bayesian analysis of mixture models with an unknown number of components an alternative to reversible jump methods richardson and green present a method of performing a bayesian analysis of data from a finite mixture distribution with an unknown number of components their method is a markov chain monte carlo mcmc approach which makes use of the reversible jump methodology described by green we describe an alternative mcmc method which views the parameters of the model as a marked point process extending methods suggested by ripley to create a markov birth death process with an appropriate stationary distribution our method is easy to implement even in the case of data in more than one dimension and we illustrate it on both univariate and bivariate data there appears to be considerable potential for applying these ideas to other contexts as an alternative to more general reversible jump methods and we conclude with a brief discussion of how this might be achieved

modeling schizophrenic behavior using general mixture components this article proposes a novel and general mixture component model the features of which include a hierarchical structure with random effects mixture components characterized by anova like linear regressions and mixing mechanisms governed by logistic regressions the model was developed as a consequence of attending to long standing psychological theory about schizophrenic behavior scientifically revealing results are obtained by fitting the model to a data set concerning nonschizophrenic and schizophrenic eye tracking behavior under different conditions included are descriptions of the algorithms for model fitting specifically the ecm secm algorithms for large sample modal inference and the gibbs sampler for simulating the posterior distribution for guidance on model comparison and selection we use posterior predictive check distributions to obtain posterior predictive p values for likelihood ratio statistics which do not have asymptotic chi 2 reference distributions these posterior predictive p values suggest that all the mixture components in our model are necessary the final model is selected using a combination of scientific parsimony the posterior predictive p values and the posterior distributions of relevant parameters

the dirichlet cauchy problem for nonlinear hyperbolic equations in a domain with edges abstract we study the dirichlet cauchy problem for nonlinear hyperbolic equation of second order in a domain with edges the aim of this paper is to prove the regularity of solution in weighted sobolev spaces

existence of the global solution for fractional logarithmic schrodinger equation abstract in this paper we consider the initial boundary value problem for a class of fractional logarithmic schrodinger equation by using the fractional logarithmic sobolev inequality and introducing a family of potential wells we give some properties of the family of potential wells and obtain existence of global solution

a quasi monte carlo approach to particle simulation of the heat equation the convergence of the monte carlo method for numerical integration can often be improved by replacing random numbers with more uniformly distributed numbers known as quasi random in this paper the convergence of monte carlo particle simulation is studied when these quasi random sequences are used for the one dimensional heat equation discretized in both space and time convergence is proved for a quasi random simulation using reordering of the particles according to their position experimental results are presented for the spatially continuous heat equation in one and two dimensions the results indicate that a significant improvement in both magnitude of error and convergence rate can be achieved over standard monte carlo simulations for certain low dimensional problems

existence of a solution of the wave equation with nonlinear damping and source terms abstract we study the nonlinear wave equation involving the nonlinear damping term u t u t m 1 and a source term of type u u p 1 for 1 p m we prove a global existence theorem with large initial data for 1 m p a blow up result is established for sufficiently large initial data

global existence and blow up of solutions for cauchy problem of generalized boussinesq equation abstract we study the cauchy problem of generalized boussinesq equation u t t u x x u x x f u x x 0 where f u u p or u p 1 u p 1 by introducing a family of potential wells we obtain invariant sets vacuum isolating and threshold result of global existence and nonexistence of solution

bayesian inference for finite mixtures of generalized linear models with random effects we present an hierarchical bayes approach to modeling parameter heterogeneity in generalized linear models the model assumes that there are relevant subpopulations and that within each subpopulation the individual level regression coefficients have a multivariate normal distribution however class membership is not known a priori so the heterogeneity in the regression coefficients becomes a finite mixture of normal distributions this approach combines the flexibility of semiparametric latent class models that assume common parameters for each sub population and the parsimony of random effects models that assume normal distributions for the regression parameters the number of subpopulations is selected to maximize the posterior probability of the model being true simulations are presented which document the performance of the methodology for synthetic data with known heterogeneity and number of sub populations an application is presented concerning preferences for various aspects of personal computers

