cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

on minima of a functional of the gradient necessary conditions in this paper we propose a new method for texture segmentation based on the use of texture feature detectors derived from a decorrelation procedure of a modified version of a pseudo wigner distribution pwd the decorrelation procedure is accomplished by a cascade recursive least squared crls principal component pc neural network the goal is to obtain a more eacient analysis of images by combining the advantages of using a high resolution joint representation given by the pwd with an eaective adaptive principal component analysis pca through the use of feedforward neural networks 1999 elsevier science b v all rights reserved

approximate random variate generation from infinitely divisible distributions with applications to bayesian inference summary stochastic processes with independent increments play a central role in bayesian nonparametric inference the distributions of the increments of these processes aside from fixed points of discontinuity are infinitely divisible and their laplace and or fourier transforms in the levy representation are usually known conventional bayesian inference in this context has been limited largely to providing point estimates of the random quantities of interest although markov chain monte carlo methods have been used to obtain a fuller analysis in the context of dirichlet process priors in this paper we propose and implement a general method for simulating infinitely divisible random variates when their fourier or laplace transforms are available in the levy representation theoretical justification is established by proving a convergence theorem that is a sampling form of a classical theorem in probability the results provide a method for implementing bayesian nonparametric inference by using a wide range of stochastic processes as priors

a bayesian nonparametric approach to reliability abstract it is suggested that problems in a reliability context may be handled by a bayesian non parametric approach a stochastic process is defined whose sample paths may be assumed to be either increasing hazard rates or decreasing hazard rates by properly choosing the parameter functions of the process the posterior distribution of the hazard rates are derived for both exact and censored data bayes estimates of hazard rates c d f s densities and means are found under squared error type loss functions some simulation is done and estimates graphed to better understand the estimators finally estimates of the c d f from some data in a paper by kaplan and meier are constructed author

reml estimation for survival models with frailty a method of estimation for generalised mixed models is applied to the estimation of regression parameters in proportional hazards models for failure times when there are repeated observations of failure on each subject the subject effect is incorporated into the model as a random frailty term best linear unbiased predictors are used as an initial step in the computation of maximum likelihood and residual maximum likelihood estimates

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

on the minimum problem for a class of noncoercive nonconvex functionals we are concerned with the problem of existence of solutions to the variational problem min left int 0 r g t v t dt v in ac 0 r v r 0 right with only one fixed endpoint prescribed the map g colon 0 r times mathbb r to overline mathbb r is a normal integrand for which neither convexity nor superlinear growth conditions are assumed as an application we give an existence result for the radially symmetric variational problem min u in wuu b r int b r f pt mod x mod nabla u x a x u x dx where b r is the ball of mathbb r n centered at the origin and with radius r 0 the map f colon 0 r times 0 infty to overline mathbb r is a normal integrand and a in l 0 r again neither convexity nor superlinear growth conditions are made on f these kinds of problems with nonconvex lagrangians with respect to nabla u arise in different fields of mathematical physics such as optimal design and nonlinear elasticity

semiparametric bayesian analysis of survival data abstract this review article investigates the potential of bayes methods for the analysis of survival data using semiparametric models based on either the hazard or the intensity function the nonparametric part of every model is assumed to be a realization of a stochastic process the parametric part which may include a regression parameter or a parameter quantifying the heterogeneity of a population is assumed to have a prior distribution with possibly unknown hyperparameters careful applications of some recently popular computational tools including sampling based algorithms are used to find posterior estimates of several quantities of interest even when dealing with complex models and unusual data structures the methodologies developed herein are motivated and aimed at analyzing some common types of survival data from different medical studies here we focus on univariate survival data in the presence of fixed and time dependent covariates multiple event time data for repeated nonfatal events

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

nonparametric bayes estimators based on beta processes in models for life history data the article studies the problem of finding bayes estimators for cumulative hazard rates and related quantities w r t prior distributions that correspond to cumulative hazard rate processes with nonnegative independent increments a particular class of prior processes termed beta processes is introduced and is shown to constitute a conjugate class an important bonus of the approach based on cumulative hazards is that more complicated models for life history data than the simple life table situation can be treated for example time inhomogeneous markov chains we find posterior distributions and derive bayes estimators in such models and present a semiparametric bayesian analysis of the cox regression model

