and unknown nuisance parameters and thus permits a direct measure of the discrepancy between sample and population quantities the tail area probability for a test statistic is then found under the joint posterior distribution of replicate data and the nuisance parameters both conditional on the null hypothesis this posterior predictive p value can also be viewed as the posterior mean of a classical p value averaging over the posterior distribution of nuisance parameters under the null hypothesis and thus it provides one general method for dealing with nuisance parameters two classical examples including the behrens fisher problem are used to illustrate the posterior predictive p value and some of its interesting properties which also reveal a new bayesian interpretation for some classical p values an application to multiple imputation inference is also presented a frequency evaluation shows that in general if the replication is defined by new nuisance parameters and new data then the type i frequentist error of an level posterior predictive test is often close to but less than and will never exceed 2

an outer approximation algorithm for a class of mixed integer nonlinear programs an outer approximation algorithm is presented for solving mixed integer nonlinear programming problems of a particular class linearity of the integer or discrete variables and convexity of the nonlinear functions involving continuous variables are the main features in the underlying mathematical structure based on principles of decomposition outer approximation and relaxation the proposed algorithm effectively exploits the structure of the problems and consists of solving an alternating finite sequence of nonlinear programming subproblems and relaxed versions of a mixed integer linear master program convergence and optimality properties of the algorithm are presented as well as a general discussion on its implementation numerical results are reported for several example problems to illustrate the potential of the proposed algorithm for programs in the class addressed in this paper finally a theoretical comparison with generalized benders decomposition is presented on the lower bounds predicted by the relaxed master programs

a simple and efficient simulation smoother for state space time series analysis a simulation smoother in state space time series analysis is a procedure for drawing samples from the conditional distribution of state or disturbance vectors given the observations we present a new technique for this which is both simple and computationally efficient the treatment includes models with diffuse initial conditions and regression effects computational comparisons are made with the previous standard method two applications are provided to illustrate the use of the simulation smoother for gibbs sampling for bayesian inference and importance sampling for classical inference 2002 biometrika trust

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

pointwise estimates of solution for the navier stokes poisson equations in multi dimensions abstract the cauchy problem of the navier stokes poisson equations in multi dimensions n 3 is considered we obtain the pointwise estimates of the solution when it is a perturbation of the constant state then we have the optimal l p r n p 1 convergence rate of the solution

a randomized algorithm to optimize over certain convex sets this paper presents a randomized polynomial time algorithm to nearly minimize a linear function over an up monotone convex set in the positive orthant given only by a membership oracle our original motivation for this is a stochastic optimization problem called the component commonality problem in the literature

an algebraic approach to integer portfolio problems abstract integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model we propose an algebraic approach to maximize the expected return under a given admissible level of risk measured by the covariance matrix to reach an optimal portfolio it is an essential ingredient the computation of different test sets via grobner basis of linear subproblems that are used in a dual search strategy

global existence of strong solutions of the navier stokes equations for isentropic compressible fluids with density dependent viscosity abstract this paper is concerned with global strong solutions of the isentropic compressible navier stokes equations with density dependent viscosity coefficient in one dimensional bounded intervals precisely the viscosity coefficient and the pressure p is proportional to with 1 the important point in this paper is that the initial density may vanish in an open subset we also show that the strong solution obtained above is unique provided that the initial data satisfies additional regularity and a compatible condition compared with former results obtained by hyunseok kim in h kim global existence of strong solutions of the navier stokes equations for one dimensional isentropic compressible fluids available at http com2mac postech ac kr papers 2001 01 38 pdf we deal with density dependent viscosity coefficient

a geometric buchberger algorithm for integer programming let ip a c denote the family of integer programs of the form min cx ax b x nn obtained by varying the right hand side vector b but keeping a and c fixed a test set for ipa c is a set of vectors in zn such that for each nonoptimal solution to a program in this family there is at least one element g in this set such that g has an improved cost value as compared to we describe a unique minimal test set for this family called the reduced grobner basis of ip a c an algorithm for its construction is presented which we call a geometric buchberger algorithm for integer programming and we show how an integer program may be solved using this test set the reduced grobner basis is then compared with some other known test sets from the literature we also indicate an easy procedure to construct test sets with respect to all cost functions for a matrix a zn 2 n of full row rank

