bayesian analysis of dichotomous quantal response models abstract qualitative response models qrm s are analyzed from the bayesian point of view using diffuse and informative prior distributions exact finite sample bayesian and large sample bayesian and non bayesian estimation results are compared in addition the paper provides 1 plots and discussion of the properties of likelihood functions for qrm s 2 posterior distributions for logit models derivatives and elasticities 3 bayesian prediction procedures for qrm s 4 new estimates for the median and other fractiles of the logistic distribution 5 posterior odds ratios for model selection problems and 6 comparisons of two alternative monte carlo numerical integration procedures it is concluded that asymptotic approximations are not accurate for small to moderate sized samples even when only a single input variable is used and that operational bayesian methods are available for providing both exact small sample and large sample approximate inferences for drm s

reconstructing an unknown time dependent function in the boundary conditions of a parabolic pde this work investigates the parabolic inverse problem of reconstructing an unknown time dependent function in the boundary conditions from additional terminal integral or point observations a numerical scheme is developed for obtaining an approximate solution for this problem the method consists of reducing the solution of the inverse problem to a system of integral equations the properties of sinc function are then utilized for replacing the resulting integral equations by a system of linear algebraic equations several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method

bayesian predictive inference for time series count data summary correlated count data arise often in practice especially in repeated measures situations or instances in which observations are collected over time in this paper we consider a parametric model for a time series of counts by constructing a likelihood based version of a model similar to that of zeger 1988 biometrika75 621 629 the model has the advantage of incorporating both over dispersion and autocorrelation we consider a bayesian approach and propose a class of informative prior distributions for the model parameters that are useful for prediction the prior specification is motivated from the notion of the existence of data from similar previous studies called historical data which is then quantified into a prior distribution for the current study we derive the bayesian predictive distribution and use a bayesian criterion called the predictive l measure for assessing the predictions for a given time series model the distribution of the predictive l measure is also derived which will enable us to compare the predictive ability for each model under consideration our methodology is motivated by a real data set involving yearly pollen counts which is examined in some detail

when should epidemiologic regressions use random coefficients summary regression models with random coefficients arise naturally in both frequentist and bayesian approaches to estimation problems they are becoming widely available in standard computer packages under the headings of generalized linear mixed models hierarchical models and multilevel models i here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed effects models now prevalent in epidemiology the argument invokes an antiparsimony principle attributed to l j savage which is that models should be rich enough to reflect the complexity of the relations under study it also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything often used to justify parsimony regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable selection algorithms and their attendant distortion of uncertainty assessments these points are illustrated with an analysis of data on diet nutrition and breast cancer

predictive variable selection in generalized linear models here we extend predictive method for model selection of laud and ibrahim to the generalized linear model this prescription avoids the need to directly specify prior probabilities of models and prior densities for the parameters instead a prior prediction for the response induces the required priors we propose normal and conjugate priors for generalized linear models each using a single prior prediction for the mean response to induce suitable priors for each variable subset model in this way an informative prior is used to select a subset of variables in addition to producing a ranking of models by size of the predictive criterion the standard deviation of the criterion is used as a calibration number to produce a set of equally good models a straightforward markov chain monte carlo algorithm is used to accomplish the necessary computations we illustrate this method with real and simulated datasets and compare results with the bayes factors and the akaike information and bayes information model

statistical methods for eliciting probability distributions elicitation is a key task for subjectivist bayesians although skeptics hold that elicitation cannot or perhaps should not be done in practice it brings statisticians closer to their clients and subject matter expert colleagues this article reviews the state of the art reflecting the experience of statisticians informed by the fruits of a long line of psychological research into how people represent uncertain information cognitively and how they respond to questions about that information in a discussion of the elicitation process the first issue to address is what it means for an elicitation to be successful that is what criteria should be used our answer is that a successful elicitation faithfully represents the opinion of the person being elicited it is not necessarily true in some objectivistic sense and cannot be judged in that way we see that elicitation as simply part of the process of statistical modeling indeed in a hierarchical model at which point the likelihood ends and the pr

