heat polynomial analogues for equations with higher order time derivatives abstract we generalize the heat polynomials for the heat equation to more general partial differential equations of higher order with respect to both the time variable and the space variables whereas the heat equation requires only one family of polynomials for an equation of the lth order with respect to time we introduce l families of polynomials these families correspond to the l initial conditions specified by the cauchy problem

an exact likelihood analysis of the multinomial probit model abstract we develop new methods for conducting a finite sample likelihood based analysis of the multinomial probit model using a variant of the gibbs sampler an algorithm is developed to draw from the exact posterior of the multinomial probit model with correlated errors this approach avoids direct evaluation of the likelihood and thus avoids the problems associated with calculating choice probabilities which affect both the standard likelihood and method of simulated moments approaches both simulated and actual consumer panel data are used to fit six dimensional choice models we also develop methods for analyzing random coefficient and multiperiod probit models

bayesian isotonic regression and trend analysis in many applications the mean of a response variable can be assumed to be a nondecreasing function of a continuous predictor controlling for covariates in such cases interest often focuses on estimating the regression function while also assessing evidence of an association this article proposes a new framework for bayesian isotonic regression and order restricted inference approximating the regression function with a high dimensional piecewise linear model the nondecreasing constraint is incorporated through a prior distribution for the slopes consisting of a product mixture of point masses accounting for flat regions and truncated normal densities to borrow information across the intervals and smooth the curve the prior is formulated as a latent autoregressive normal process this structure facilitates efficient posterior computation since the full conditional distributions of the parameters have simple conjugate forms point and interval estimates of the regression function and posterior probabilities of an association for different regions of the predictor can be estimated from a single mcmc run generalizations to categorical outcomes and multiple predictors are described and the approach is applied to an epidemiology application

operational methods fractional operators and special polynomials we use methods of operational nature to deal with families of partial differential equations of evolution type to treat problems involving fractional differential operators we also discuss the properties of families of special polynomials or special functions like the riemann z function naturally associated with the proposed formalism

boolean versus continuous dynamics on simple two gene modules we investigate the dynamical behavior of simple modules composed of two genes with two or three regulating connections continuous dynamics for mrna and protein concentrations is compared to a boolean model for gene activity using a generalized method we study within a single framework different continuous models and different types of regulatory functions and establish conditions under which the system can display stable oscillations these conditions depend only on general features such as the ratio of the relevant time scales the degree of cooperativity of the regulating interactions and the logical structure of the interactions our results combine and generalize the findings of several disconnected previous studies

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

operational methods and differential equations with applications to initial value problems the authors present and develop a general method of operational nature in order to explore and investigate such families of orthogonal polynomials and functions as the classical and generalized hermite and laguerre polynomials as well as their higher order and multi index cases they also consider several applications of these operational techniques to the solutions of a wide class of partial differential equations including for example the heat wave and transport equations some of which involve second order laguerre derivatives

illustration of bayesian inference in normal data models using gibbs sampling abstract the use of the gibbs sampler as a method for calculating bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models including variance components unordered and ordered means hierarchical growth curves and missing data in a crossover trial in all cases the approach is straightforward to specify distributionally and to implement computationally with output readily adapted for required inference summaries

operational rules and arbitrary order hermite generating functions operational identities often exploited in the theory of exponential operators are used to derive generating functions of hermite and kampe de feriet polynomials the method we propose allows us to obtain unilateral bilinear and bilateral generating functions by using the same procedure possible extensions of the technique are also discussed

order restricted bayesian estimation of the age composition of a population of atlantic cod abstract the management of a commercial fishery often requires estimates of the age composition these estimates are typically based on age and length data obtained from sampling the commercial landings from the fishery and the catches from a research vessel survey we use data from annual research cruises of georges bank conducted by the canadian department of fisheries and oceans to show how inferences for atlantic cod gadus morhua can be improved traditionally two phase stratified sampling is used with fish length or weight as the stratification variable letting pi denote the proportion of fish belonging to length stratum i and ij denote the proportion of fish belonging to age class j in stratum i we use bayesian methods to estimate p j i ij the proportion of fish that are age j specifications of smoothness expressed as unimodal order relations among the ij within and between the length strata are incorporated into the prior distributions uncertainty about both the locations