iis branch and cut for joint chance constrained stochastic programs and application to optimal vaccine allocation we present a new method for solving stochastic programs with joint chance constraints with random technology matrices and discretely distributed random data the problem can be reformulated as a large scale mixed 0 1 integer program we derive a new class of optimality cuts called iis cuts and apply them to our problem the cuts are based on irreducibly infeasible subsystems iis of an lp defined by requiring that all scenarios be satisfied we propose a method for improving the upper bound of the problem when no cut can be found we derive and implement a branch and cut algorithm based on iis cuts and refer to this algorithm as the iis branch and cut algorithm we report on computational results with several test instances from optimal vaccine allocation the computational results are promising as the iis branch and cut algorithm gives better results than a state of the art commercial solver on one class of problems

testing a point null hypothesis the irreconcilability of p values and evidence abstract the problem of testing a point null hypothesis or a small interval null hypothesis is considered of interest is the relationship between the p value or observed significance level and conditional and bayesian measures of evidence against the null hypothesis although one might presume that a small p value indicates the presence of strong evidence against the null such is not necessarily the case expanding on earlier work especially edwards lindman and savage 1963 and dickey 1977 it is shown that actual evidence against a null as measured say by posterior probability or comparative likelihood can differ by an order of magnitude from the p value for instance data that yield a p value of 05 when testing a normal mean result in a posterior probability of the null of at least 30 for any objective prior distribution objective here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null other definiti

bayes factors for outlier models using the device of imaginary observations abstract suppose we think that most observations in a sample have been generated from a distribution with density f x but we fear that a few outliers from a distribution with density g x may have contaminated our sample in many situations we might assume that f x is a density depending on a parameter and that g x is of the same form as f but with parameter or a number of bayesian models for this problem when f is normal have been discussed by freeman he points out that with a vague improper prior for contaminating parameters most posterior weight is put on the model allowing for the largest number of outliers he therefore confines attention to proper priors when trying to answer the question of how many outliers however in many situations we do not have very certain information on the contaminating parameters and would like to make inferences about outliers when using improper priors for the parameters of the model in this article we apply the ideas of spiegelhalter and smith to

testing and modeling threshold autoregressive processes abstract the threshold autoregressive model is one of the nonlinear time series models available in the literature it was first proposed by tong 1978 and discussed in detail by tong and lim 1980 and tong 1983 the major features of this class of models are limit cycles amplitude dependent frequencies and jump phenomena much of the original motivation of the model is concerned with limit cycles of a cyclical time series and indeed the model is capable of producing asymmetric limit cycles the threshold autoregressive model however has not received much attention in application this is due to a the lack of a suitable modeling procedure and b the inability to identify the threshold variable and estimate the threshold values the primary goal of this article therefore is to suggest a simple yet widely applicable model building procedure for threshold autoregressive models based on some predictive residuals a simple statistic is proposed to test for threshold nonlinearity and specify the

bayesian inference and prediction for mean and variance shifts in autoregressive time series abstract this article is concerned with statistical inference and prediction of mean and variance changes in an autoregressive time series we first extend the analysis of random mean shift models to random variance shift models we then consider a method for predicting when a shift is about to occur this involves appending to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables the basic computational tool we use in the proposed analysis is the gibbs sampler for illustration we apply the analysis to several examples

local existence of strong solution for a class of compressible non newtonian fluids with non newtonian potential the aim of this paper is to discuss the existence and uniqueness of local solutions for a class of isentropic compressible non newtonian fluids with non newtonian potential in one dimensional bounded intervals the first difficult point in this paper is that we allow the initial vacuum another one is that the viscosity term and newtonian potential term are fully nonlinear that is the viscosity term adopts the o a ladyzhenskaya model p 2 the potential term employs the q laplace form 1

estimating and testing linear models with multiple structural changes this paper develops the statistical theory for testing and estimating multiple change points in regression models the rate of convergence and limiting distribution for the estimated parameters are obtained several test statistics are proposed to determine the existence as well as the number of change points a partial structural change model is considered the authors study both fixed and shrinking magnitudes of shifts in addition the models allow for serially correlated disturbances mixingales an estimation strategy for which the location of the breaks need not be simultaneously determined is discussed instead the authors method successively estimates each break point