hierarchical poisson regression modeling abstract the poisson model and analyses here feature nonexchangeable gamma distributions although exchangeable following a scale transformation for individual parameters with standard deviations proportional to means a relatively uninformative prior distribution for the shrinkage values eliminates the ill behavior of maximum likelihood estimators of the variance components when tested in simulation studies the resulting procedure provides better coverage probabilities and smaller risk than several other published rules and thus works well from bayesian and frequentist perspectives alike the computations provide fast accurate density approximations to individual parameters and to structural regression coefficients the computer program is publicly available through statlib

a boundary condition with memory for kirchhoff plates equations in this paper we study the stability of solutions for kirchhoff plates equations with a memory condition working at the boundary we show that such dissipation is strong enough to produce exponential decay to the solution provided the relaxation functions also decays exponentially when the relaxation functions decays polynomially we show that the solution decays polynomially and with the same rate

a score test for zero inflation in a poisson distribution when analyzing poisson count data sometimes a lot of zeros are observed when there are too many zeros a zero inflated poisson distribution can be used a score test is presented to test whether the number of zeros is too large for a poisson distribution to fit the data well

simulation of stochastic reaction diffusion processes on unstructured meshes we model stochastic chemical systems with diffusion by a reaction diffusion master equation on a macroscopic level the governing equation is a reaction diffusion equation for the averages of the chemical species on a mesoscopic level the master equation for a well stirred chemical system is combined with a discretized brownian motion in space to obtain the reaction diffusion master equation the space is covered in our method by an unstructured mesh and the diffusion coefficients on the mesoscale are obtained from a finite element discretization of the laplace operator on the macroscale the resulting method is a flexible hybrid algorithm in that the diffusion can be handled either on the meso or on the macroscale level the accuracy and the efficiency of the method are illustrated in three numerical examples inspired by molecular biology

zero inflated poisson regression with an application to defects in manufacturing zero inflated poisson zip regression is a model for count data with excess zeros it assumes that with probability p the only possible observation is 0 and with probability 1 p a poisson random variable is observed for example when manufacturing equipment is properly aligned defects may be nearly impossible but when it is misaligned defects may occur according to a poisson distribution both the probability p of the perfect zero defect state and the mean number of defects in the imperfect state may depend on covariates sometimes p and are unrelated other times p is a simple function of such as p l 1 t for an unknown constant t in either case zip regression models are easy to fit the maximum likelihood estimates mle s are approximately normal in large samples and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the mle s simulations suggest that the confidence intervals based on likelihood ratio test

global well posedness of solutions for fourth order dispersive wave equation with nonlinear weak damping linear strong damping and logarithmic nonlinearity abstract to understand the characteristics of dynamical behavior especially the kinetic evolution for logarithmic nonlinearity we aim to study the global well posedness of nonlinear fourth order wave equations with logarithmic source term where the dispersive the nonlinear weak damping and linear strong damping are taken into account based on the potential well method the main ingredient of this paper is to construct several conditions for initial data leading to the solution global existence or infinite time blow up with subcritical initial energy moreover we extend the results to the critical initial energy which is realized by introducing scaling technique finally surrounding the blow up at arbitrarily high initial energy we compare and discuss the research program stemming from two different strategies in the first one it is assumed that the blow up result is bound to the original logarithmic source by weakening the dispersive dissipative structure while the second one is based on the nonlinear wave equation with complete dispersive dissipative structure but the logarithmic source is replaced by an enhanced version through these two strategies we explain the mechanism of these two structures respectively and establish two kinds of sufficient conditions for initial data leading to high energy blow up

second harmonics effects in random duffing oscillators we consider a stochastic model for duffing oscillators where the nonlinearity and the randomness are scaled in such a way that they interact strongly a typical feature is the appearance of second harmonics effects an asymptotic statistical analysis for these oscillators is performed in the diffusion limit when a suitable absorbing boundary condition is imposed according to the underlying physical problem the related fokker planck equation has been numerically solved to obtain the first two moments of the oscillator s displacement from its rest position dependence on the nonlinearity strength and on the location of the absorbing boundary has also been investigated such results have been compared with those computed solving the corresponding stochastic ito differential equations by a monte carlo method where quasi random sequences of numbers have been efficiently used