optimal two phase stratified sampling for estimation of the age composition of a fish population the provision of biological advice for the management of a commercial fish stock requires among other things an estimate of the age composition this estimate is usually obtained from length and age information collected by sampling the commercial landings associated with that fish stock the sampling methods used and the types of problems encountered are discussed by quinn et al 1983 and stevenson 1983 the final stage of the sample design is typically a two phase stratified sample of a large catch from a commercial vessel quinn et al 1983 stevenson 1983 southward 1976 at the first phase a large simple random sample srs of size n is selected and each fish is assigned to a stratum consisting of all fish having lengths in a specified range denote by nf the number of sampled fish in length stratum i at the second phase a srs of size ni is chosen from stratum i i 1 i each of these ni fish is aged with nij fish found to be agej j 1 j the problems are i estimation of ipj j 1 j where p j is the population proportion of age j fish ii given n and in i 1 i how to select ini i 1 i and iii for a specified cost function and given budget how to select n smith and sedransk 1982 provide methods for i and ii for ii their approach is flexible in that currently used or proposed allocation schemes are shown to be optimal under appropriate specifications in the current paper we i review the smith sedransk methodology ii show how to determine the optimal value of n and iii exhibit potential gains from using two phase sampling in section 3 we give a numerical illustration of the

hermite based appell polynomials properties and applications abstract by employing certain operational methods the authors introduce hermite based appell polynomials some properties of hermite appell polynomials are considered which proved to be useful for the derivation of identities involving these polynomials the possibility of extending this technique to introduce hermite based sheffer polynomials for example hermite laguerre and hermite sister celine s polynomials is also investigated

analysis on binary responses with ordered covariates and missing data summary we consider the situation of two ordered categorical variables and a binary outcome variable where one or both of the categorical variables may have missing values the goal is to estimate the probability of response of the outcome variable for each cell of the contingency table of categorical variables while incorporating the fact that the categorical variables are ordered the probability of response is assumed to change monotonically as each of the categorical variables changes level a probability model is used in which the response is binomial with parameters pij for each cell i j and the number of observations in each cell is multinomial estimation approaches that incorporate gibbs sampling with order restrictions on pij induced via a prior distribution two dimensional isotonic regression and multiple imputation to handle missing values are considered the methods are compared in a simulation study using a fully bayesian approach with a strong prior distribution to induce ordering can lead to large gains in efficiency but can also induce bias utilizing isotonic regression can lead to modest gains in efficiency while minimizing bias and guaranteeing that the order constraints are satisfied a hybrid of isotonic regression and gibbs sampling appears to work well across a variety of scenarios the methods are applied to a pancreatic cancer case control study with two biomarkers copyright q 2007 john wiley sons ltd

markov chain estimation for test theory without an answer key this study develops markov chain monte carlo mcmc estimation theory for the general condorcet model gcm an item response model for dichotomous response data which does not presume the analyst knows the correct answers to the test a priori answer key in addition to the answer key respondent ability guessing bias and difficulty parameters are estimated with respect to data fit the study compares between the possible gcm formulations using mcmc based methods for model assessment and model selection real data applications and a simulation study show that the gcm can accurately reconstruct the answer key from a small number of respondents

generalized and mixed type gegenbauer polynomials abstract in this paper a new generalized form of the gegenbauer polynomials is introduced by using the integral representation method further the hermite gegenbauer and the laguerre gegenbauer polynomials are introduced by using the operational identities associated with the generalized hermite and laguerre polynomials of two variables

maximum likelihood variance components estimation for binary data abstract we consider a class of probit normal models for binary data and describe ml and reml estimation of variance components for that class as well as best prediction for the realized values of the random effects ml estimates are calculated using an em algorithm for complicated models em includes a gibbs step the computations are illustrated through two examples

when the telegrapher s equation furnishes a better approximation to the transport equation than the diffusion approximation it has been suggested that a solution to the transport equation which includes anisotropic scattering can be approximated by the solution to a telegrapher s equation a j ishimaru appl opt 28 2210 1989 we show that in one dimension the telegrapher s equation furnishes an exact solution to the transport equation in two dimensions we show that since the solution can become negative the telegrapher s equation will not furnish a usable approximation a comparison between simulated data in three dimensions indicates that the solution to the telegrapher s equation is a good approximation to that of the full transport equation at the times at which the diffusion equation furnishes an equally good approximation s1063 651x 97 04205 0