fractional bayes factors for model comparison bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves however there are difficulties with this approach when prior information about the parameters of the various models is weak partial bayes factors offer a resoiution of the problem by setting aside part of the data as a training sampie the training sampie is used to obtain an initiai informative posterior distribution of the parameters in each model model comparison is then based on a bayes factor calculated from the remaining data properties of partial bayes factors are discussed particularly in the context of weak prior information and they are found to have advantages over other proposed methods of model comparison a new variant of the partial bayes factor the fractional bayes factor is advocated on grounds of consistency simplicity robustness and coherence

estimation and comparison of multiple change point models this paper provides a new bayesian approach for models with multiple change points the centerpiece of the approach is a formulation of the change point model in terms of a latent discrete state variable that indicates the regime from which a particular observation has been drawn this state variable is specified to evolve according to a discrete time discrete state markov process with the transition probabilities constrained so that the state variable can either stay at the current value or jump to the next higher value this parameterization exactly reproduces the change point model the model is estimated by markov chain monte carlo methods using an approach that is based on chib 1996 this methodology is quite valuable since it allows for the fitting of more complex change point models than was possible before methods for the computation of bayes factors are also developed all the techniques are illustrated using simulated and real data sets

solving stochastic programs with integer recourse by enumeration a framework using gro bner basis reductions in this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right hand side vector using grobner basis methods from computational algebra to solve the numerous second stage integer programs using structural properties of the expected integer recourse function we prove that under mild conditions an optimal solution is contained in a finite set furthermore we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed

efficient bayesian inference for dynamic mixture models abstract a bayesian approach is presented for estimating a mixture of linear gaussian state space models such models are used to model interventions in time series and nonparametric regression markov chain monte carlo sampling is usually necessary to obtain the posterior distributions of such mixture models because it is difficult to obtain them analytically the methodological contribution of the article is to derive a set of recursions for dynamic mixture models that efficiently implement a markov chain monte carlo sampling scheme that converges rapidly to the posterior distribution the methodology is illustrated by fitting an autoregressive model subject to interventions to zinc concentration in sludge

global existence for compressible navier stokes poisson equations in three and higher dimensions the compressible navier stokes poisson system is concerned in the present paper and the global existence and uniqueness of the strong solution is shown in the framework of hybrid besov spaces in three and higher dimensions

a strong solution for a class of compressible full non newtonian models abstract the aim of this paper is to discuss the existence and uniqueness of a local solution for a class of isentropic compressible full non newtonian models in one dimensional bounded intervals the first important point in this paper is that we allow the initial vacuum another one is that the viscosity term and the newtonian potential term are fully nonlinear

solving stochastic programs with integer recourse by enumeration a framework using grobner basis in this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right hand side vector using grobner basis methods from computational algebra to solve the numerous second stage integer programs using structural properties of the expected integer recourse function we prove that under mild conditions an optimal solution is contained in a finite set furthermore we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed

bayesian analysis of a poisson process with a change point summary a bayesian approach to estimation and hypothesis testing for a poisson process with a change point is developed and an example given

the signal extraction approach to nonlinear regression and spline smoothing abstract this article shows how to fit a smooth curve polynomial spline to pairs of data values yi xi prior specification of a parametric functional form for the curve is not required the resulting curve can be used to describe the pattern of the data and to predict unknown values of y given x both point and interval estimates are produced the method is easy to use and the computational requirements are modest even for large sample sizes our method is based on maximum likelihood estimation of a signal in noise model of the data we use the kalman filter to evaluate the likelihood function and achieve significant computational advantages over previous approaches to this problem

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

bayesianly justifiable and relevant frequency calculations for the applied statistician a common reaction among applied statisticians is that the bayesian statistician s energies in an applied problem must be directed at the a priori elicitation of one model specification from which an optimal design and all inferences follow automatically by applying bayes s theorem to calculate conditional distributions of unknowns given knowns i feel however that the applied bayesian statistician s tool kit should be more extensive and include tools that may be usefully labeled frequency calculations three types of bayesianly justifiable and relevant frequency calculations are presented using examples to convey their use for the applied statistician

