a new auxiliary function method for solving the generalized coupled hirota satsuma kdv system abstract in this letter a new auxiliary function method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations the main idea of this method is to take full advantage of the solutions of the elliptic equation to construct exact travelling wave solutions of nonlinear partial differential equations more new exact travelling wave solutions are obtained for the generalized coupled hirota satsuma kdv system

on conditional and intrinsic autoregressions summary gaussian conditional autoregressions have been widely used in spatial statistics and bayesian image analysis where they are intended to describe interactions between random variables at fixed sites in euclidean space the main appeal of these distributions is in the markovian interpretation of their full conditionals intrinsic autoregressions are limiting forms that retain the markov property despite being improper they can have advantages over the standard autoregressions both conceptually and in practice for example they often avoid difficulties in parameter estimation without apparent loss or exhibit appealing invariances as in texture analysis however on small arrays and in nonlattice applications both forms of autoregression can lead to undesirable second order characteristics either in the variables themselves or in contrasts among them this paper discusses standard and intrinsic autoregressions and describes how the problems that arise can be alleviated using dempster s 1972 algorithm or an appropriate modification the approach represents a partial synthesis of standard geostatistical and gaussian markov random field formulations some nonspatial applications are also mentioned

a bayesian approach to multiscale inverse problems with on the fly scale determination abstract a bayesian computational approach is presented to provide a multi resolution estimate of an unknown spatially varying parameter from indirect measurement data in particular we are interested in spatially varying parameters with multiscale characteristics in our work we consider the challenge of not knowing the characteristic length scale s of the unknown a priori and present an algorithm for on the fly scale determination our approach is based on representing the spatial field with a wavelet expansion wavelet basis functions are hierarchically structured localized in both spatial and frequency domains and tend to provide sparse representations in that a large number of wavelet coefficients are approximately zero for these reasons wavelet bases are suitable for representing permeability fields with non trivial correlation structures moreover the intra scale correlations between wavelet coefficients form a quadtree and this structure is exploited to identify additional basis functions to refine the model bayesian inference is performed using a sequential monte carlo smc sampler with a markov chain monte carlo mcmc transition kernel the smc sampler is used to move between posterior densities defined on different scales thereby providing a computationally efficient method for adaptive refinement of the wavelet representation we gain insight from the marginal likelihoods by computing bayes factors for model comparison and model selection the marginal likelihoods provide a termination criterion for our scale determination algorithm the bayesian computational approach is rather general and applicable to several inverse problems concerning the estimation of a spatially varying parameter the approach is demonstrated with permeability estimation for groundwater flow using pressure sensor measurements

the sine cosine method for obtaining solutions with compact and noncompact structures in this paper we establish compact and noncompact solutions for nonlinear dispersive equations a sine cosine method is used to demonstrate this work the different physical structures of the focusing branch and the defocusing branch are emphasized many models are approached to illustrate the usage of our main results

hierarchical bayesian inference for ill posed problems via variational method this paper investigates a novel approximate bayesian inference procedure for numerically solving inverse problems a hierarchical formulation which determines automatically the regularization parameter and the noise level together with the inverse solution is adopted the framework is of variational type and it can deliver the inverse solution and regularization parameter together with their uncertainties calibrated it approximates the posteriori probability distribution by separable distributions based on kullback leibler divergence two approximations are derived within the framework and some theoretical properties e g variance estimate and consistency are also provided algorithms for their efficient numerical realization are described and their convergence properties are also discussed extensions to nonquadratic regularization nonlinear forward models are also briefly studied numerical results for linear and nonlinear cauchy type problems arising in heat conduction with both smooth and nonsmooth solutions are presented for the proposed method and compared with that by markov chain monte carlo the results illustrate that the variational method can faithfully capture the posteriori distribution in a computationally efficient way

multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system compared with most of the existing tanh methods the jacobi elliptic function method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters the solutions obtained in this paper include a kink shaped and bell shaped soliton solutions b rational solutions c triangular periodic solutions and d jacobi and weierstrass doubly periodic wave solutions among them the jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition the efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper kdv mkdv ito s fifth mkdv hirota nizhnik novikov veselov broer kaup generalized coupled hirota satsuma coupled schrodinger kdv 2 1 dimensional dispersive long wave 2 1 dimensional davey stewartson equations in addition as an illustrative sample the properties of the soliton solutions and jacobi doubly periodic solutions for the hirota equation are shown by some figures the links among our proposed method the tanh method extended tanh method and the jacobi elliptic function method are clarified generally

similarity reductions from extended painleve expansions for nonintegrable evolution equations abstract the use of singular manifold expansions to find exact solutions to nonintegrable evolution equations is extended to include arbitrary resonance coefficients in such a way as to make the resulting infinite series exactly resummable the technique involves the use of a rescaling ansatz analogous to that used to analyze the psi series of nonintegrable ordinary differential equations the result is a similarity reduction of the equation in which the constrained singular manifold plays the role of a similarity variable the method is capable of yielding new solutions corresponding to either classical or nonclassical conditional lie symmetries