multi variable hermite matrix polynomials properties and applications abstract in this paper the multi variable hermite matrix polynomials are introduced by algebraic decomposition of exponential operators their properties are established using operational methods the matrix forms of the chebyshev and truncated polynomials of two variable are also introduced which are further used to derive certain operational representations and expansion formulae

minkowski weyl priors for models with parameter constraints an analysis of the biocycle study we propose a general framework for performing full bayesian analysis under linear inequality parameter constraints the proposal is motivated by the biocycle study a large cohort study of hormone levels of healthy women where certain well established linear inequality constraints on the log hormone levels should be accounted for in the statistical inferential procedure based on the minkowski weyl decomposition of polyhedral regions we propose a class of priors that are fully supported on the parameter space with linear inequality constraints and we fit a bayesian linear mixed model to the biocycle data using such a prior we observe positive associations between estrogen and progesterone levels and f2 isoprostanes a marker for oxidative stress these findings are of particular interest to reproductive epidemiologists

determinantal approach to certain mixed special polynomials related to gould hopper polynomials in this article the gould hopper sheffer polynomials are introduced by means of generating function and determinantal definition certain properties of these polynomials are established and operational relations between the sheffer and gould hopper sheffer polynomials are derived examples of some members belonging to the gould hopper sheffer and gould hopper appell polynomials families are considered and the corresponding numbers for certain polynomials are also obtained

laguerre 2d functions and their application in quantum optics a set of orthonormalized and complete functions of two real variables in complex representation involving laguerre polynomials as a substantial part is introduced and is referred to as the set of laguerre two dimensional 2d functions the properties of the set of laguerre 2d functions are discussed and the fourier and radon transforms of these functions are calculated the laguerre 2d functions form a basis for a realization of the five dimensional lie algebra to the heisenberg weyl group for a two mode system real representation of this set of functions by a sum over products of hermite functions involving jacobi polynomials at the zero argument as coefficients is derived and it leads to new connections between laguerre and hermite polynomials in both directions the set of laguerre 2d functions is the most appropriate set of functions for the fock state representation of quasi probabilities in quantum optics the wigner quasi probability in fock state representation is up to a factor and an argument scaling directly given for each matrix element by a corresponding laguerre 2d function the properties of orthonormality and completeness of the laguerre 2d functions provide the fock state matrix elements of the density operator directly from the quasi probabilities the perina mista representation of the glauber sudarshan quasi probability can be represented with advantage by the laguerre 2d functions the fock state matrix elements of the displacement operator and the scalar product of displaced fock states are closely related to laguerre 2d functions

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

moment conditions and bayesian non parametrics models phrased through moment conditions are central to much of modern inference here these moment conditions are embedded within a non parametric bayesian set up handling such a model is not probabilistically straightforward as the posterior has support on a manifold we solve the relevant issues building new probability and computational tools by using hausdorff measures to analyse them on real and simulated data these new methods which involve simulating on a manifold can be applied widely including providing bayesian analysis of quasi likelihoods linear and non linear regression missing data and hierarchical models

physiological pharmacokinetic analysis using population modeling and informative prior distributions abstract we describe a general approach using bayesian analysis for the estimation of parameters in physiological pharmacokinetic models the chief statistical difficulty in estimation with these models is that any physiological model that is even approximately realistic will have a large number of parameters often comparable to the number of observations in a typical pharmacokinetic experiment e g 28 measurements and 15 parameters for each subject in addition the parameters are generally poorly identified akin to the well known ill conditioned problem of estimating a mixture of declining exponentials our modeling includes a hierarchical population modeling which allows partial pooling of information among different experimental subjects b a pharmacokinetic model including compartments for well perfused tissues poorly perfused tissues fat and the liver and c informative prior distributions for population parameters which is possible because the parameters represent real physiological

certain results for the 2 variable apostol type and related polynomials in this article the 2 variable general polynomials are taken as base with apostol type polynomials to introduce a family of 2 variable apostol type polynomials these polynomials are framed within the context of monomiality principle and their properties are established certain summation formulae for these polynomials are also derived examples of some members belonging to this family are considered and numbers related to some mixed special polynomials are also explored