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

inferences on the association parameter in copula models for bivariate survival data we investigate two stage parametric and two stage semi parametric estimation procedures for the association parameter in copula models for bivariate survival data where censoring in either or both components is allowed we derive asymptotic properties of the estimators and compare their performance by simulations both parametric and semi parametric estimators of the association parameter are efficient at independence and the parameter estimates in the margins have high efficiency and are robust to misspecification of dependency structures in addition we propose a consistent variance estimator for the semi parametric estimator of the association parameter we apply the proposed methods to an aids data set for illustration

a theory of strongly continuous semigroups in terms of lie generators letxdenote a complete separable metric space and let c x denote the linear space of all bounded continuous real valued functions onx a semigrouptof transformations fromxintoxis said to be jointly continuous if the mapping t x t t xis jointly continuous from 0 xintox the lie generator of such a semigrouptis the linear operator in c x consisting of all ordered pairs f g such thatf g c x and for eachx x g x is the derivative at 0 off t x we completely characterize such lie generators and establish the canonical exponential formula for the original semigroup in terms of powers of resolvents of its lie generator the only topological notions needed in the characterization are two notions of sequential convergence pointwise and strict a sequence in c x converges strictly if the sequence is uniformly bounded in the supremum norm and converges uniformly on compact subsets ofx

a predictive approach to the analysis of designed experiments abstract viewing the analysis of designed experiments as a model selection problem we introduce the use of a predictive bayesian criterion in this context based on the predictive density of a replicate experiment pdre a calibration of the criterion is provided to assist in the model choice the relationships of the proposed criterion to other prevalent criteria such as aic bic and mallows s c p are given an information theoretic criterion based on the pdre s of two competing models is also introduced and compared with the usual f statistic for two nested models examples are given to illustrate the proposed methodology

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

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

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

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

on minima of radially symmetric functionals of the gradient where b is the unit ball of ir and the map u g r v is lower semicontinuous but not necessarily convex problems of this kind arise in domains as different as nonlinear elasticity fluid dynamics and shape optimization and either for the problem of the existence of solutions or for the properties of the relaxed problem are considered in l 7 in particular the very same problem is considered in 7 our results present the following features a no smoothness on g or h is required g is either a normal integrand or a lower semicontinuous function b the case h 0 is allowed in this case the assumption on g reduces for the existence of solutions to g being lower semicontinuous and growing at infinity as is to be expected for the uniqueness in addition to g being strictly increasing as is also to be expected c the case h au is allowed for a 0 our theorems yield at once existence and uniqueness of solutions with no further assumptions on g besides lower semicontinuity and growth at infinity

on use of the em algorithm for penalized likelihood estimation summary the em algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation this paper discusses properties of the em algorithm in such contexts concentrating on rates of conver gence and presents an alternative that is usually more practical and converges at least as quickly the em algorithm is a general approach to maximum likelihood estimation rather than a specific algorithm dempster et al 1977 discussed the method and derived basic properties demonstrating that a variety of procedures previously developed rather informally could be unified the common strand to problems where the approach is applicable is a notion of incomplete data this includes the conventional sense of missing data but is much broader than that the em algorithm demon strates its strength in situations where some hypothetical experiment yields data from which estimation is particularly convenient and economical the incomplete data actually at hand are regarded as observable functions of these complete data the resulting algorithms while usually slow to converge are often extremely simple and remain practical in large problems where no other approaches may be feasible dempster et al 1977 briefly refer to the use of the same approach to the problem of finding the posterior mode maximum a posteriori estimate in a bayesian estima

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

marginal bayesian semiparametric modeling of mismeasured multivariate interval censored data motivated by data gathered in an oral health study we propose a bayesian nonparametric approach for population averaged modeling of correlated time to event data when the responses can only be de

existence of solutions for a class of non convex minimum problems p celada1 s perrotta2 g treu3 1 dipartimento di scienze matematiche universita degli studi di trieste p le europa 1 i 34127 trieste italia e mail celada univ trieste it 2 dipartimento di matematica pura ed applicata g vitali universita degli studi di modena via campi 213 b i 41100 modena italia e mail perrotta c220 unimo it 3 dipartimento di matematica ed informatica universita degli studi di udine v le delle scienze 206 i 33100 udine italia e mail treu dimi uniud it

semiparametric bayesian analysis of multiple event time data abstract multiple event time data e g carcinogenic growths in different times and locations multiple attacks of cardiac arrest arise in various medical studies a bayesian analysis of such data based on proportional intensity model of multiple event time data is presented in this paper the bayesian structure is somewhat analogous to that used by kalbfleisch in a proportional hazard model an unobserved random frailty component is used in the proportional intensity model to take care of heterogeneity among the intensity processes in different subjects the monte carlo method of sampling from multivariate distributions the so called gibbs sampler is used to sample from the joint posterior distribution of the unknown parameters the methodology developed here is exemplified with the well known data set on rat tumors of gail santner and brown

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

bayesian nonparametric estimation for incomplete data via successive substitution sampling in the problem of estimating an unknown distribution function f in the presence of censoring one can use a nonparametric estimator such as the kaplan meier estimator or one can consider parametric modeling there are many situations where physical reasons indicate that a certain parametric model holds approximately in these cases a nonparametric estimator may be very inefficient relative to a parametric estimator on the other hand if the parametric model is only a crude approximation to the actual model then the parametric estimator may perform poorly relative to the nonparametric estimator and may even be inconsistent the bayesian paradigm provides a reasonable framework for this problem in a bayesian approach one would try to put a prior distribution on f that gives most of its mass to small neighborhoods of the entire parametric family we show that certain priors based on the dirichlet process prior can be used to accomplish this for these priors the posterior distribution of f given the censored data appears to be analytically intractable we provide a method for approximating this posterior distribution through the use of a successive substitution sampling algorithm we also show convergence of the algorithm

predictive model selection we consider the problem of selecting one model from a large class of plausible models a predictive bayesian viewpoint is advocated to avoid the specification of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model using criteria derived from a certain predictive density and a prior specification that emphasizes the observables we implement the proposed methodology for three common problems arising in normal linear models variable subset selection selection of a transformation of predictor variables and estimation of a parametric variance function interpretation of the relative magnitudes of the criterion values for various models is facilitated by a calibration of the criteria relationships between the proposed criteria and other well known criteria are examined

bayesian confidence intervals for the cross validated smoothing spline summary we consider the model y t g ti ei i 17 2 n where g t t 0 1 is a smooth function and the ei are independent n 0 a2 errors with g2 unknown the cross validated smoothing spline can be used to estimate g non parametrically from

existence and regularity of minimizers of nonconvex functionals depending onuand u abstract we consider variational problems of the form min f u x g x u x dx u u 0 h 1 0 wheref r n 0 is a possibly nonconvex function with quadratic growth at infinity andg x u is lipschitz continuous and strictly increasing decreasing inu we prove the existence and local lipschitz regularity of solutions for every boundary datumu0 h1 l on the basis of the structure of the epigraph of the convex envelope off

time dependent association measures for bivariate survival distributions abstract we propose time dependent association measures for application to bivariate survival analysis such association measures provide informative summaries for data on twins ophthalmic and auditory studies and for other matched pair designs we develop several desirable properties of time dependent association measures and study three measures motivated by these properties we examine the measures from a general bivariate survival perspective and for the proportional hazards frailty model we use monozygotic mz and dizygotic dz twin data from the danish twin registry to illustrate how these measures depend on the specification of the proportional hazards frailty model this model consists of two components a baseline hazard function and a frailty distribution we produce gamma and nonparametric maximum likelihood estimates of the frailty distribution and estimate a gompertz baseline hazard function for two of the measures a nonparametric estimate provides a comparison to the model based estim

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

a general framework for random effects survival analysis in the cox proportional hazards setting summary the use of random effects modeling in statistics has increased greatly in recent years the introduction of such modeling into event time analysis has proceeded more slowly however previously random effects models for survival data have either required assumptions regarding the form of the baseline hazard function or restrictions on the classes of models that can be fit in this paper we develop a method of random effect analysis of survival data the hierarchical cox model that is an extension of cox s original formulation in that the baseline hazard function remains unspecified this method also allows an arbitrary distribution for the random effects we accomplish this using markov chain monte carlo methods in a bayesian setting the method is illustrated with three models for a dataset with times to multiple occurrences of mammory tumors for 48 rats treated with a carcinogen and then randomized to either treatment or control this analysis is more satisfying than standard approaches such as studying the first event for each subject which does not fully use the data or assuming independence which in this case would overestimate the precision

some covariance models for longitudinal count data with overdispersion a family of covariance models for longitudinal counts with predictive covariates is presented these models account for overdispersion heteroscedasticity and dependence among repeated observations the approach is a quasi likelihood regression similar to the formulation given by liang and zeger 1986 biometrika 73 13 22 generalized estimating equations for both the covariate parameters and the variance covariance parameters are presented large sample properties of the parameter estimates are derived the proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures

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

model choice a minimum posterior predictive loss approach summary model choice is a fundamental and much discussed activity in the analysis of datasets nonnested hierarchical models introducing random effects may not be handled by classical methods bayesian approaches using predictive distributions can be used though the formal solution which includes bayes factors as a special case can be criticised we propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values we obtain this criterion by minimising posterior loss for a given model and then for models under consideration selecting the one which minimises this criterion for a broad range of losses the criterion emerges as a form partitioned into a goodness of fit term and a penalty term we illustrate its performance with an application to a large dataset involving residential property transactions

higher order semiparametric frequentist inference with the profile sampler we consider higher order frequentist inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution the first order validity of this procedure established by lee kosorok and fine 2005 is extended to second order validity in the setting where the infinite dimensional nuisance parameter achieves the parametric rate specifically we obtain higher order estimates of the maximum profile likelihood estimator and of the efficient fisher information moreover we prove that an e frequentist confidence interval for the parametric component at level alpha can be estimated by the alpha level credible set from the profile sampler with an error of order op n 1 as far as we are aware these results are the first higher order frequentist results obtained for semiparametric estimation a fully bayesian interpretation is established under a certain data dependent prior the theory is verified for three specific examples 1 introduction the focus of this paper is on higher order frequentist inference for the parametric component of a semiparametric model in addition to the d dimensional euclidean parameter semiparametric models also have an infinite dimensional parameter which is sometimes called the nuisance parameter a classic example is the cox proportional hazards model for right censored survival data 7 where interest focuses on the log hazard ratios for the regression covariate vector z the integrated baseline hazard function is the infinite dimensional nuisance parameter the involvement of an infinite dimensional nuisance parameter in semiparametric models generally complicates maximum likelihood inference for in particular estimating the limiting variance of n n 0 where 0 is the true value of usually requires estimating an infinite dimensional operator of course this is not a problem with the cox model since the profile likelihood for does not involve the nuisance parameter but for most semiparametric models this simplification of the profile likelihood does not occur and supported in part by grant ca075142

semiparametric bayesian analysis of structural equation models with fixed covariates latent variables play the most important role in structural equation modeling in almost all existing structural equation models sems it is assumed that the distribution of the latent variables is normal as this assumption is likely to be violated in many biomedical researches a semiparametric bayesian approach for relaxing it is developed in this paper in the context of sems with covariates we provide a general bayesian framework in which a semiparametric hierarchical modeling with an approximate truncation dirichlet process prior distribution is specified for the latent variables the stick breaking prior and the blocked gibbs sampler are used for efficient simulation in the posterior analysis the developed methodology is applied to a study of kidney disease in diabetes patients a simulation study is conducted to reveal the empirical performance of the proposed approach supplementary electronic material for this paper is available in wiley interscience at http www mrw interscience wiley com suppmat 1097 0258 suppmat

minimization of functionals of the gradient by baire s theorem we give sufficient conditions for the existence of solutions of the minimum problem cal p u 0 qquad hbox minimize quad int omega g du x dx quad u in u 0 w 0 1 p omega bbb r based on the structure of the epigraph of the lower convex envelope of g which is assumed be lower semicontinuous and to grow at infinity faster than the power p with p larger than the dimension of the space no convexity conditions are required on g and no assumptions are made on the boundary datum u 0 in w 0 1 p omega bbb r

lipschitzian semigroups and abstract functional differential equations abstract the paper is devoted to studying an abstract functional differential equation by a nonlinear semigroup approach we first prove in details the equivalence of the well posedness of an abstract functional differential equation and an associated abstract cauchy problem in the sense of strong solutions secondly a sufficient condition is derived for well posedness of the abstract functional differential equation thirdly we present principles of linearized stability for the abstract functional differential equation finally the results obtained are applied to a reaction diffusion equation with delays

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

bayesian analysis of proportional hazards models built from monotone functions we consider the usual proportional hazards model in the case where the baseline hazard the covariate link and the covariate coefficients are all unknown both the baseline hazard and the covariate link are monotone functions and thus are characterized using a dense class of such functions which arises upon transformation as a mixture of beta distribution functions we take a bayesian approach for fitting such a model since interest focuses more upon the likelihood we consider vague prior specifications including jeffreys s prior computations are carried out using sampling based methods model criticism is also discussed finally a data set studying survival of a sample of lung cancer patients is analyzed

model selection and accounting for model uncertainty in graphical models using occam s window abstract we consider the problem of model selection and accounting for model uncertainty in high dimensional contingency tables motivated by expert system applications the approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic p values leading to the selection of a single model inference is then conditional on the selected model the sampling properties of such a strategy are complex and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest in principle a panacea is provided by the standard bayesian formalism that averages the posterior distributions of the quantity of interest under each of the models weighted by their posterior model probabilities furthermore this approach is optimal in the sense of maximizing predictive ability but this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large often greater than 1

a novel dual approach to nonlinear semigroups of lipschitz operators lipschitzian semigroup refers to a one parameter semigroup of lipschitz operators that is strongly continuous in the parameter it contains c 0 semigroup nonlinear semigroup of contractions and uniformly k lipschitzian semigroup as special cases in this paper through developing a series of lipschitz dual notions we establish an analysis approach to lipschitzian semigroup it is mainly proved that a nonlinear lipschitzian semigroup can be isometrically embedded into a certain c 0 semigroup as application results two representation formulas of lipschitzian semigroup are established and many asymptotic properties of c 0 semigroup are generalized to lipschitzian semigroup

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

mixed poisson likelihood regression models for longitudinal interval count data summary in many longitudinal studies it is desired to estimate and test the rate over time of a particular recurrent event often only the event counts corresponding to the elapsed time intervals between each subject s successive observation times and baseline covariate data are available the intervals may vary substantially in length and number between subjects so that the corresponding vectors of counts are not directly comparable a family of poisson likelihood regression models incorporating a mixed random multiplicative component in the rate function of each subject is proposed for this longitudinal data structure a related empirical bayes estimate of random effect parameters is also described these methods are illustrated by an analysis of dyspepsia data from the national cooperative gallstone study

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

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

on semiparametric inference for modulated renewal processes summary modulated renewal processes suggested by d r cox give a flexible way to introduce dependencies into point processes we discuss the asymptotics of partial likelihood inference for modulated renewal processes when the random covariate for the process involves its history we show in some generality that the estimators of the regression parameter and the cumulative hazard have the same asymptotic distributions that they would have under the usual proportional hazards model even though the martingale justification for partial likelihood no longer applies because of a reordering of the time scale an example is given to illustrate the ideas a simulation study is presented to confirm the theoretical results

a dynamic frailty model for multivariate survival data summary we consider the statistical modeling of data consisting of many study subjects with serially correlated multivariate survival responses the ordinary frailty model handles the serial correlation in such data by introducing an unobserved multiplicative random effect term called the frailty in the hazard function the frailties are often assumed to be identical for the survival times from the same unit we have generalized the frailty model by allowing the frailties to vary stochastically with the indices we have proposed a simple scheme to update the dynamic frailties this approach assumes that the random effects are gamma distributed at each occurrence the two gamma parameters are updated according to the past information in terms of their marginal distributions the dynamic frailties form a multiplicative random walk this approach results in a tractable likelihood the small sample behavior of the mle is studied via a simulation experiment the model is then illustrated with a data set from an animal carcinogenesis experiment

a semiparametric model for regression analysis of interval censored failure time data left right and interval censored response time data arise in a variety of settings including the analyses of data from laboratory animal carcinogenicity experiments clinical trials and longitudinal studies for such incomplete data the usual regression techniques such as the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model are inapplicable in this paper we present a method for regression analysis which accommodates interval censored data we present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy a small animal tumorigenicity study and a clinical trial

dynamic modelling and penalized likelihood estimation for discrete time survival data summmary this paper describes a dynamic or state space approach for analyzing discrete time or grouped survival data simultaneous estimation of baseline hazard functions and of timevarying covariate effects is based on maximization of posterior densities or equivalently a penalized likelihood leading to kalman type smoothing algorithms data driven choice of unknown smoothing parameters is possible via an em type procedure the methods are illustrated by applications to real data