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

a new generalized riccati equation rational expansion method to a class of nonlinear evolution equations with nonlinear terms of any order abstract with the aid of symbolic computation a new algebraic method named generalize riccati equation rational expansion grere method is devised for constructing travelling wave solutions for nonlinear evolution equations nees with nonlinear terms of any order compared with most existing tanh methods for finding travelling wave solutions the proposed method not only recovers the results by most known algebraic methods but also provides new and more general solutions for illustration we apply the generalized method to a class of nonlinear evolution equations with nonlinear term of any order as a result we obtain several new kinds of exact solutions this approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order

exact solutions of the bogoyavlenskii equation using the multiple g g expansion method in this work exact traveling wave solutions of the bogoyavlenskii equation are studied by the g g expansion method and its variants the solutions obtained are general solutions which are in the form of hyperbolic trigonometric and rational functions and a variety of special solutions like kink shaped antikink shaped bell type soliton solutions etc can easily be derived from the general results under certain domain these methods are more effective and simple than other methods and a number of solutions can be obtained at the same time in order to visualize the underlying dynamics of the obtained solutions two and three dimensional plots are drawn

bayesian hypothesis testing in latent variable models hypothesis testing using bayes factors bfs is known not to be well defined under the improper prior in the context of latent variable models an additional problem with bfs is that they are difficult to compute in this paper a new bayesian method based on the decision theory and the em algorithm is introduced to test a point hypothesis in latent variable models the new statistic is a by product of the bayesian mcmc output and hence easy to compute it is shown that the new statistic is appropriately defined under improper priors because the method employs a continuous loss function in addition it is easy to interpret the method is illustrated using a one factor asset pricing model and a stochastic volatility model with jumps

local model influence abstract this article develops a general method for assessing the influence of model assumptions in a bayesian analysis we assume that model choices are indexed by a hyperparameter with some given initial choice we use the term model to encompass both the sampling model and the prior distribution we wish to assess the effect of changing the hyperparameter away from the initial choice we are performing a sensitivity analysis with the hyperparameter defining our perturbations we use the kullback leibler divergence to measure the difference between posteriors corresponding to different choices of the hyperparameter we also measure the change in priors if small changes in the priors lead to large changes in posteriors the choice of hyperparameter is influential the second order difference in the kullback leibler divergence is expressed by fisher information matrices the relative change in posteriors compared with priors may be summarized by the relative eigenvalue of the posterior and prior fishe

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

the intrinsic bayes factor for model selection and prediction abstract in the bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions it is typically not possible to utilize standard noninformative or default prior distributions this has led bayesians to use conventional proper prior distributions or crude approximations to bayes factors in this article we introduce a new criterion called the intrinsic bayes factor which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual bayes factors the criterion can be used for nested or nonnested models and for multiple model comparison and prediction from another perspective the development suggests a general definition of a reference prior for model comparison

a test of the efficiency of a given portfolio a test for the ex ante efficiency of a given portfolio of assets is analyzed the relevant statistic has a tractable small sample distribution its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post mean variance efficient frontier several intuitive interpretations of the test are provided including a simple mean standard deviation geometric explanation a univariate test equivalent to our multivariate based method is derived and it suggests some useful diagnostic tools which may explain why the null hypothesis is rejected empirical examples suggest that the multivariate approach can lead to more appropriate conclusions than those based on traditional inference which relies on a set of dependent univariate statistics

computer experiments with both qualitative and quantitative variables computer experiments have received a great deal of attention in many fields of science and technology most literature assumes that all the input variables are quantitative however researchers often encounter computer experiments involving both qualitative and quantitative variables bqqv in this article a new interface on design and analysis for computer experiments with bqqv is proposed the new designs are one kind of sliced latin hypercube designs with points clustered in the design region and possess good uniformity for each slice for computer experiments with bqqv such designs help to measure the similarities among responses of different level combinations in the qualitative variables an adaptive analysis strategy intended for the proposed designs is developed the proposed strategy allows us to automatically extract information from useful auxiliary responses to increase the precision of prediction for the target response the interface between the proposed design and the analysis strategy