a quasi monte carlo scheme using nets for a linear boltzmann equation a quasi monte carlo particle simulation for solving a linear boltzmann equation is constructed and a convergence proof is given the analysis is restricted to the three dimensional equation in the space homogeneous case and the velocity domain is normalized to be i 3 0 1 3 a particle simulation is described it combines a euler scheme in time with quasi monte carlo integration in velocity space the quadratures use 0 m s nets which are sets with a very regular distribution behavior the particles are reordered according to the components of their velocity at each time step a deterministic error bound is obtained finally numerical experiments are presented for some test problems where an exact solution is known the accuracy of the quasi monte carlo scheme is compared with a standard monte carlo algorithm the results show an improvement in both magnitude of error and convergence rate of quasi monte carlo over monte carlo approach

global existence and blow up of solution for semilinear hyperbolic equation with logarithmic nonlinearity abstract in this paper we consider the semilinear wave equation with logarithmic nonlinearity by modifying and using potential well combined with logarithmic sobolev inequality we derive the global existence and infinite time blow up of the solution at low energy level e 0 d then these results are extended in parallel to the critical case e 0 d besides with additional assumptions on initial data the infinite time blow up result is given with arbitrary positive initial energy e 0 0

fast simulations of stochastic dynamical systems a number of features relevant to stochastic dynamical systems such as moments of solutions and first passage times can be efficiently computed resorting to sequences of quasi random numbers low discrepancy sequences this method represents an alternative choice to the use of pseudorandom numbers provided that a special care is paid to keep sufficiently uncorrelated as well as uniform the former sequences

global solution and blow up of a semilinear heat equation with logarithmic nonlinearity abstract we study the initial boundary value problem of a semilinear heat equation with logarithmic nonlinearity by using the logarithmic sobolev inequality and a family of potential wells we obtain the existence of global solution and blow up at under some suitable conditions on the other hand the results for decay estimates of the global solutions are also given our result in this paper means that the polynomial nonlinearity is a critical condition of blow up in finite time for the solutions of semilinear heat equations

testing goodness of fit for the poisson assumption when observations are not identically distributed abstract tests for detecting negative binomial departures from a poisson model are studied for the one way layout and regression through the origin cases approximations to the null and alternative distributions of these test statistics are presented locally optimal tests and tests suggested in the literature are compared in terms of asymptotic relative efficiency small sample comparisons are included

low discrepancy sequences for solving the boltzmann equation abstract some new quasi monte carlo methods for the solution of the boltzmann equation in a simplified case are described the errors of the methods are estimated by means of the discrepancies of the sequences used for performing the monte carlo quadratures their accuracy is assessed through computation of effective errors in an example where an exact solution is known

probabilistically induced domain decomposition methods for elliptic boundary value problems monte carlo as well as quasi monte carlo methods are used to generate only few interfacial values in two dimensional domains where boundary value elliptic problems are formulated this allows for a domain decomposition of the domain a continuous approximation of the solution is obtained interpolating on such interfaces and then used as boundary data to split the original problem into fully decoupled subproblems the numerical treatment can then be continued implementing any deterministic algorithm on each subdomain both monte carlo or quasi monte carlo simulations and the domain decomposition strategy allow for exploiting parallel architectures scalability and natural fault tolerance are peculiarities of the present algorithm examples concern helmholtz and poisson equations whose probabilistic treatment presents additional complications with respect to the case of homogeneous elliptic problems without any potential term and source

domain decomposition solution of elliptic boundary value problems via monte carlo and quasi monte carlo methods domain decomposition of two dimensional domains on which boundary value elliptic problems are formulated is accomplished by probabilistic monte carlo as well as by quasi monte carlo methods generating only a few interfacial values and interpolating on them continuous approximations for the trace of solution are thus obtained to be used as boundary data for the subproblems the numerical treatment can then proceed by standard deterministic algorithms separately in each of the so obtained subdomains monte carlo and quasi monte carlo simulations may naturally exploit multiprocessor architectures leading to parallel computing as well as the ensuing domain decomposition does the advantages such as scalability obtained by increasing the number of processors are shown both theoretically and experimentally in a number of test examples and the possibility of using clusters of computers grid computing is emphasized