assessing influence on regression coefficients in generalized linear models summary suggested diagnostics for influence on the estimated regression coefficients in a generalized linear model have generally approximated the effect of deleting a single case we apply the local influence method of cook 1986 to assess the effect of small perturbations of the data including the vector of responses case weights explanatory variables and the components of one case the resulting diagnostics allow one to check for different kinds of influence and may give insight into its workings two examples illustrate some of the diagnostics

an stable numerical algorithm for identifying the solution of an inverse problem in this paper we consider an inverse parabolic problem with space dependent coefficient mathematical model of the problem consists a parabolic equation in which the condition is unknown at the one of the boundary and to be determined from an overspecified data measured at an interior point inside the body uniqueness of the solution of under study inverse problem will be shown our concern for the numerical procedure for this inverse problem is based on a finite differences scheme stability conditions for numerical solution to inverse problem are stated the approach of proposed method is approximated the unknown function by a set of chebyshev polynomials where the unknown set of expansion coefficients in unknown function are determined from the minimizing the least squares method some numerical examples will be given in the last section

using historical controls to adjust for covariates in trend tests for binary data abstract historical data often play an important role in helping interpret the results of a current study this article is motivated primarily by one specific application the analysis of data from rodent carcinogenicity studies by proposing a suitable informative prior distribution on the relationship between control outcome data and covariates we derive modified trend test statistics that incorporate historical control information to adjust for covariate effects frequentist and fully bayesian methods are presented and novel computational techniques are developed to compute the test statistics several attractive theoretical and computational properties of the proposed priors are derived in addition a semiautomatic elicitation scheme for the priors is developed our approach is used to modify a widely used prevalence test for carcinogenicity studies the proposed methodology is applied to data from a national toxicology program carcinogenicity experiment and is shown to provide helpful insight on t

nonlinear experiments optimal design and inference based on likelihood abstract nonlinear experiments involve response and regressors that are connected through a nonlinear regression type structure examples of nonlinear models include standard nonlinear regression logistic regression probit regression poisson regression gamma regression inverse gaussian regression and so on the fisher information associated with a nonlinear experiment is typically a complex nonlinear function of the unknown parameter of interest as a result we face an awkward situation designing an efficient experiment will require knowledge of the parameter but the purpose of the experiment is to generate data to yield parameter estimates our principal objective here is to investigate proper designing of nonlinear experiments that will let us construct efficient estimates of parameters we focus our attention on a very general nonlinear setup that includes many models commonly encountered in practice the experiments considered have two fundamental stages a static design in the initial stage

finite volume method for solving a one dimensional parabolic inverse problem in this paper finite volume method is used to solve a one dimensional parabolic inverse problem with source term and neumann boundary conditions for the first time some advantages of this approach are developing difference schemes and maintaining certain properties of the physics of the problems especially for the treatment of the source term and the unknown boundary conditions numerical results show that our method is more effective

identifying a control function in parabolic partial differential equations from overspecified boundary data determination of an unknown time dependent function in parabolic partial differential equations plays a very important role in many branches of science and engineering in the current investigation the adomian decomposition method is used for finding a control parameter p t in the quasilinear parabolic equation u t u x x p t email protected in 0 1 x 0 t with known initial and boundary conditions and subject to an additional condition in the form of 0 1k x u x t dx e t email protected email protected t which is called the boundary integral overspecification the main approach is to change this inverse problem to a direct problem and then solve the resulting equation using the well known adomian decomposition method the decomposition procedure of adomian provides the solution in a rapidly convergent series where the series may lead to the solution in a closed form furthermore due to the rapid convergence of adomian s method a truncation of the series solution with sufficiently large number of implemented components can be considered as an accurate approximation of the exact solution this method provides a reliable algorithm that requires less work if compared with the traditional techniques some illustrative examples are presented to show the efficiency of the presented method

bayesian semiparametric roc curve estimation and disease diagnosis we develop a novel semiparametric modeling framework involving mixtures of polya trees for screening data with the dual purpose of diagnosing infection or disease status and of assessing the accuracy of continuous diagnostic measures in this framework we obtain i predictive probabilities of disease based on continuous diagnostic test outcomes in conjunction with other information including relevant covariates and results from one or more independent binary diagnostic tests an example would be the modeling of a serum enzyme linked immunosorbent assay elisa procedure for detecting antibodies to an infectious agent when used in conjunction with culture for antigen detection our second goal is to ii characterize measures of diagnostic performance of continuous tests by estimating receiver operating characteristic curves and area under the curve primarily when such extra information is available when true disease status is unknown parametric and nonparametric analyses require sufficient separation between the distributions of outcome values for the diseased and nondiseased populations however this overlap becomes less problematic when additional information in the form of either an informative prior that is based on real preferably data based scientific input or when additional information or both are available the additional information can be used to distinguish diseased from nondiseased individuals we present an example using simulated data that illustrates this point we also present an example involving data from an animal health survey for johne s disease where the performance of a serum elisa is evaluated using additional information obtained from fecal culture issues related to identifiability and partial identifiability are also discussed

application of sinc collocation method for solving an inverse problem in this article the identification of an unknown time dependent source term in an inverse problem of parabolic type with nonlocal boundary conditions is considered the main approach is to change the inverse problem to a system of volterra integral equations the resulting integral equations are convolution type which by using sinc collocation method are replaced by a system of linear algebraic equations the convergence analysis is included and it is shown that the error in the approximate solution is bounded in the infinity norm by the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system to show the efficiency of the present method an example is presented the method is easy to implement and yields very accurate results

an inverse heat conduction problem with a nonlinear source term abstract in this paper the nonlinear problem of an inhomogeneous heat equation with linear boundary conditions will be considered the surface heat flux history of a heated conducting body will be identified the approach of the proposed method is to approximate the unknown function using linear polynomial pieces which are determined consecutively from the solution of the minimization problem on the basis of overspecified data some numerical examples will also be presented

specifying a prior distribution in structured regression problems abstract the problem of assessing the prior mean and covariance matrix of the vector of regression coefficients in the normal multiple linear regression model is considered arguments are advanced for using expectations regarding the form of the design matrix in specifying the prior for problems with a structure that can aid in specifying these expectations this is illustrated with models having second order terms an example is given

multiple imputation of industry and occupation codes in census public use samples using bayesian logistic regression abstract we describe methods used to create a new census data base that can be used to study comparability of industry and occupation classification systems this project represents the most extensive application of multiple imputation to date and the modeling effort was considerable as well hundreds of logistic regressions were estimated one goal of this article is to summarize the strategies used in the project so that researchers can better understand how the new data bases were created another goal is to show how modifications of maximum likelihood methods were made for the modeling and imputation phases of the project to multiply impute 1980 census comparable codes for industries and occupations in two 1970 census public use samples logistic regression models were estimated with flattening constants for many of the regression models considered the data were too sparse to support conventional maximum likelihood analysis so some alternative had to be employed these methods solve existence and

a new perspective on priors for generalized linear models abstract this article deals with specifications of informative prior distributions for generalized linear models our emphasis is on specifying distributions for selected points on the regression surface the prior distribution on regression coefficients is induced from this specification we believe that it is inherently easier to think about conditional means of observables given the regression variables than it is to think about model dependent regression coefficients previous use of conditional means priors seems to be restricted to logistic regression with one predictor variable and to normal theory regression we expand on the idea of conditional means priors and extend these to arbitrary generalized linear models we also consider data augmentation priors where the prior is of the same form as the likelihood we show that data augmentation priors are special cases of conditional means priors with current monte carlo methodology such as importance sampling and gibbs sampling our priors result in

a numerical method for solving of a nonlinear inverse diffusion problem in this paper we will first study the existence and uniqueness of the solution for a one dimensional nonlinear inverse diffusion problem via an auxiliary problem and the schauder fixed point theorem furthermore a numerical algorithm based on the finite difference method and the least squares scheme for solving a nonlinear inverse problem is proposed at the beginning of the numerical algorithm taylor s series expansion is employed to linearize nonlinear terms and then the finite difference method is used to discretize the problem domain the present approach is to rearrange the matrix forms of the differential governing equations and estimate the unknown diffusion coefficient the least squares method is adopted to find the solution it is assumed that no prior information is available on the functional form of the unknown diffusion coefficient in the present study and thus it is classified as the function estimation in inverse calculation results show that an excellent estimation on the diffusion coefficient can be obtained within a couple of minutes of cpu time on a pentium iv 2 4ghz pc

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

a bayesian goodness of fit test and semiparametric generalization of logistic regression with measurement data summary logistic regression is a popular tool for risk analysis in medical and population health science with continuous response data it is common to create a dichotomous outcome for logistic regression analysis by specifying a threshold for positivity fitting a linear regression to the nondichotomized response variable assuming a logistic sampling model for the data has been empirically shown to yield more efficient estimates of odds ratios than ordinary logistic regression of the dichotomized endpoint we illustrate that risk inference is not robust to departures from the parametric logistic distribution moreover the model assumption of proportional odds is generally not satisfied when the condition of a logistic distribution for the data is violated leading to biased inference from a parametric logistic analysis we develop novel bayesian semiparametric methodology for testing goodness of fit of parametric logistic regression with continuous measurement data the testing procedures hold for any cutoff threshold and our approach simultaneously provides the ability to perform semiparametric risk estimation bayes factors are calculated using the savage dickey ratio for testing the null hypothesis of logistic regression versus a semiparametric generalization we propose a fully bayesian and a computationally efficient empirical bayesian approach to testing and we present methods for semiparametric estimation of risks relative risks and odds ratios when parametric logistic regression fails theoretical results establish the consistency of the empirical bayes test results from simulated data show that the proposed approach provides accurate inference irrespective of whether parametric assumptions hold or not evaluation of risk factors for obesity shows that different inferences are derived from an analysis of a real data set when deviations from a logistic distribution are permissible in a flexible semiparametric framework

bayesian inference for a generalized population attributable fraction the impact of early vitamin a levels on chronic lung disease in very low birthweight infants in this paper the population attributable fraction is studied using the potential responses framework of rubin s causal model this framework facilitates definition of a general measure of population attributable effect which can accommodate many valued and multivariate exposures as well as many valued responses inferential issues are considered from the bayesian perspective finite population inference is emphasized with inference in the case of a fully observed population given particular attention the key inferential issue concerns computation of the posterior distribution of unobserved potential responses given observed responses exposures and covariates a dependency on model parameters about which observed data are uninformative is highlighted and this reflects the unobservable nature of causal effects in an application to a small cohort study of respiratory problems in very low birthweight infants posterior inferences were found to be insensitive to assumptions concerning the joint distribution of potential response variables but sensitive to the assumption of weak ignorability a weaker form of the more familiar assumption of no confounding by omitted covariates in a model based set up the weak ignorability assumption is identified with setting a model parameter to zero and consequently uncertainty concerning this assumption can in principle be handled via the prior distribution for the model parameters

a new convex edge preserving median prior with applications to tomography in a bayesian tomographic maximum a posteriori map reconstruction an estimate of the object f is computed by iteratively minimizing an objective function that typically comprises the sum of a log likelihood data consistency term and prior or penalty term the prior can be used to stabilize the solution and to also impose spatial properties on the solution one such property preservation of edges and locally monotonic regions is captured by the well known median root prior mrp an empirical method that has been applied to emission and transmission tomography we propose an entirely new class of convex priors that depends on f and also on m an auxiliary field in register with f we specialize this class to our median prior mp the approximate action of the median prior is to draw at each iteration an object voxel toward its own local median this action is similar to that of mrp and results in solutions that impose the same sorts of object properties as does mrp our map method is not empirical since the problem is stated completely as the minimization of a joint on f and m objective we propose an alternating algorithm to compute the joint map solution and apply this to emission tomography showing that the reconstructions are qualitatively similar to those obtained using mrp

dynamic generalized linear models and bayesian forecasting abstract dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters this leads to the calculation of closed standard form predictive distributions for forecasting and model criticism the structure of the models depends on the time evolution of underlying state variables and the feedback of observational information to these variables is achieved using linear bayesian prediction methods data analytic aspects of the models concerning scale parameters and outliers are discussed and some applications are provided dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and

numerical solution of one dimensional parabolic inverse problem this paper is concerned with numerical techniques for the solution of a one dimensional parabolic inverse problem with a control parameter the discrete approximation of the problem is based on the finite difference schemes these techniques are presented for identifying the control parameter which produces at each time a desired temperature at a given point in a spatial domain the main idea behind the finite difference methods for obtaining the solution of a given partial differential equation is to approximate the derivatives appearing in the equation by a set of values of the function at a selected number of points the most usual way to generate these approximations is through the use of taylor series the methods developed here are based on the modified equivalent partial differential equation as described by warming and hyett j comput phys 14 2 1974 159 this approach allows the simple determination of the theoretical order of accuracy thus allowing methods to be compared with one another also from the truncation error of the modified equivalent equation it is possible to eliminate the dominant error terms associated with the finite difference equations that contain free parameters weights thus leading to more accurate methods the results of a numerical experiment are presented and accuracy and the central processor cpu time needed for the parabolic inverse problem are discussed

computational methods using a bayesian hierarchical generalized linear model abstract suppose we observe y 1 yn where yi has the exponential density f yi i exp i yi i b i c yi i the parameters of interest are not the canonical parameters i but the means i b i in the usual generalized linear model glm setup suppose the means 1 n are believed to satisfy a specific p dimensional glm g i xt i where the link function g and the regression coefficients xi are known and the regression vector is unknown two problems of interest are the assessment of the goodness of fit of the glm and the estimation of the means i the approach to these problems is by the use of a bayesian two stage prior distribution a generalization of a model used by lindley and smith 1972 in the normal mean estimation problem at the first stage of the model we assign independent conjugate distributions to 1 n where the prior means of the i satisfy the glm there are p 1 unknown hyperparameters in this specification the elements of the regression

binomial regression with misclassification motives par l etude de l infection a virus papilloma humain chez la femme nous presentons une analyse de regression binomiale bayesienne dans laquelle la reponse est sujette a un processus d erreur de classement sans contrainte notre approche iterative fournit des inferences pour les parametres qui decrivent la relation des covariables avec la reponse et pour les probabilites d erreur de classement de plus notre approche s applique a n importe quel modele lineaire generalise pertinent rendant possible la selection de modele et il est immediat de l etendre a un contexte multinomial

putting background information about relative risks into conjugate prior distributions in bayesian and empirical bayes analyses of epidemiologic data the most easily implemented prior specifications use a multivariate normal distribution for the log relative risks or a conjugate distribution for the discrete response vector this article describes problems in translating background information about relative risks into conjugate priors and a solution traditionally conjugate priors have been specified through flattening constants an approach that leads to conflicts with the true prior covariance structure for the log relative risks one can however derive a conjugate prior consistent with that structure by using a data augmentation approximation to the true log relative risk prior although a rescaling step is needed to ensure the accuracy of the approximation these points are illustrated with a logistic regression analysis of neonatal death risk

on bayesian analysis of generalized linear models using jeffreys s prior abstract generalized linear models glm s have proved suitable for modeling various kinds of data consisting of exponential family response variables with covariates bayesian analysis of such data requires specification of a prior for the regression parameters in the model used uniform priors are very commonly used as conventional noninformative priors we show however that uniform priors for glm s can lead to improper posterior distributions thus making them undesirable alternative reference priors may be constructed from jeffreys s rule in this article we give two theorems that support the use of jeffreys s priors for glm s with intrinsically fixed or known scale parameters these theorems provide i sufficient and ii necessary and sufficient conditions for the propriety of the i posterior and ii prior distributions as well as for the existence of moments implications of these theorems for some commonly used glm s are discussed finally an illustrative example is given for the binomial

generalized conjugate priors for bayesian analysis of risk and survival regressions le choix pour les analyses bayesiennes portant sur les risques relatifs de distributions a priori conjuguees peut etre tres limitant du fait que la forme de cette distribution depend du parametre de valeur centrale cependant en introduisant separement ce parametre on generalise ces distributions a priori ce qui permet de modeliser une tres large palette d opinions a priori tout en conservant les proprietes de simplicite des calculs propres aux analyses conjuguees cet article illustre les resultats fournis par ces analyses avec des conjuguees generalisees a partir d exemples sur des enquetes cas x temoins dont le but etait d etudier le lien des amenagements en c bles electriques wire codes en zone residentielle et des champs magnetiques avec les cas de leucemie chez l enfant

scale parameters a bayesian treatment a definition of a scale parameter is given which includes the usual definition of a scale parameter in the exponential family some suggestions for the estimation of and approximations to the marginal posterior distribution of a vector valued parameter of primary interest are made in particular the possibility of a 2 approximation to the posterior distribution of leading to h p d regions for based on the f distribution is explored two examples are discussed where observations are from a normal and gamma distribution

prior elicitation variable selection and bayesian computation for logistic regression models summary bayesian selection of variables is often difficult to carry out because of the challenge in specifying prior distributions for the regression parameters for all possible models specifying a prior distribution on the model space and computations we address these three issues for the logistic regression model for the first we propose an informative prior distribution for variable selection several theoretical and computational properties of the prior are derived and illustrated with several examples for the second we propose a method for specifying an informative prior on the model space and for the third we propose novel methods for computing the marginal distribution of the data the new computational algorithms only require gibbs samples from the full model to facilitate the computation of the prior and posterior model probabilities for all possible models several properties of the algorithms are also derived the prior specification for the first challenge focuses on the observables in that the elicitation is based on a prior prediction yo for the response vector and a quantity ao quantifying the uncertainty in yo then yo and ao are used to specify a prior for the regression coefficients semi automatically examples using real data are given to demonstrate the methodology

a galerkin procedure for the diffusion equation subject to the specification of mass continuous and discrete galerkin procedures are derived and analyzed for the numerical solution of the diffusion equation u 1 u xx 0 x 1 0 t leqq t u x 0 f x u x 1 t g t and the specification of the mass int 0 b u x t dx m t 0 b 1 some numerical experiments are also presented

bayesian estimation of item response curves item response curves for a set of binary responses are studied from a bayesian viewpoint of estimating the item parameters for the two parameter logistic model with normally distributed ability restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the em algorithm the procedure is illustrated by data from a mathematics test

numerical techniques for a parabolic equation subject to an overspecified boundary condition an inverse problem concerning diffusion equation with a control parameter is considered a new numerical scheme is developed for obtaining approximate solutions to an initial boundary value problem for the semi linear parabolic partial differential equation subject to an overspecified boundary condition the space derivative in the pde is approximated by finite difference replacements the solution of the resulting system of first order ordinary differential equations odes satisfies a recurrence relation which involves a matrix exponential function the accuracy in time can be controlled by choosing several pade approximants to replace this matrix exponential term a numerical technique is developed to compute the required solution using a splitting method leading to algorithms for sequential and parallel implementation the algorithms are tested on a model problem from the literature the results of a numerical experiment are presented and the accuracy and central processor cpu time needed for this inverse problem are discussed