computing solitary wave solutions of coupled nonlinear hirota and helmholtz equations abstract in this article we obtain the exact solutions two coupled models one integrable system namely coupled nonlinear hirota cnhi equation and another non integrable system namely coupled nonlinear helmholtz cnhe equation via the exp e expansion method the obtained travelling wave solutions are structured in rational trigonometric and hyperbolic functions these solutions lead to diverse types of solitary optical waves for free choices of parameters that guarantee the sustainability of such solutions also 3d illustrations for the free choices of the physical parameters is provided to understand the physical explanation of the problems these results further enrich and deepen the understanding of the dynamics of higher dimensional soliton propagation

a further improved extended fan sub equation method for 2 1 dimensional breaking soliton equations in this paper a further improved extended fan sub equation method is used to construct exact solutions of the 2 1 dimensional breaking soliton equations as a result many new and more general non travelling wave and coefficient function solutions are obtained including soliton like solutions triangular like solutions single and combined non degenerate jacobi elliptic wave function like solutions weierstrass elliptic doubly like periodic solutions each of which contains an arbitrary function of two variables the results show the proposed method give new and more general exact solutions more importantly the method with the aid of symbolic computation provides a very effective and powerful mathematical tool for solving a great many non linear partial differential equations in mathematical physics

the sine cosine and the tanh methods reliable tools for analytic treatment of nonlinear dispersive equations the sine cosine method and the tanh method are used for analytic treatment of nonlinear dispersive equations nonlinear variants of boussinesq equation are used as vehicles to show the strength of these methods solutions of distinct physical structures solitons compactons solitary patterns solutions and periodic solutions are formally derived the results show that the change in physical structures of the obtained solutions depends mainly on exponents and on the coefficients of the derivatives involved

markov chain monte carlo methods for stochastic volatility models this paper is concerned with simulation based inference in generalized models of stochastic volatility defined by heavy tailed student t distributions with unknown degrees of freedom and exogenous variables in the observation and volatility equations and a jump component in the observation equation by building on the work of kim shephard and chib rev econom stud 65 1998 361 we develop efficient markov chain monte carlo algorithms for estimating these models the paper also discusses how the likelihood function of these models can be computed by appropriate particle filter methods computation of the marginal likelihood by the method of chib j amer statist assoc 90 1995 1313 is also considered the methodology is extensively tested and validated on simulated data and then applied in detail to daily returns data on the s p 500 index where several stochastic volatility models are formally compared under different priors on the parameters

inference for a proton accelerator using convolution models proton beams present difficulties in analysis because of the limited data that can be collected the study of such beams must depend on complex computer simulators that incorporate detailed physical equations the statistical problem of interest is to infer the initial state of the beam from the limited data collected as the beam passes through a series of focusing magnets we are thus faced with a classic inverse problem where the computer simulator links the initial state to the observables we propose a new model for the initial distribution that is derived from the discretized process convolution approach this model provides a computationally tractable method for this highly challenging problem taking a bayesian perspective allows better estimation of the uncertainty and propagation of this uncertainty

on weierstrass elliptic function solutions for a n 1 dimensional potential kdv equation this paper is concerned with several aspects of travelling wave solutions for a n 1 dimensional potential kdv equation the weierstrass elliptic function solutions the jaccobi elliptic function solutions solitary wave solutions periodic wave solutions to the equation are acquired under certain circumstances it is shown that the coefficients of derivative terms in the equation cause the qualitative changes of physical structures of the solutions

the extended g g expansion method and its applications to the whitham broer kaup like equations and coupled hirota satsuma kdv equations in this paper based on a new general ansatze the extended g g expansion method is proposed to seek exact solutions of nonlinear evolution equations being concise and straightforward this method is applied to construct travelling wave solutions of whitham broer kaup like equations and coupled hirota satsuma kdv equations by using this method new exact solutions involving parameters expressed by three types of functions which are the hyperbolic functions the trigonometric functions and the rational functions are obtained when the parameters are taken as special values some solitary wave solutions are derived from the hyperbolic function solutions