average case complexity of multivariate integration we study the average case complexity of multivariate integration for the class of continuous functions of d variables equipped with the classical wiener sheet measure to derive the average case complexity one needs to obtain optimal sample points we prove that optimal design is closely related to discrepancy theory which has been extensively studied for many years this relation enables us to show that optimal sample points can be derived from hammersley points extending the result of roth and using the recent result of wasilkowski we conclude that the average case complexity is e 1 lne 1 d 1 2

global existence and nonexistence in a system of petrovsky in this paper we consider the nonlinearly damped semilinear petrovsky equationutt 2u aut ut m 2 bu u p 2in a bounded domain where a b 0 we prove the existence of a local weak solution and show that this solution blows up in finite time if p m and the energy is negative we also show that the solution is global if m p

on potential wells and vacuum isolating of solutions for semilinear wave equations abstract in this paper we study the initial boundary value problem of semilinear wave equations u tt u u p 1 u x t 0 u x 0 u 0 x u t x 0 u 1 x x u x t 0 x t 0 where r n is a bounded domain 1 1 n 2 n 2 for n 3 first by using a new method we introduce a family of potential wells which include the known potential well as a special case then by using it we obtain some new existence theorems of global solutions and prove that for any e 0 d d is the depth of the known potential well all solutions with initial energy e 0 satisfying 0 h 0 1

a particle method for some parabolic equations abstract we present a quasi monte carlo particle simulation of some multidimensional linear parabolic equations with constant coefficients we approximate the elliptic operator in space by a finite difference operator we discretize time into intervals of length t the discrete representation of the solution at time t n n t is a sum of dirac delta measures using the explicit euler scheme the resulting approximation at time t n 1 is recovered by a quasi monte carlo integration we make use of a technique involving renumbering the simulated particles in every time step we state and prove a convergence theorem for the method experimental results are presented for some model problems the results suggest that the quasi monte carlo simulation tends to give more accurate solutions than a monte carlo simulation when the correct renumbering technique is used other choices can result in significant loss of efficiency

invariance and existence analysis for semilinear hyperbolic equations with damping and conical singularity abstract in this paper we will discuss about the invariance of solution set and present the existence and non existence of the global solutions a class of initial boundary value problems with dissipative terms is considered for a class of semilinear degenerate hyperbolic equations on the cone sobolev spaces first we will discuss the invariance of some sets corresponding to the problem 1 1 and then by using a family of potential wells and concavity methods we obtain existence and non existence results of global solutions with exponential decay and show the blow up in finite time of solutions on a manifold with conical singularities

exponential decay rates for the solutions of euler bernoulli equations with boundary dissipation occurring in the moments only abstract we shall derive uniform decay rates for the total energy of the solutions to the euler bernoulli equations wherein energy dissipation occurs on the boundary the main feature which distinguishes this paper from other related works is the fact that the boundary feedback is acting through the moments only the key technical element responsible for the proof of the main result is a new regularity estimate for the solutions to the nonhomogeneous schrodinger equation

a score test for overdispersion in zero inflated poisson mixed regression model count data with extra zeros are common in many medical applications the zero inflated poisson zip regression model is useful to analyse such data for hierarchical or correlated count data where the observations are either clustered or represent repeated outcomes from individual subjects a class of zip mixed regression models may be appropriate however the zip parameter estimates can be severely biased if the non zero counts are overdispersed in relation to the poisson distribution in this paper a score test is proposed for testing the zip mixed regression model against the zero inflated negative binomial alternative sampling distribution and power of the test statistic are evaluated by simulation studies the results show that the test statistic performs satisfactorily under a wide range of conditions the test procedure is applied to pancreas disorder length of stay that comprised mainly same day separations and simultaneous prolonged hospitalizations

on potential wells and applications to semilinear hyperbolic equations and parabolic equations abstract in this paper we generalize the family of potential wells to the initial boundary value problem of semilinear hyperbolic equations and parabolic equations u tt u f u x t 0 u x 0 u 0 x u t x 0 u 1 x x u x t 0 x t 0 and u t u f u x t 0 u x 0 u 0 x x u x t 0 x t 0 not only give a threshold result of global existence and nonexistence of solutions but also obtain the vacuum isolating of solutions finally we prove the global existence of solutions for above problem with critical initial conditions i u 0 0 e 0 d or i u 0 0 j u 0 d so payne and sattinger s results are generalized and improved in essential