bayesian inference of survival probabilities under stochastic ordering constraints abstract in the statistical analysis of survival data arising from two populations it often happens that the analyst knows a priori that the life lengths in one population are stochastically shorter than those in the other nevertheless survival probability estimates if determined separately from the corresponding samples may not be consistent with this prior assumption because of inherent statistical variability in the observations this problem has been considered in a number of papers during the past decade by adopting a generalized maximum likelihood approach our approach is bayesian and in essence nonparametric the a priori assumption regarding stochastic ordering is formulated naturally in terms of a joint prior distribution defined for pairs of survival functions nonparametric specification of the model based on hazard rates and using a few hyperparameters allows for sufficient flexibility in practical applications the numerical computations are based on a coupled version of the m

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

incomplete 2d hermite polynomials properties and applications incomplete forms of two variable two index hermite polynomials are introduced their link with laguerre polynomials is discussed and it is shown that they are a useful tool to study quantum mechanical harmonic oscillator entangled states the possibility of developing the theory of complete 2d hermite polynomials from the point of view of the incomplete forms is analyzed too the orthogonality properties of the associated harmonic oscillator functions are finally discussed

importance weighted marginal bayesian posterior density estimation abstract markov chain sampling schemes generate dependent observations i 0 i n from a full joint posterior distribution data frequently only certain marginals of this full posterior density are of interest thus an interesting problem is how to estimate the marginal posterior densities based on the dependent observations i 0 i n from data we propose a new importance weighted marginal density estimation iwmde method an iwmde is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting conditional density w the asymptotic properties for the iwmde and the guidelines for choosing a weighting conditional density w are also considered a bivariate normal model and a constrained linear multiple regression model are used to illustrate how to derive the iwmde s for the marginal posterior densities

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

2 variable laguerre matrix polynomials and lie algebraic techniques the authors introduce 2 variable forms of laguerre and modified laguerre matrix polynomials and derive their special properties further the representations of the special linear lie algebra sl 2 and the harmonic oscillator lie algebra g 0 1 are used to derive certain results involving these polynomials furthermore the generating relations for the ordinary as well as matrix polynomials related to these matrix polynomials are derived as applications

evolution of non spreading airy wavepackets in time dependent linear potentials abstract we report on the use of the algebraic methods to obtain the explicit form of the solution of the schrodinger equation with a linear potential we consider the case of the explicitly time dependent hamiltonian and formulate the general conditions that allow for the solutions to be found that are expressed in terms of airy functions yielding non spreading wave packets the relevant physical meaning of these solutions is analyzed and the examples of their applications are given the role played by the airy transform and its relevance to the problems involving linear potentials is discussed eventually we present a thorough discussion on the analogy between the airy and the gauss weierstrass transform often employed in the solutions of the heat type equations

on monte carlo methods for estimating ratios of normalizing constants recently estimating ratios of normalizing constants has played an important role in bayesian computations applications of estimating ratios of normalizing constants arise in many aspects of bayesian statistical inference in this article we present an overview and discuss the current monte carlo methods for estimating ratios of normalizing constants then we propose a new ratio importance sampling method and establish its theoretical framework we find that the ratio importance sampling method can be better than the current methods for example the bridge sampling method meng and wong and the path sampling method gelman and meng in the sense of minimizing asymptotic relative mean square errors of estimators an example is given for illustrative purposes finally we present two special applications and the general implementation issues for estimating ratios of normalizing constants

analytical solutions for heat diffusion beyond fourier law we obtain solutions for differential equations describing a broad range of physical problems by the operational method with recourse to inverse differential operators integral transforms and operational exponent generalized families of orthogonal polynomials and special functions are also employed with recourse to their operational definitions the evolutional type problems for heat transfer in various heat conduction models are studied exact analytical solutions for guyer krumhansl hyperbolic heat equation are obtained and compared with those of fourier and cattaneo equations modelling heat pulse propagation from a laser source is performed in the framework of fourier cattaneo and guyer krumhansl heat transfer models compliance of obtained solutions with the maximum principle is studied

operational methods and laguerre gould hopper polynomials abstract in this paper the authors introduce the laguerre gould hopper polynomials by combining the operational methods with the principle of monomiality generating function series definition differential equation and certain other properties of laguerre gould hopper polynomials are derived further operational representations of these polynomials are established which are used to get integral representations and expansion formulae for these polynomials