a bayesian chi squared test for hypothesis testing abstract a new bayesian test statistic is proposed to test a point null hypothesis based on a quadratic loss the proposed test statistic may be regarded as the bayesian version of the lagrange multiplier test its asymptotic distribution is obtained based on a set of regular conditions and follows a chi squared distribution when the null hypothesis is correct the new statistic has several important advantages that make it appealing in practical applications first it is well defined under improper prior distributions second it avoids jeffrey lindley s paradox third it always takes a non negative value and is relatively easy to compute even for models with latent variables fourth its numerical standard error is relatively easy to obtain finally it is asymptotically pivotal and its threshold values can be obtained from the chi squared distribution the method is illustrated using some real examples in economics and finance

new exact jacobi elliptic functions solutions for the generalized coupled hirota satsuma kdv system abstract in this paper an generalized jacobi elliptic functions expansion method with computerized symbolic computation is used for constructing more new exact jacobi elliptic functions solutions of the generalized coupled hirota satsuma kdv system as a result eight families of new doubly periodic solutions are obtained by using this method some of these solutions are degenerated to solitary wave solutions and triangular functions solutions in the limit cases when the modulus of the jacobi elliptic functions m 1 or 0 which shows that the applied method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics

exact travelling wave solutions of some nonlinear equations by g g expansion method abstract here we find exact solutions of some nonlinear evolution equations within the framework of the g g expansion method exact solutions of five nonlinear equations of physical importance viz the coupled schrodinger kdv equation the coupled nonlinear reaction diffusion equation the foam drainage equation the phi four equation and the dodd bullough mikhailov equation are obtained these general solutions can be reduced in some standard results derived by some other methods two and three dimensional plots of some of the results are also presented

comparison of three semi analytical methods for solving 1 1 dimensional dispersive long wave equations in this work we consider how adomian s decomposition method adm the homotopy analysis method ham and the homotopy perturbation method hpm can be used to investigate wave solutions of 1 1 dimensional dispersive long wave equations it is also worth noting that the advantage of the approximation of the series methodologies is a fast convergence of the solutions

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

bayesian uncertainty quantification for subsurface inversion using a multiscale hierarchical model we consider a bayesian approach to nonlinear inverse problems in which the unknown quantity is a random field spatial or temporal the bayesian approach contains a natural mechanism for regularization in the form of prior information can incorporate information from heterogeneous sources and provide a quantitative assessment of uncertainty in the inverse solution the bayesian setting casts the inverse solution as a posterior probability distribution over the model parameters the karhunen loeve expansion is used for dimension reduction of the random field furthermore we use a hierarchical bayes model to inject multiscale data in the modeling framework in this bayesian framework we show that this inverse problem is well posed by proving that the posterior measure is lipschitz continuous with respect to the data in total variation norm computational challenges in this construction arise from the need for repeated evaluations of the forward model e g in the context of mcmc and are compounded by

a new general algebraic method with symbolic computation to construct new travelling wave solution for the 1 1 dimensional dispersive long wave equation with the aid of symbolic computation a new algebraic method named riccati equation rational expansion rere method is devised for constructing multiple travelling wave solutions for nonlinear evolution equations nees compared with most existing tanh methods for finding travelling wave solutions the proposed method not only recover the results by most known algebraic methods but also provides new and more general solutions with the aid of symbolic computation we choose 1 1 dimensional dispersive long wave equation dlwe to illustrate our method as a result we obtain many types of solutions including rational form solitary wave solutions triangular periodic wave solutions and rational wave solutions the properties of the new solitary wave solutions are shown by some figures

the improved g g expansion method and its applications to the broer kaup equations and approximate long water wave equations by introducing a new general ansatze the improved g g expansion method is proposed to construct exact solutions of both broer kaup equations and approximate long water wave equations as a result some new travelling wave solutions involving parameters expressed by three types of functions which are the hyperbolic functions the trigonometric functions and the rational functions are obtained when the parameters are taken as special values the solitary wave solutions are derived from the hyperbolic function solutions the proposed method is straightforward concise and effective and can be applied to other nonlinear evolution equations in mathematical physics

information distinguishability with application to analysis of failure data abstract in maximum entropy me modeling the information discrepancy between two distributions is measured in terms of their entropy difference in discrimination information statistics the information discrepancy between two distributions is measured in terms of the kullback leibler function i e relative entropy or cross entropy this article presents an equivalence between kullback leibler functions and entropy differences involving an me distribution based on this equivalence the concept of information discrimination id distinguishability is introduced as a unifying framework for the two methods of measuring information discrepancy between distributions applications of id distinguishability as diagnostics for examining robustness of parametric procedures and sensitivity of nonparametric statistics across parametric families of distributions is proposed the equivalence result facilitates estimation of kullback leibler functions in terms of entropy estimates application of the id distinguish