the analysis of repeated measures data on schizophrenic reaction times using mixture models reaction times for schizophrenic individuals in a simple visual tracking experiment can be substantially more variable than for non schizophrenic individuals current psychological theory suggests that at least some of this extra variability arises from an attentional lapse that delays some but not all of each schizophrenic s reaction times based on this theory we pursue models in which measurements from non schizophrenics arise from a normal linear model with a separate mean for each individual whereas measurements from schizophrenics arise from a mixture of i a component analogous to the distribution of response times for non schizophrenics and ii a mean shifted component we fit four mixture models within this framework where the distinctions between models arise from assumptions about the variance of the shifted observations and the exchangeability of schizophrenic individuals some of these models can be fit by maximum likelihood using the em algorithm and all can be fit using the ecm algorithm where the covariance matrices associated with the parameters are calculated by the sem and secm algorithms respectively bayesian model monitoring using posterior predictive checks is invoked to discard models that fail to reproduce certain observed features of the data and to stimulate the development of better models

generating quasi random paths for stochastic processes the need to simulate stochastic processes numerically arises in many fields frequently this is done by discretizing the process into small time steps and applying pseudorandom sequences to simulate the randomness this paper addresses the question of how to use quasi monte carlo methods to improve this simulation special techniques must be applied to avoid the problem of high dimensionality which arises when a large number of time steps is required two such techniques the generalized brownian bridge and particle reordering are described here these methods are applied to a problem from finance the valuation of a 30 year bond with monthly coupon payments assuming a mean reverting stochastic interest rate when expressed as an integral this problem is nominally 360 dimensional the analysis of the integrand presented here explains the effectiveness of the quasi random sequences on this high dimensional problem and suggests methods of variance reduction which can be used in conjunction with the quasi random sequences

multidimensional viscoelasticity equations with nonlinear damping and source terms abstract in this paper we study the initial boundary value problem of multidimensional viscoelasticity equations u tt u t i 1 n x i i u x i f u t g u x t 0 u x 0 u 0 x u t x 0 u 1 x x u x t 0 x t 0 where r n is a bounded domain i s1 i s2 s1 s2 0 f s s 0 g s s 0 and satisfy some growth conditions first we introduce a family of potential wells by using a new method then using it we obtain some new existence theorems of global solutions and behaviour of vacuum isolation of solutions

error bounds for quasi monte carlo integration with nets we analyze the error introduced by approximately calculating the s dimensional lebesgue measure of a jordan measurable subset of i s 0 1 s we give an upper bound for the error of a method using a t m s net which is a set with a very regular distribution behavior when the subset of i s is defined by some function of bounded variation on i s 1 the error is estimated by means of the variation of the function and the discrepancy of the point set which is used a sharper error bound is established when a t m s net is used finally a lower bound of the error is given for a method using a 0 m s net the special case of the 2 dimensional hammersley point set is discussed

on family of potential wells and applications to semilinear hyperbolic equations and parabolic equations abstract we study the initial boundary value problem for semilinear hyperbolic equations and parabolic equations with convex function nonlinear terms by introducing a family of potential wells we not only obtain the invariant sets and vacuum isolation of solutions but also give a threshold result of global existence and nonexistence of solutions moreover we discuss the global existence of solution for problem with critical initial condition e 0 d or j u 0 d which fills some important gaps regarding this problem finally we prove the global nonexistence of solution and asymptotic behavior of solution for semilinear parabolic equations

hyperbolic and parabolic equations with several opposite sign source at critical initial energy level in heat and vibrating systems abstract we study semilinear hyperbolic equations and parabolic equations with several opposite sign source terms under the dirichlet boundary condition in heat and vibrating systems for the above problems we prove the global nonexistence of solution and give the sharp conditions at critical energy level furthermore we prove that the existence of global solution of parabolic equation vanishes to zero as time goes to infinity which is different from the behavior of solution of the hyperbolic equation

particle simulations of the kac model of the boltzmann equation abstract we consider a simplified mathematical model of the boltzmann equation which was introduced by kac a quasi monte carlo particle simulation using t m s nets is described the particle movement is shown to be an evaluation of the volume of a subset of i4 0 1 4 an error bound for quasi monte carlo approximation of the volume of a generalized quadrant set is derived when a t m s net is used convergence of the simulation is proved when the particles are reordered according to their velocity in every time step quasi monte carlo and monte carlo particle simulations are compared in computational experiments the results indicate that quasi monte carlo simulation outperforms standard monte carlo approaches

concomitant variable latent class models abstract this article introduces and illustrates a new type of latent class model in which the probability of latent class membership is functionally related to concomitant variables with known distribution the function or so called submodel may be logistic exponential or another suitable form concomitant variable models supplement latent class models incorporating grouping by providing more parsimonious representations of data for some cases also concomitant variable models are useful when grouping models involve a greater number of parameters than can be meaningfully fit to existing data sets although parameter estimates may be calculated using standard iterative procedures such as the newton raphson method sample analyses presented here employ a derivative free approach known as the simplex method a general procedure for imposing linear constraints on the parameter estimates is introduced a data set involving arithmetic test items in a mastery testing context is used to illustrate fitting a

the existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term abstract in this paper we consider a plate equation with a logarithmic nonlinearity in the presence of a frictional damping we prove for a suitably chosen initial data a global existence as well as a decay result

optimization of a large scale water reservoir network by stochastic dynamic programming with efficient state space discretization a numerical solution to a 30 dimensional water reservoir network optimization problem based on stochastic dynamic programming is presented in such problems the amount of water to be released from each reservoir is chosen to minimize a nonlinear cost or maximize benefit function while satisfying proper constraints experimental results show how dimensionality issues given by the large number of basins and realistic modeling of the stochastic inflows can be mitigated by employing neural approximators for the value functions and efficient discretizations of the state space such as orthogonal arrays latin hypercube designs and low discrepancy sequences

global nonexistence for a semilinear petrovsky equation abstract in this paper we consider a semilinear petrovsky equation with damping and source terms it is proved that the solution blows up in finite time if the positive initial energy satisfies a suitable condition moreover for the linear damping case we show that the solution blows up in finite time even for vanishing initial energy this is an important breakthrough since it is only well known that the solution blows up in finite time if the initial energy is negative from all the previous literature

on potential wells to a semilinear hyperbolic equation with damping and conical singularity abstract this article deals with a semilinear hyperbolic equation with damping and conical singularity that was built by alimohammady et al 2017 1 where the weak solution with low initial energy i 0 d d is the potential well depth was considered we extend the previous results in the following three aspects firstly we consider the vacuum isolating behavior of the solution for initial energy i 0 0 and 0 i 0 d respectively we find that there are two explicit vacuum regions an annulus and a ball moreover we obtain the asymptotic behavior of the energy functional as t tends to the maximal existence time and then two necessary and sufficient conditions for the weak solution existing globally and blowing up in finite time are obtained secondly we discuss the weak solution with critical initial energy and establish the global existence and nonexistence results finally the weak solution with arbitrary positive initial energy is studied in this case the initial conditions such that the weak solution exists globally and blows up in finite time are given

global existence and nonexistence of the initial boundary value problem for the dissipative boussinesq equation abstract a class of multidimensional dissipative boussinesq equations is considered under three different cases of initial energy we prove the existence and uniqueness of global solutions in the energy space and provide sufficient conditions of finite time blow up solutions the sharp result is given as e 0 d particular attention is paid to initial energy at supercritical initial energy e 0 d level which is novel contribution of this paper and new methods will be introduced and some analysis techniques are needed in addition the asymptotic behavior of the global solutions is studied

fourth order wave equations with nonlinear strain and source terms abstract in this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms first we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions then we obtain a threshold result of global existence and nonexistence finally we discuss the global existence of solutions for the problem with critical initial condition i u 0 0 e 0 d so the esquivel avila s results are generalized and improved

potential well method for cauchy problem of generalized double dispersion equations abstract in this paper we study cauchy problem of generalized double dispersion equations u t t u x x u x x t t u x x x x f u x x where f u u p p 1 or u 2 k k 1 2 by introducing a family of potential wells we not only get a threshold result of global existence and nonexistence of solutions but also obtain the invariance of some sets and vacuum isolating of solutions in addition the global existence and finite time blow up of solutions for problem with critical initial conditions e 0 d i u 0 0 or i u 0 0 are proved

global existence blow up and extinction for a class of thin film equation abstract in this paper we use the modified method of potential wells to study the properties of solutions for a class of higher order nonlinear parabolic equations with p laplace term u x p 2 u x x and nonlocal source u q 1 u 1 u q 1 u d x global existence uniqueness blow up in finite time and asymptotic behavior of solutions will be proved under different initial conditions furthermore a numerical example is given to illustrate the blow up of solutions in finite time

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

a comparative study of pseudo and quasi random sequences for the solution intergral equations a numerical study for the solution of integral equations using random numbers from congruential generators and the halton and the faure sequences is presented the results indicate that for high precision monte carlo quasi random sequences yield better results in general the relative performance of the quasi random sequences is better with monte carlo schemes which reduce the dimensionality of the problem

decay estimates for second order evolution equations with memory abstract this paper develops a unified method to derive decay estimates for general second order integro differential evolution equations with semilinear source terms depending on the properties of convolution kernels at infinity we show that the energy of a mild solution decays exponentially or polynomially as t our approach is based on integral inequalities and multiplier techniques these decay results can be applied to various partial differential equations we discuss three examples a semilinear viscoelastic wave equation a linear anisotropic elasticity model and a petrovsky type system

a hierarchical finite mixture model that accommodates zero inflated counts non independence and heterogeneity a number of mixture modeling approaches assume both normality and independent observations however these two assumptions are at odds with the reality of many data sets which are often characterized by an abundance of zero valued or highly skewed observations as well as observations from biologically related i e non independent subjects we present here a finite mixture model with a zero inflated poisson regression component that may be applied to both types of data this flexible approach allows the use of covariates to model both the poisson mean and rate of zero inflation and can incorporate random effects to accommodate non independent observations we demonstrate the utility of this approach by applying these models to a candidate endophenotype for schizophrenia but the same methods are applicable to other types of data characterized by zero inflation and non independence

quasi random sequences and their discrepancies quasi random also called low discrepancy sequences are a deterministic alternative to random sequences for use in monte carlo methods such as integration and particle simulations of transport processes the error in uniformity for such a sequence of n points in the s dimensional unit cube is measured by its discrepancy which is of size log n s n 1 for large n as opposed to discrepancy of size log log n 1 2 n 1 2 for a random sequence i e for almost any randomly chosen sequence several types of discrepancies one of which is new are defined and analyzed a critical discussion of the theoretical bounds on these discrepancies is presented computations of discrepancies are presented for a wide choice of dimension s number of points n and different quasi random sequences in particular for moderate or large s there is an intermediate regime in which the discrepancy of a quasi random sequence is almost exactly the same as that of a randomly chosen sequence a simplified p

global existence of solution for cauchy problem of multidimensional generalized double dispersion equations abstract we study the cauchy problem of a class of multidimensional generalized double dispersion equations u t t u u t t 2 u k u t f u we prove the global existence of weak solution under some assumptions on the nonlinear term and the initial data

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

one dimensional klein gordon equation with logarithmic nonlinearities in this paper we consider the relativistic version of the logarithmic schrodinger equation namely the logarithmic klein gordon equation we show the existence of classical solutions and we investigate weak solutions finally we examine the traveling waves of this model

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

testing the number of components in a normal mixture we demonstrate that under a theorem proposed by vuong the likelihood ratio statistic based on the kullback leibler information criterion of the null hypothesis that a random sample is drawn from a k 0 component normal mixture distribution against the alternative hypothesis that the sample is drawn from a k 1 component normal mixture distribution is asymptotically distributed as a weighted sum of independent chi squared random variables with one degree of freedom under general regularity conditions we report simulation studies of two cases where we are testing a single normal versus a two component normal mixture and a two component normal mixture versus a three component normal mixture an empirical adjustment to the likelihood ratio statistic is proposed that appears to improve the rate of convergence to the limiting distribution