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

a parametric approach to flexible nonlinear inference author s hamilton james d abstract this paper proposes a new framework for determining whether a given relationship is nonlinear what the nonlinearity looks like and whether it is adequately described by a particular parametric model the paper studies a regression or forecasting model of the form yt xt et where the functional form of is unknown we propose viewing itself as the outcome of a random process the paper introduces a new stationary random random field m that generalizes finite differenced brownian motion to a vector field and whose realizations could represent a broad class of possible forms for we view the parameters that characterize the relation between a given realization of m and the particular value of for a given sample as population parameters to be estimated by maximum likelihood or bayesian methods we show that the resulting inference about the functional relation also yields consistent estimates for a broad class of deterministic functions the paper further develops a new test of the null hypothesis of linearity based on the lagrange multiplier principle and small sample confidence intervals based on numerical bayesian methods an empirical application suggests that properly accounting for the nonlinearity of the inflation unemployment tradeoff may explain the previously reported uneven empirical success of the phillips curve

bayesian variants of some classical semiparametric regression techniques abstract this paper develops new bayesian methods for semiparametric inference in the partial linear normal regression model y z f x e where f is an unknown function these methods draw solely on the normal linear regression model with natural conjugate prior hence posterior results are available which do not suffer from some problems which plague the existing literature such as computational complexity methods for testing parametric regression models against semiparametric alternatives are developed we discuss how these methods can at some cost in terms of computational complexity be extended to other models e g qualitative choice models or those involving censoring or truncation and provide precise details for a semiparametric probit model we show how the assumption of normal errors can easily be relaxed

bayesian model choice asymptotics and exact calculations abstract model determination is a fundamental data analytic task here we consider the problem of choosing amongst a finite with loss of generality we assume two set of models after briefly reviewing classical and bayesian model choice strategies we present a general predictive density which includes all proposed bayesian approaches we are aware of using laplace approximations we can conveniently assess and compare asymptotic behavior of these approaches concern regarding the accuracy of these approximation for small to moderate sample sizes encourages the use of monte carlo techniques to carry out exact calculations a data set fit with nested non linear models enables comparison between proposals and between exact and asymptotic values

an algebraic geometry algorithm for scheduling in presence of setups and correlated demands we study here a problem of schedulingn job types onm parallel machines when setups are required and the demands for the products are correlated random variables we model this problem as a chance constrained integer program

uniform boundedness of the solutions for a one dimensional isentropic model system of compressible viscous gas this paper studies an initial boundary value problem for a one dimensional isentropic model system of compressible viscous gas with large external forces represented by v t u x 0 u t av x u x v x f 0 vdx t with v x 0 u x 0 v 0 x u 0 x u 0 t u 1 t 0 especially the uniform boundedness of the solution in time is investigated it is proved that for arbitrary large initial data and external forces the problem uniquely has an uniformly bounded global in time solution with also uniformly positive mass density provided the adiabatic constant 1 is suitably close to 1 the proof is based on l 2 energy estimates and a technique used in 9

global behavior of spherically symmetric navier stokes poisson system with degenerate viscosity coefficients in this paper we study a free boundary problem for compressible spherically symmetric navier stokes poisson equations with degenerate viscosity coefficients and without a solid core under certain assumptions that are imposed on the initial data we obtain the global existence and uniqueness of the weak solution and give some uniform bounds with respect to time of the solution moreover we obtain some stabilization rate estimates of the solution the results show that such a system is stable under small perturbations and could be applied to the astrophysics

calculating posterior distributions and modal estimates in markov mixture models abstract this paper is concerned with finite mixture models in which the populations from one observation to the next are selected according to an unobserved markov process a new full bayesian approach based on the method of gibbs sampling is developed calculations are simplified by data augmentation achieved by introducing a population index variable into the list of unknown parameters it is shown that the latent variables one for each observation can be simulated from their joint distribution given the data and the remaining parameters this result serves to accelerate the convergence of the gibbs sample modal estimates are also computed by stochastic versions of the em algorithm these provide an alternative to a full bayesian approach and to existing methods of locating the maximum likelihood estimate the ideas are applied in detail to poisson data mixtures of multivariate normal distributions and autoregressive time series

segmenting mean nonstationary time series via trending regressions abstract in this paper we provide a segmentation procedure for mean nonstationary time series the segmentation is obtained by casting the problem into the framework of detecting structural breaks in trending regression models in which the regressors are generated by suitably smooth functions as test statistics we propose to use the maximally selected likelihood ratio statistics and a related statistics based on partial sums of weighted residuals the main theoretical contribution of the paper establishes the extreme value distribution of these statistics and their consistency to circumvent the slow convergence to the extreme value limit we propose to employ a version of the circular bootstrap this procedure is completely data driven and does not require knowledge of the time series structure in an empirical part we show in a simulation study and applications to air carrier traffic and s p 500 data that the finite sample performance is very satisfactory