a bayesian approach to testing the arbitrage pricing theory abstract we consider new methods of testing the restrictions imposed on asset returns implied by an equilibrium version of the arbitrage pricing theory in the competitive equilibrium version of the apt see for example connor and korajczyk 1988 excess returns on a collection of portfolios or individual assets are related to measured factors in a multivariate regression model without intercepts the traditional significance testing approach uses estimates of these intercept terms and a likelihood ratio procedure for statistical testing in our approach we quantify differences between the restricted and unrestricted models by computing posterior model probabilities these posterior model probabilities are combined to form posterior odds ratios which represent the weight of prior and sample evidence for or against the pricing restrictions a dramatic simplification of the odds ratio calculation is achieved by using the savage density ratio method the special structure of the apt model with factors extracted by principal components is exploited to produce a simple prior the sensitivity of the odds ratio to different prior specifications is explored we apply these new methodologies to tests of the apt with a collection of ten size based portfolios the factors are extracted by a principal components technique developed by connor and korajczyk using all listed amex nyse firms over the period 1964 1983 the odds ratios show that the sample evidence is weak and does not favor the apt pricing restrictions we are able to gauge the strength of the evidence in the data by examining the sensitivity of the odds ratio to the prior

a bayesian robust chi squared test for testing simple hypotheses abstract in this paper we introduce a new bayesian chi squared test based on an adjusted quadratic loss function for testing a simple null hypothesis we show that the asymptotic null distribution of our suggested test is a central chi squared distribution under some assumptions required for the bayesian large sample theory we refer to our test as the bayesian robust chi squared test since it is robust to parametric misspecification in the alternative model that is the limiting null distribution of our test is a central chi squared distribution irrespective of parametric misspecification in the alternative model in addition to being robust to parametric misspecification our test also shares properties of the test suggested by li et al 2015 based on a quadratic loss function we provide four examples to illustrate the implementation of our suggested bayesian test statistic

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

review of parameter identification procedures in groundwater hydrology the inverse problem the purpose of this survey is to review parameter identification procedures in groundwater hydrology and to examine computational techniques which have been developed to solve the inverse problem parameter identification methods are classified under the error criterion used in the formulation of the inverse problem the problem of ill posedness in connection with the inverse problem is addressed typical inverse solution techniques are highlighted the review also includes the evaluation of methods used for computing the sensitivity matrix statistics which can be used to estimate the parameter uncertainty are outlined attempts have been made to compare and contrast representative inverse procedures and direction for future research is suggested

dimensionality reduction and polynomial chaos acceleration of bayesian inference in inverse problems we consider a bayesian approach to nonlinear inverse problems in which the unknown quantity is a spatial or temporal field endowed with a hierarchical gaussian process prior computational challenges in this construction arise from the need for repeated evaluations of the forward model e g in the context of markov chain monte carlo and are compounded by high dimensionality of the posterior we address these challenges by introducing truncated karhunen loeve expansions based on the prior distribution to efficiently parameterize the unknown field and to specify a stochastic forward problem whose solution captures that of the deterministic forward model over the support of the prior we seek a solution of this problem using galerkin projection on a polynomial chaos basis and use the solution to construct a reduced dimensionality surrogate posterior density that is inexpensive to evaluate we demonstrate the formulation on a transient diffusion equation with prescribed source terms inferring the spatially varying diffusivity of the medium from limited and noisy data

fully bayesian reconstructions from single photon emission computed tomography data abstract with suitably chosen priors bayesian models are useful in image reconstruction i consider reconstructions from single photon emission computerized tomography data using a gibbs pairwise difference prior a fully bayesian approach is presented where the prior parameters are considered drawn from hyperpriors the approach is problematical because the normalization constant in the prior is an intractable function of its parameters here the constant is estimated off line by reverse logistic regression markov chain monte carlo methods are used on simulated and real data to gain estimates of the posterior mean and pixelwise credibility bounds the resulting reconstructions are compared to those obtained by filtered back projection maximum likelihood em and the one step late solution to the fixed parameter posterior mode

a bayesian significance test of the stationarity of regression parameters this paper presents a bayesian significance test for stationarity of a regression equation using the highest posterior density credible set in addition a solution to the behrensfisher problem is provided from a monte carlo simulation study it has been shown that the bayesian significance test has stronger power than the cusum and the cusum of squares tests the bayesian significance test may be useful in detecting individual parameter nonstationarity