expert elicitation of adversary preferences using ordinal judgments we introduce a simple elicitation process where subject matter experts provide only ordinal judgments of the attractiveness of potential targets and the adversary utility of each target is assumed to involve multiple attributes probability distributions over the various attribute weights are then mathematically derived using either probabilistic inversion or bayesian density estimation this elicitation process reduces the burden of time consuming orientation and training in traditional methods of attribute weight elicitation and explicitly captures the existing uncertainty and disagreement among experts rather than attempts to achieve consensus by eliminating them we identify the relationship between the two methods and conduct sensitivity analysis to elucidate how these methods handle expert consensus or disagreement we also present a real world application on elicitation of adversarial preferences over various attack scenarios to show the applicability of our proposed methods

comments on monomiality ordinary polynomials and associated bi orthogonal functions we use laguerre and hermite polynomials to show that the monomiality principle can be exploited to study the properties of the polynomials and of the associated biorthogonal functions

orthogonality properties of the hermite and related polynomials the authors present a general method of operational nature with a view to investigating the orthogonality properties of several different families of the hermite and related polynomials in particular the classical hermite polynomials and some of their higher order and multi index generalizations are considered here

product of two hypergeometric functions with power arguments abstract the hypergeometric product formula describes the product of two hypergeometric functions with arguments xt and yt respectively the result is a power series in t whose coefficients are hypergeometric polynomials brychkov has extended the product formula such that in one argument the variable t can be squared we obtain a further extension such that in both arguments the variable t can be raised to positive integer powers

analytical search for bifurcation surfaces in parameter space the method of resultants can be used to compute hopf bifurcations in ode systems we discuss this method from the applicant s point of view furthermore we show by theory and examples that the method may be extended to cover other bifurcation situations as well among them are the real hopf situation which plays an important role in the transition to shil nikov chaos as well as some higher codimension bifurcations such as takens bogdanov gavrilov guckenheimer and double hopf bifurcations the method yields an analytical test function that can be solved analytically or by computer algebra systems in contrast to common analytical techniques based on eigenvalue computation which can only be applied to systems of size n 4 the method is applicable for systems of intermediate size n 10 we illustrate the power of the method by discussing examples from different disciplines of science a lorenz like oscillator two coupled oscillators and a five species food chain

operational solution for some types of second order differential equations and for relevant physical problems abstract we present an operational method to obtain solutions for differential equations describing a broad range of physical problems including ordinary non integer order and high order partial differential equations inverse differential operators are proposed to solve a variety of differential equations integral transforms and the operational exponent are used to obtain the solutions generalized families of orthogonal polynomials and special functions are also employed with recourse to their operational definitions examples of solutions of physical problems related to propagation of the heat and other quantities are demonstrated by the developed operational technique in particular the evolution type problems the generalizations of the black scholes of the heat conduction of the fokker planck equations are considered as well as equations involving the laguerre derivative operator

summation formulae for gould hopper generalized hermite polynomials in this article we derive summation formulae for the gould hopper generalized hermite polynomials g n m x y further we derive the summation formulae for polynomials related to g n m x y as applications furthermore we establish a summation formula for m variable generalized hermite polynomials h n 1 2 m x 1 x 2 x m

a gibbs sampler for inequality constrained geostatistical interpolation and inverse modeling 1 interpolation and inverse modeling problems are ubiquitous in environmental sciences in many applications the parameters being estimated or mapped have physical constraints such as nonnegativity e g concentration hydraulic conductivity solubility limits censored data e g due to dry wells or detection limits and other physical boundaries or missing data geostatistical interpolation and inverse modeling techniques have often been applied for estimating such parameters but these methods typically cannot enforce physical constraints this paper describes a statistically rigorous and computationally efficient gibbs sampler a markov chain monte carlo technique based on an a priori truncated gaussian distribution model which allows for multiple and variable physical constraints to be enforced within a geostatistical framework sample interpolation and inverse modeling applications confirm that estimates uncertainty bounds and conditional simulations reflect the specified constraints leading to conclusions that are more consistent with the underlying conceptual model and provide a more accurate measure of the posterior uncertainty of the parameters being estimated in addition especially in inverse modeling applications a posteriori confidence bounds are narrower even in areas where constraints are not imposed the method is applicable in multiple dimensions for data with or without measurement error and with any variogram model