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

data augmentation priors for bayesian and semi bayes analyses of conditional logistic and proportional hazards regression data augmentation priors have a long history in bayesian data analysis formulae for such priors have been derived for generalized linear models but their accuracy depends on two approximation steps this note presents a method for using offsets as well as scaling factors to improve the accuracy of the approximations in logistic regression this method produces an exceptionally simple form of data augmentation that allows it to be used with any standard package for conditional logistic or proportional hazards regression to perform bayesian and semi bayes analyses of matched and survival data the method is illustrated with an analysis of a matched case control study of diet and breast cancer

plane answers to complex questions the theory of linear models providing a wide ranging introduction to the use of linear models in analyzing data this text presents a vector space and projections approach to the subject the topics covered include anova estimation hypothesis testing multiple comparison regression analysis and experimental design also covered are testing for lack of fit models with singular covariance matrices variance component estimation best linear prediction colinearity and variable selection

a variational sinc collocation method for strong coupling problems we have devised a variational sinc collocation method vscm which can be used to obtain accurate numerical solutions to many strong coupling problems sinc functions with an optimal grid spacing are used to solve the linear and nonlinear schrodinger equations and a lattice 4 model in 1 1 our results indicate that errors decrease exponentially with the number of grid points and that a limited numerical effort is needed to reach high precision

mixtures of g priors in generalized linear models abstractmixtures of zellner s g priors have been studied extensively in linear models and have been shown to have numerous desirable properties for bayesian variable selection and model averaging

sample size calculations for surveys to substantiate freedom of populations from infectious agents summary we develop a bayesian approach to sample size computations for surveys designed to provide evidence of freedom from a disease or from an infectious agent a population is considered disease free when the prevalence or probability of disease is less than some threshold value prior distributions are specified for diagnostic test sensitivity and specificity and we test the null hypothesis that the prevalence is below the threshold sample size computations are developed using hypergeometric sampling for finite populations and binomial sampling for infinite populations a normal approximation is also developed our procedures are compared with the frequentist methods of cameron and baldock 1998a preventive veterinary medicine34 1 17 using an example of foot and mouth disease user friendly programs for sample size calculation and analysis of survey data are available at http www epi ucdavis edu diagnostictests

the focused information criterion a variety of model selection criteria have been developed of general and specific types most of these aim at selecting a single model with good overall properties for example formulated via average prediction quality or shortest estimated overall distance to the true model the akaike the bayesian and the deviance information criteria along with many suitable variations are examples of such methods these methods are not concerned however with the actual use of the selected model which varies with context and application the present article takes the view that the model selector should instead focus on the parameter singled out for interest in particular a model that gives good precision for one estimand may be worse when used for inference for another estimand we develop a method that for a given focus parameter estimates the precision of any submodel based estimator the framework is that of large sample likelihood inference using an unbiased estimate of limiting risk we propose a foc

modeling of multivariate monotone disease processes in the presence of misclassification motivated by a longitudinal oral health study the signal tandmobiel study we propose a multivariate binary inhomogeneous markov model in which unobserved correlated response variables are subject to an unconstrained misclassification process and have a monotone behavior the multivariate baseline distributions and markov transition matrices of the unobserved processes are defined as a function of covariates through the specification of compatible full conditional distributions distinct misclassification models are discussed in all cases the possibility that different examiners were involved in the scoring of the responses of a given subject across time is taken into account a full bayesian implementation of the model is described and its performance is evaluated using simulated data we provide theoretical and empirical evidence that the parameters can be estimated without any external information about the misclassification parameters finally the analyses of the motivating study are presented a

identification of time dependent source terms and control parameters in parabolic equations from overspecified boundary data abstract this paper presents a semigroup approach for inverse source problems for the abstract heat equation when the measured output data is given in subject to the integral overspecification over the spatial domain the existence of a solution to the inverse source problem is shown in appropriate function spaces and a representation formula for the solution is proposed such representation permits the derivation of sufficient conditions for the uniqueness of the solution also an approximation method based on the optimal homotopy analysis method oham is designed and the error estimates are discussed using graphical analysis moreover we conjecture that our approach can be applied for the determination of a control parameter in an inverse problem with integral overspecialization data the proposed algorithm is examined through various numerical examples for the reconstruction of continuous sources and the determination of a control parameter in parabolic equations the accuracy and stability of the method are discussed and compared with several finite difference techniques computational results show efficiency and high accuracy of the proposed algorithm