a new approach to bayesian hypothesis testing abstract in this paper a new bayesian approach is proposed to test a point null hypothesis based on the deviance in a decision theoretical framework the proposed test statistic may be regarded as the bayesian version of the likelihood ratio test and appeals in practical applications with three desirable properties first it is immune to jeffreys concern about the use of improper priors second it avoids jeffreys lindley s paradox third it is easy to compute and its threshold value is easily derived facilitating the implementation in practice the method is illustrated using some real examples in economics and finance it is found that the leverage effect is insignificant in an exchange time series and that the fama french three factor model is rejected

localized excitations in 2 1 dimensional systems by means of a special variable separation approach a common formula with some arbitrary functions has been obtained for some suitable physical quantities of various 2 1 dimensional models such as the davey stewartson ds model the nizhnik novikov veselov nnv system asymmetric nnv equation asymmetric ds equation dispersive long wave equation broer kaup kupershmidt system long wave short wave interaction model maccari system and a general n m component ablowitz kaup newell segur akns system selecting the arbitrary functions appropriately one may obtain abundant stable localized interesting excitations such as the multidromions lumps ring soliton solutions breathers instantons etc it is shown that some types of lower dimensional chaotic patterns such as the chaotic chaotic patterns periodic chaotic patterns chaotic line soliton patterns chaotic dromion patterns fractal lump patterns and fractal dromion patterns may be found in higher dimensional soliton systems the interactions between the traveling ring type soliton solutions are completely elastic the traveling ring solitons pass through each other and preserve their shapes velocities and phases some types of localized weak solutions peakons are also discussed especially the interactions between two peakons are not completely elastic after the interactions the traveling peakons also pass through each other and preserve their velocities and phases however they completely exchange their shapes

constructing of exact solutions to the kdv and burgers equations with power law nonlinearity by the extended g g expansion method abstract the extended g g expansion method is introduced to construct more general exact traveling wave solutions to the kdv and burgers equations with any order nonlinear terms the traveling wave solutions are expressed by the hyperbolic functions the trigonometric functions and the rational functions when the parameters take up special values new solitary periodic and complex solutions are also derived from the traveling wave solutions

a computational inverse method for identification of non gaussian random fields using the bayesian approach in very high dimension this paper is devoted to the identification of bayesian posteriors for the random coefficients of the high dimension polynomial chaos expansions of non gaussian tensor valued random fields using partial and limited experimental data the experimental data sets correspond to an observation vector which is the response of a stochastic boundary value problem depending on the tensor valued random field which has to be identified so an inverse stochastic problem must be solved to perform the identification of the random field a complete methodology is proposed to solve this very challenging problem in high dimension which consists in using the first four steps introduced in a previous paper followed by the identification of the posterior model the steps of the methodology are the following 1 introduction of a family of prior algebraic stochastic model pasm 2 identification of an optimal pasm in the constructed family using the partial experimental data 3 construction of a statistical reduced order optimal pasm 4 construction in high dimension of the polynomial chaos expansion with deterministic vector valued coefficients of the reduced order optimal pasm 5 substitution of these deterministic vector valued coefficients by random vector valued coefficients in order to extend the capability of the polynomial chaos expansion to represent the experimental data and for which the joint probability distribution must be identified 6 construction of the prior probability model of these random vector valued coefficients and finally 7 identification of the posterior probability model of these random vector valued coefficients using partial and limited experimental data through the stochastic boundary value problem two methods are proposed to carry out the identification of the posterior model the first one is based on the use of the classical bayesian method the second one is a new approach derived from the bayesian method which is more efficient in high dimension an application is presented for which several millions of random coefficients are identified

the compound g g expansion method and double non traveling wave solutions of 2 1 dimensional nonlinear partial differential equations abstract to seek the exact double non traveling wave solutions of nonlinear partial differential equations the compound g g expansion method is firstly proposed in this paper with the aid of symbolic computation this new method is applied to construct double non traveling wave solutions of 2 1 dimensional painleve integrable burgers equation and 2 1 dimensional breaking soliton equation as a result abundant double non traveling wave solutions including double hyperbolic function solutions double trigonometric function solutions double rational solutions and a series of complexiton solutions of these two equations are obtained via the proposed method these exact solutions contain arbitrary functions which may be helpful to explain some complex phenomena when the parameters are taken as special values the double solitary like wave solutions can be derived from double hyperbolic function solutions furthermore the time evolutions of double solitary like wave solutions are discussed in detail