the ramanujan master theorem and its implications for special functions abstract we study a number of possible extensions of the ramanujan master theorem which is formulated here by using methods of umbral nature we discuss the implications of the procedure for the theory of special functions like the derivation of formulae concerning the integrals of products of families of bessel functions and the successive derivatives of bessel type functions we stress also that the procedure we propose allows a unified treatment of many problems appearing in applications which can formally be reduced to the evaluation of exponential or gaussian like integrals

the laguerre transform in two variables and its application in partial differential equations an attempt is made to investigate some properties of the laguerre transform in two variables this technique is very effective for solving certain types of partial differential equations

sequential classification on partially ordered sets summary a general theorem on the asymptotically optimal sequential selection of experiments is presented and applied to a bayesian classification problem when the parameter space is a finite partially ordered set the main results include establishing conditions under which the posterior probability of the true state converges to 1 almost surely and determining optimal rates of convergence properties of a class of experiment selection rules are explored

a class of bayesian shared gamma frailty models with multivariate failure time data nous proposons ici dans le cadre des donnees de survie une nouvelle classe de modeles a fragilite gamma partagee en appliquant la transformation de box cox a la fonction de hasard ainsi qu au produit du risque de base et de la fragilite cette nouvelle classe de modeles offre un large eventail de formes et relations entre la fonction de hasard et le risque de base et inclut en tant que cas particuliers le modele de cox usuel a fragilite gamma ainsi qu un nouveau modele additif a fragilite gamma de par la contrainte que le risque soit non negatif ce modele a fragilite gamma partagee presente un defi calculatoire dans le paradigme bayesien les distributions conjointes a priori sont definies par une distribution conditionnelle marginale ou la distribution conditionnelle est univariee cela permet d integrer les contraintes non lineaires sur les parametres la partie marginale de la distribution a priori quant a elle est libre de toute contrainte les distributions a priori permettent de programmer facilement l integralite des distributions conditionnelles requises pour l echantillonnage de gibbs tout en integrant les contraintes un jeu reel de donnees permet d illustrer cette classe de modeles a fragilite gamma partagee

bayesian estimation of finite population parameters in categorical data models incorporating order restrictions this note describes a bayesian method for estimation of finite population parameters in general population surveys where acceptable regression type models are typically unavailable a categorical data model is adopted as in ericson 1969 section 4 however specifications of smoothness are incorporated into the prior distribution these smoothness conditions are expressed as unimodal or possibly multi modal order relations among the category probabilities emphasis is placed on posterior inference about the finite population mean of independent interest is the methodology for evaluating the posterior moments and probabilities using monte carlo integration with importance sampling

the higher order heat type equations via signed levy stable and generalized airy functions we study the higher order heat type equation with first time and mth spatial partial derivatives m 2 3 we demonstrate that its exact solutions for m even can be constructed with the help of signed levy stable functions for m odd the same role is played by a special generalization of the airy ai function that we introduce and study this permits one to generate the exact and explicit heat kernels pertaining to these equations we examine analytically and graphically the spatial and temporary evolution of particular solutions for simple initial conditions

generalized models as a universal approach to the analysis of nonlinear dynamical systems we present a universal approach to the investigation of the dynamics in generalized models in these models the processes that are taken into account are not restricted to specific functional forms therefore a single generalized models can describe a class of systems which share a similar structure despite this generality the proposed approach allows us to study the dynamical properties of generalized models efficiently in the framework of local bifurcation theory the approach is based on a normalization procedure that is used to identify natural parameters of the system the jacobian in a steady state is then derived as a function of these parameters the analytical computation of local bifurcations using computer algebra reveals conditions for the local asymptotic stability of steady states and provides certain insights on the global dynamics of the system the proposed approach yields a close connection between modelling and nonlinear dynamics we illustrate the investigation of generalized models by considering examples from three different disciplines of science a socioeconomic model of dynastic cycles in china a model for a coupled laser system and a general ecological food web

fractional exponential operators and nonlinear partial fractional differential equations in the weyl fractional derivatives in this article we introduce fractional exponential operator and give an integral representation for it moreover we obtain the formal solutions of some nonlinear partial fractional differential equations using this operator

multivariable lagrange expansion and generalization of carlitz srivastava mixed generating functions abstract families of mixed generating functions generalizing those of the carlitz srivastava type are derived here by applying methods based on the multivariable extension of the lagrange expansion it is also shown that the combination with techniques of operational nature offers a wide flexibility to explore a wealth of mixed bilateral generating functions for special functions with many variables

transformations of laguerre 2d polynomials with applications to quasiprobabilities laguerre 2d polynomials are defined and their properties are investigated the laguerre 2d functions introduced in 1 2 are related to the laguerre 2d polynomials in such a way that they also include the weight function for the orthonormalization of the laguerre 2d polynomials a one parameter group of transformations applicable to certain classes of polynomials and discrete sets of functions is investigated and applied in particular to hermite polynomials and to laguerre 2d polynomials these transformations allow us to represent the polynomials of the corresponding classes by superpositions of the same kind of polynomials with stretched arguments they contain limiting cases with delta functions and their derivatives and lead to regularized representations of the delta functions and their derivatives as demonstrated for hermite and laguerre 2d polynomials applications of the laguerre 2d polynomials and 2d functions and their transformations to problems of quantum optics as the representation of quasiprobabilities in the fock state basis and by normally and otherwise ordered moments are considered the inversion of these representations is obtained in all cases a restricted design of quasiprobabilities should become possible

generalized polynomials operational identities and their applications abstract it is shown that an appropriate combination of methods relevant to generalized operational calculus and to special functions can be a very useful tool to treat a large body of problems both in physics and mathematics we discuss operational methods associated with multivariable hermite laguerre legendre and other polynomials to derive a wealth of identities useful in quantum mechanics electromagnetism optics etc or to derive new identities between special functions as e g mehler or mixed type generating functions

second order exponential differential operator and generalized hermite polynomials abstract both univariate and multivariate generalized hermite polynomials are defined by introducing second order exponential differential operator corresponding probabilistic expressions are given explicitly based on those expectation expressions their generating functions recursion relations and other properties are derived conveniently in connection to stein s identities in particular orthogonality are investigated and associated expressions are presented accordingly additionally some other classical identities related to hermite polynomials are proved by an alternative way and some examples and remarks are presented

some properties of hermite based sheffer polynomials abstract in this paper the concepts and the formalism associated with monomiality principle and sheffer sequences are used to introduce family of hermite based sheffer polynomials some properties of hermite sheffer polynomials are considered further an operational formalism providing a correspondence between sheffer and hermite sheffer polynomials is developed furthermore this correspondence is used to derive several new identities and results for members of hermite sheffer family

a new approach to legendre truncated exponential based sheffer sequences via riordan arrays abstract the significance of multi variable special polynomials has been identified both in mathematical and applied frameworks the article aims to focus on a new class of 3 variable legendre truncated exponential based sheffer sequences and to investigate their properties by means of riordan array techniques the quasi monomiality of these sequences is studied within the context of riordan arrays these sequences are expressed in determinant forms by utilizing the relation between the sheffer sequences and riordan arrays certain special sheffer sequences are used to construct the legendre truncated exponential based chebyshev polynomials the same polynomials are used as base to introduce the hybrid classes involving the exponential polynomials and the euler polynomials of higher order as illustrative examples of the aforementioned general class of polynomials the shapes are shown and zeros are computed for these sequences by using mathematical software the main purpose is to demonstrate the advantage of using numerical investigation and computations to discover fascinating pattern of scattering of zeros through graphical representations

on bayesian testing of additive conjoint measurement axioms using synthetic likelihood this article introduces a bayesian method for testing the axioms of additive conjoint measurement the method is based on an importance sampling algorithm that performs likelihood free approximate bayesian inference using a synthetic likelihood to overcome the analytical intractability of this testing problem this new method improves upon previous methods because it provides an omnibus test of the entire hierarchy of cancellation axioms beyond double cancellation it does so while accounting for the posterior uncertainty that is inherent in the empirical orderings that are implied by these axioms together the new method is illustrated through a test of the cancellation axioms on a classic survey data set and through the analysis of simulated data

bayesian analysis of constrained parameter and truncated data problems using gibbs sampling abstract constrained parameter problems arise in a wide variety of applications including bioassay actuarial graduation ordinal categorical data response surfaces reliability development testing and variance component models truncated data problems arise naturally in survival and failure time studies ordinal data models and categorical data studies aimed at uncovering underlying continuous distributions in many applications both parameter constraints and data truncation are present the statistical literature on such problems is very extensive reflecting both the problems widespread occurrence in applications and the methodological challenges that they pose however it is striking that so little of this applied and theoretical literature involves a parametric bayesian perspective from a technical viewpoint this perhaps is not difficult to understand the fundamental tool for bayesian calculations in typical realistic models is multidimensional numerical integration which often is problem

bayesian estimation and model selection in ordered latent class models for polytomous items in a latent class irt model in which the latent classes are ordered on one dimension the class specific response probabilities are subject to inequality constraints the number of these inequality constraints increase dramatically with the number of response categories per item if assumptions like monotonicity or double monotonicity of the cumulative category response functions are postulated a markov chain monte carlo method the gibbs sampler can sample from the multivariate posterior distribution of the parameters under the constraints bayesian model selection can be done by posterior predictive checks and bayes factors a simulation study is done to evaluate results of the application of these methods to ordered latent class models in three realistic situations also an example of the presented methods is given for existing data with polytomous items it can be concluded that the bayesian estimation procedure can handle the inequality constraints on the parameters very well however the application of bayesian model selection methods requires more research

some properties of legendre gould hopper polynomials and operational methods abstract in this paper the author introduces the legendre gould hopper polynomials by combining the operational methods with the principle of monomiality generating functions series definition differential equation and certain other properties of legendre gould hopper polynomials are derived further operational representations of these polynomials are established which are used to get integral representations and expansion formulae certain summation formulae for these polynomials are also obtained

modeling symbiosis by interactions through species carrying capacities abstract we introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others the modeled entities can pertain to biological and ecological societies or to social economic and financial societies our model includes three basic types symbiosis with direct mutual interactions symbiosis with asymmetric interactions and symbiosis without direct interactions in all cases we provide a complete classification of all admissible dynamical regimes the proposed model of symbiosis turned out to be very rich as it exhibits four qualitatively different regimes convergence to stationary states unbounded exponential growth finite time singularity and finite time death or extinction of species

bayesian inference for stable distributions abstract very little work on stable distribution parameter estimation and inference appears in the literature due to the nonexistence of the probability density function this has led in particular to a dearth of bayesian work in this area but bayesian computation via markov chain monte carlo allows us to sample from the distribution of the parameters of the stable distributions by exploiting a particular mathematical representation involving the stable density

bayesian optimization of the estimation of the age composition of a fish population abstract to estimate the age distribution of a fish population a two phase stratified sample design is proposed bayesian methods are employed to determine a optimal estimators of the desired population proportions and b the optimal choice of second phase sample sizes subject to a fixed budget a summary of the results of some numerical examples is presented these examples demonstrate typical expected gains obtained by using the bayesian optima as compared to alternative choices of second phase sample sizes suggested in the substantive literature

monte carlo methods for bayesian analysis of constrained parameter problems summary constraints on the parameters in a bayesian hierarchical model typically make bayesian computation and analysis complicated posterior densities that contain analytically intractable integrals as normalising constants depending on the hyperparameters often make implementation of gibbs sampling or the metropolis algorithms difficult by using reweighting mixtures geyer 1995 we develop alternative simulation based methods to determine properties of the desired bayesian posterior distribution necessary theory and two illustrative examples are provided

on fractional calculus of a2n 1 x function abstract in this article we consider the a 2 n 1 x function the generalized airy function a 2 n 1 x 0 cos zx 1 n 1 z 2 n 1 2 n 1 dz and find some properties of this function and its derivatives these properties are included in integral representations for product of a 2 n 1 x function a 2 n 1 x wavelets and integral and series identities moreover the a 2 n 1 x polynomials are derived and bi orthogonality properties with their associated functions are obtained

symbolic operational images and decomposition formulas for hypergeometric functions based upon the classical derivative and integral operators we introduce a new operator which allows the derivation of new symbolic operational images for hypergeometric functions by means of these symbolic operational images a number of decomposition formulas involving quadruple series are then found other closely related results are also considered