multiple kink solutions and multiple singular kink solutions for the 2 1 dimensional burgers equations abstract in this work we study the 2 1 dimensional painleve integrable burgers equation multiple kink solutions and multiple singular kink solutions are formally derived for this equation the analysis depends mainly on the hirota s bilinear method

consistency of the maximum likelihood estimator for general hidden markov models consider a parametrized family of general hidden markov models where both the observed and unobserved components take values in a complete separable metric space we prove that the maximum likelihood estimator mle of the parameter is strongly consistent under a rather minimal set of assumptions as special cases of our main result we obtain consistency in a large class of nonlinear state space models as well as general results on linear gaussian state space models and finite state models a novel aspect of our approach is an information theoretic technique for proving identifiability which does not require an explicit representation for the relative entropy rate our method of proof could therefore form a foundation for the investigation of mle consistency in more general dependent and non markovian time series also of independent interest is a general concentration inequality for v uniformly ergodic markov chains

on leverage in a stochastic volatility model this paper is concerned with the specification for modelling financial leverage effect in the context of stochastic volatility sv models two alternative specifications co exist in the literature one is the euler approximation to the well known continuous time sv model with leverage effect and the other is the discrete time sv model of jacquier et al j econometrics 122 2004 185 using a gaussian nonlinear state space form with uncorrelated measurement and transition errors i show that it is easy to interpret the leverage effect in the conventional model whereas it is not clear how to obtain and interpret the leverage effect in the model of jacquier et al empirical comparisons of these two models via bayesian markov chain monte carlo mcmc methods further reveal that the specification of jacquier et al is inferior simulation experiments are conducted to study the sampling properties of bayes mcmc for the conventional model

markov random field models for high dimensional parameters in simulations of fluid flow in porous media we give an approach for using flow information from a system of wells to characterize hydrologic properties of an aquifer in particular we consider experiments where an impulse of tracer fluid is injected along with the water at the input wells and its concentration is recorded over time at the uptake wells we focus on characterizing the spatially varying permeability field which is a key attribute of the aquifer for determining flow paths and rates for a given flow experiment as is standard for estimation from such flow data we use complicated subsurface flow code that simulates the fluid flow through the aquifer for a particular well configuration and aquifer specification in particular the permeability field over a grid the solution to this ill posed problem requires that some regularity conditions be imposed on the permeability field typically this regularity is accomplished by specifying a stationary gaussian process model for the permeability field here we use an intrinsically stationary

a multi resolution non parametric bayesian framework for identification of spatially varying model parameters this paper proposes a hierarchical multi resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output such parameters are frequently encountered in pde based models and correspond to quantities such as density or pressure fields elasto plastic moduli and internal variables in solid mechanics conductivity fields in heat diffusion problems permeability fields in fluid flow through porous media etc the proposed model has all the advantages of traditional bayesian formulations such as the ability to produce measures of confidence for the inferences made and providing not only predictive estimates but also quantitative measures of the predictive uncertainty in contrast to existing approaches it utilizes a parsimonious non parametric formulation that favors sparse representations and whose complexity can be determined from the data the proposed framework in non intrusive and makes use of a sequence of forward solvers operating at various resolutions as a result inexpensive coarse solvers are used to identify the most salient features of the unknown field s which are subsequently enriched by invoking solvers operating at finer resolutions this leads to significant computational savings particularly in problems involving computationally demanding forward models but also improvements in accuracy it is based on a novel adaptive scheme based on sequential monte carlo sampling which is embarrassingly parallelizable and circumvents issues with slow mixing encountered in markov chain monte carlo schemes the capabilities of the proposed methodology are illustrated in problems from nonlinear solid mechanics with special attention to cases where the data is contaminated with random noise and the scale of variability of the unknown field is smaller than the scale of the grid where observations are collected

painleve analysis lie symmetries and invariant solutions of potential kadomstev petviashvili equation with time dependent coefficients in this paper the painleve analysis of 2 1 dimensional variable coefficients potential kadomstev petviashvili vcpkp equation s x email protected t s email protected x email protected t s x x x email protected t s y y 0 has been performed to study the painleve properties the vcpkp equation is also reduced to a 1 1 dimensional partial differential equation via classical lie group method and reduced equations are further studied to obtain certain general solutions

a bayesian approach to stochastic capture zone delineation incorporating tracer arrival times conductivity measurements and hydraulic head observations this paper presents a methodology to invert tracer arrival times and to incorporate travel time data in the delineation of well capture zones within a bayesian framework the observed arrival times are used to obtain probability based weights for each realization of the hydraulic conductivity field realizations that closely reproduce the observed arrival times are more likely to represent the true or real conductivity field than realizations yielding worse predictions and are consequently characterized by a higher conditional probability in the prediction of the capture zones the realizations are weighted by their respective probability we combine the arrival time data with conductivity measurements and head observations to delineate stochastic capture zones the conductivity measurements update the prior distributions specified for the unknown structural parameters of the conductivity field and are used as conditioning data in the generation of conditional conductivity fields the parameter values used to generate the conductivity realizations are sampled by monte carlo from the updated parameter distributions the head and travel time observations are subsequently used to assign probability based weights to the conductivity realizations by applying bayes theorem the hyperparameters of the error model are assumed unknown and their effect is accounted for by marginalization a synthetic flow setup consisting of a single extraction well in a fully confined aquifer under a regional gradient is used to illustrate the method we evaluate the relative worth of the different data types by introducing them sequentially in the inverse methodology results indicate that the different data types are complementary and that the travel time data are essential to improve the predictions of the capture zones this is confirmed by the results for the case where uncertainty in the homogeneous porosity is accounted for

auxiliary equation method for the mkdv equation with variable coefficients abstract by using solutions of an ordinary differential equation an auxiliary equation method is described to seek exact solutions of nonlinear evolution equations with variable coefficients being concise and straightforward this method is applied to the mkdv equation with variable coefficients as a result new explicit solutions including solitary wave solutions and trigonometric function solutions are obtained with the aid of symbolic computation

fully bayesian estimation of gibbs hyperparameters for emission computed tomography data in recent years many investigators have proposed gibbs prior models to regularize images reconstructed from emission computed tomography data unfortunately hyperparameters used to specify gibbs priors can greatly influence the degree of regularity imposed by such priors and as a result numerous procedures have been proposed to estimate hyperparameter values from observed image data many of these procedures attempt to maximize the joint posterior distribution on the image scene to implement these methods approximations to the joint posterior densities are required because the dependence of the gibbs partition function on the hyperparameter values is unknown here the authors use recent results in markov chain monte carlo mcmc sampling to estimate the relative values of gibbs partition functions and using these values sample from joint posterior distributions on image scenes this allows for a fully bayesian procedure which does not fix the hyperparameters at some estimated or specified value but enables uncertainty about these values to be propagated through to the estimated intensities the authors utilize realizations from the posterior distribution for determining credible regions for the intensity of the emission source the authors consider two different markov random field mrf models the power model and a line site model as applications they estimate the posterior distribution of source intensities from computer simulated data as well as data collected from a physical single photon emission computed tomography spect phantom

model selection criteria for missing data problems using the em algorithm we consider novel methods for the computation of model selection criteria in missing data problems based on the output of the em algorithm the methodology is very general and can be applied to numerous situations involving incomplete data within an em framework from covariates missing at random in arbitrary regression models to nonignorably missing longitudinal responses and or covariates toward this goal we develop a class of information criteria for missing data problems called ic h q which yields the akaike information criterion and the bayesian information criterion as special cases the computation of ic h q requires an analytic approximation to a complicated function called the h function along with output from the em algorithm used in obtaining maximum likelihood estimates the approximation to the h function leads to a large class of information criteria called ic h k q theoretical properties of ic h k q including consistency are investigated in detail to eliminate the analytic approximation to the h function a computationally simpler approximation to ic h q called ic q is proposed the computation of which depends solely on the q function of the em algorithm advantages and disadvantages of ic h k q and ic q are discussed and examined in detail in the context of missing data problems extensive simulations are given to demonstrate the methodology and examine the small sample and large sample performance of ic h k q and ic q in missing data problems an aids data set also is presented to illustrate the proposed methodology

a bayesian approach to characterizing uncertainty in inverse problems using coarse and fine scale information the bayesian approach allows one to easily quantify uncertainty at least in theory in practice however the markov chain monte carlo mcmc method can be computationally expensive particularly in complicated inverse problems we present a methodology for improving the speed and efficiency of an mcmc analysis by combining runs on different scales by using a coarser scale the chain can run faster particularly when there is an external forward simulator involved in the likelihood evaluation and better explore the posterior being less likely to become stuck in local maxima we discuss methods for linking the coarse chain back to the original fine scale chain of interest the resulting coupled chain can thus be run more efficiently without sacrificing the accuracy achieved at the finer scale

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea