correlated random measures abstractwe develop correlated random measures random measures where the atom weights can exhibit a flexible pattern of dependence and use them to develop powerful hierarchical bayesian nonparametric models hierarchical bayesian nonparametric models are usually built from completely random measures a poisson process based construction in which the atom weights are independent completely random measures imply strong independence assumptions in the corresponding hierarchical model and these assumptions are often misplaced in real world settings correlated random measures address this limitation they model correlation within the measure by using a gaussian process in concert with the poisson process with correlated random measures for example we can develop a latent feature model for which we can infer both the properties of the latent features and their dependency pattern we develop several other examples as well we study a correlated random measure model of pairwise count data we derive an eff

bayes estimation from a markov renewal process a procedure for bayes nonparametric estimation from a markov renewal process is developed it is based on a conjugate class of a priori distributions on the parameter space of semi markov transition distributions the class is characterized by a dirichlet family of distributions for random markov matrices and a beta family of levy processes for random cumulative hazard functions the main result is the derivation of the posterior law from an observation of the markov renewal process over a period of time

on inconsistent bayes estimates of location on montre que dans certaines situations relativement naturelles les estimateurs de position bayesiens sont inconsistants

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

a bernstein von mises theorem in the nonparametric right censoring model in the recent bayesian nonparametric literature many examples have been reported in which bayesian estimators and posterior distributions do not achieve the optimal convergence rate indicating that the bernstein von mises theorem does not hold in this article we give a positive result in this direction by showing that the bernstein von mises theorem holds in survival models for a large class of prior processes neutral to the right we also show that for an arbitrarily given convergence rate n with 0 1 2 a prior process neutral to the right can be chosen so that its posterior distribution achieves the convergence rate n

nonparametric bayesian estimators for counting processes this paper is concerned with nonparametric bayesian inference of the aalen s multiplicative counting process model for a desired nonparametric prior distribution of the cumulative intensity function a class of l6vy processes is considered and it is shown that the class of l6vy processes is conjugate for the multiplicative counting process model and formulas for obtaining a posterior process are derived finally our results are applied to several practically important models such as one point processes for right censored data poisson processes and markov processes

nonparametric inference for a class of semi markov processes with censored observations a class of semi markov models those which have proportional hazards and which are forward going if state can be reached from i then i cannot be reached from j are shown to fit into the multiplicative intensity model of counting processes after suitable random time changes standard large sample results for counting processes following this multiplicative model can therefore be used to make inferences on the above class of semi markov models including the case where observations may be censored large sample results for a fourstate model used in clinical trials are presented

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

bayesian poisson process partition calculus with an application to bayesian levy moving averages this article develops and describes how to use results concerning disintegrations of poisson random measures these results are fashioned as simple tools that can be tailor made to address inferential questions arising in a wide range of bayesian nonparametric and spatial statistical models the poisson disintegration method is based on the formal statement of two results concerning a laplace functional change of measure and a poisson palm fubini calculus in terms of random partitions of the integers 1 n the techniques are analogous to but much more general than techniques for the dirichlet process and weighted gamma process developed in ann statist 12 1984 351 3571 and ann inst statist math 41 1989 227 245 in order to illustrate the flexibility of the approach large classes of random probability measures and random hazards or intensities which can be expressed as functionals of poisson random measures are described we describe a unified posterior analysis of classes of discrete random probability which identifies and exploits features common to all these models the analysis circumvents many of the difficult issues involved in bayesian nonparametric calculus including a combinatorial component this allows one to focus on the unique features of each process which are characterized via real valued functions h the applicability of the technique is further illustrated by obtaining explicit posterior expressions for levy cox moving average processes within the general setting of multiplicative intensity models in addition novel computational procedures similar to efficient procedures developed for the dirichlet process are briefly discussed for these models

dynamic versus thermodynamic approach to non canonical equilibrium abstract we study the dynamic and thermodynamic origin of non canonical equilibria and we discuss their connection with the generalized central limit theorem and the micro canonical boltzmann principle we reach the conclusion that the zeroth law of thermodynamics and the boltzmann principle are fulfilled thanks to an apparent fault turned into a benefit the dynamic approach can only produce a truncated form of inverse power law equilibrium

beta stacy processes and a generalization of the polya urn scheme beta stacy process is dened it is shown to be neutral to the right and a generalization of the dirichlet process the posterior distribution is also a beta stacy process given independent and identically distributed iid observations possibly with right censoring from f a generalization of the p olya urn scheme is introduced which characterizes the discrete betastacy process 1 introduction let f be the space of cumulative distribution functions cdfs oni0 1e this paper considers placing a probability distribution on f by dening a stochastic process f onei0 1e ae where a is the borel eld of subsets such that fe0e d 0 a s f is a s nondecreasing a s right continuous and lim t 1 fete d 1 a s thus with probability 1 the sample paths of f are cdf s previous work includes the dirichlet process ferguson 1973 1974 neutral to the right processes doksum 1974 the extended gamma process dykstra and laud 1981 the beta process hjort 1990 and p olya trees lavine 1992 1994 mauldin sudderth and williams 1992 the purpose of this paper is twofold 1 to introduce a new stochastic process which generalizes the dirichlet process in that more exible prior beliefs are able to be represented and unlike the dirichlet process is conjugate to right censored observations and 2 to introduce a generalization of the p olyaurn scheme in order to characterize the discrete time version of the process the property of conjugacy to right censored observations is also a feature of the beta process however with the beta process the statistician is required to consider hazard rates and cumulative hazards when constructing the prior the beta stacy process only requires considerations on the distribution of the observations the process is shown to be neutral to the right the present paper is restricted to considering the estimation of an unknown cdf oni0 1e although it is trivially extended to includee1 1e finally for ease of notation f is written to mean either the cdf or the corresponding probability measure the organization of the paper is as follows in section 2 the process is dened and its connections with other processes given we also provide an

bnp seq bayesian nonparametric differential expression analysis of sequencing count data abstractwe perform differential expression analysis of high throughput sequencing count data under a bayesian nonparametric framework removing sophisticated ad hoc pre processing steps commonly required in existing algorithms we propose to use the gamma beta negative binomial process which takes into account different sequencing depths using sample specific negative binomial probability dispersion parameters to detect differentially expressed genes by comparing the posterior distributions of gene specific negative binomial dispersion probability parameters these model parameters are inferred by borrowing statistical strength across both the genes and samples extensive experiments on both simulated and real world rna sequencing count data show that the proposed differential expression analysis algorithms clearly outperform previously proposed ones in terms of the areas under both the receiver operating characteristic and precision recall curves supplementary materials for this article are avai

fluctuation dissipation process without a time scale we study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long range correlations we make the assumption that the perturbation process involved is of the same kind as those recently studied numerically and theoretically with a good agreement between theory and numerical treatment as a result of this assumption the equilibrium distribution departs from the ordinary canonical distribution the distribution tails are truncated the distribution border is signaled by sharp peaks and in the weak dissipation limit the central distribution body becomes identical to a truncated l evy distribution

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

a bayesian bootstrap for censored data a bayesian bootstrap for a censored data model is introduced its small sample distributional properties are discussed and found to be similar to efron s bootstrap for censored data in the absence of censoring the bayesian bootstrap for censored data reduces to rubin s bayesian bootstrap for complete data a first order large sample theory is developed this theory shows that both censored data bootstraps are consistent bootstraps for approximating the sampling distribution of the kaplan meier estimator it also shows that both bootstraps are consistent bootstraps for approximating a posterior distribution of the survival function with respect to each member of the class of conjugate beta neutral process priors

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

combinatorial clustering and the beta negative binomial process we develop a bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual we introduce a combinatorial stochastic process known as the negative binomial process rm nbp as an infinite dimensional prior appropriate for such problems we show that the rm nbp is conjugate to the beta process and we characterize the posterior distribution under the beta negative binomial process rm bnbp and hierarchical models based on the rm bnbp the rm hbnbp we study the asymptotic properties of the rm bnbp and develop a three parameter extension of the rm bnbp that exhibits power law behavior we derive mcmc algorithms for posterior inference under the rm hbnbp and we present experiments using these algorithms in the domains of image segmentation object recognition and document analysis

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

the bernstein von mises theorem for the proportional hazard model we study large sample properties of bayesian analysis of the proportional hazard model with neutral to the right process priors on the baseline hazard function we show that the posterior distribution of the baseline cumulative hazard function and regression coefficients centered at the maximum likelihood estimator is jointly asymptotically equivalent to the sampling distribution of the maximum likelihood estimator

effects of exponentially small terms in the perturbation approach to localized buckling localized buckling solutions are known to exist in the heuristic model of an elastic strut resting on an elastic winkler foundation the primary localized solution emerging from the critical buckling state consists of an amplitude envelope of approximately the form of a hyperbolic secant function which modulates a fast varying sinusoidal oscillation in previous works such solutions have been tracked for the entire post buckling regime both numerically and through a rayleigh ritz approach a very rich structure is known to exist in the subcritical load range but has been proved to exist for only a certain family of reversible systems studies have concentrated on symmetric homoclinic solutions and the asymmetric solutions which bifurcate from these solution paths the primary solution is known to exist for the entire subcritical parameter range and all other symmetric and associated asymmetric solutions exist strictly for values less than critical here we uncover a new family of antisymmetric solutions and some asymptotic analysis suggests that the primary antisymmetric solution exists over the same range as does the primary symmetric solution a perturbation approach can be used so as to describe the bifurcation hierarchy for the novel antisymmetric forms we illustrate a unified approach which is able to predict the circumstances under which non divergent localized solutions are possible and the results of the analysis are compared with some numerical solutions

on posterior consistency of survival models ghosh and ramamoorthi studied posterior consistency for survival models and showed that the posterior was consistent when the prior on the distribution of survival times was the dirichlet process prior in this paper we study posterior consistency of survival models with neutral to the right process priors which include dirichlet process priors a set of sufficient conditions for posterior consistency with neutral to the right process priors are given interestingly not all the neutral to the right process priors have consistent posteriors but most of the popular priors such as dirichlet processes beta processes and gamma processes have consistent posteriors with a class of priors which includes beta processes a necessary and sufficient condition for the consistency is also established an interesting counter intuitive phenomenon is found suppose there are two priors centered at the true parameter value with finite variances surprisingly the posterior with smaller prior variance can be inconsistent while that with larger prior variance is consistent

a nonparametric approach to a survival study with surrogate endpoints a nonparametric estimator for the joint distribution of a survival time and surrogate response time which may occur earlier during follow up is presented in the absence of the surrogate response variable the estimator reduces to the kaplan meier nonparametric estimator for the survival time alone the estimator derived in this paper is done so in a particular novel way using an exchangeable process reinforced random walks to model individual observations the methodology introduced in the paper is readily extended to modelling multiple state processes

a method for combining inference across related nonparametric bayesian models summary we consider the problem of combining inference in related nonparametric bayes models analogous to parametric hierarchical models the hierarchical extension formalizes borrowing strength across the related submodels in the nonparametric context modelling is complicated by the fact that the random quantities over which we define the hierarchy are infinite dimensional we discuss a formal definition of such a hierarchical model the approach includes a regression at the level of the nonparametric model for the special case of dirichlet process mixtures we develop a markov chain monte carlo scheme to allow efficient implementation of full posterior inference in the given model

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

the multivariate beta process and an extension of the polya tree model we introduce a novel stochastic process that we term the multivariate beta process the process is defined for modelling dependent random probabilities and has beta marginal distributions we use this process to define a probability model for a family of unknown distributions indexed by covariates the marginal model for each distribution is a polya tree prior an important feature of the proposed prior is the easy centring of the nonparametric model around any parametric regression model we use the model to implement nonparametric inference for survival distributions the nonparametric model that we introduce can be adopted to extend the support of prior distributions for parametric regression models

bayesian survival analysis using a mars model a bayesian multivariate adaptive regression spline fitting approach is used to model univariate and multivariate survival data with censoring the possible models contain the proportional hazards model as a subclass and automatically detect departures from this a reversible jump markov chain monte carlo algorithm is described to obtain the estimate of the hazard function as well as the survival curve

a study of a class of weighted bootstraps for censored data edgeworth expansions are derived for a class of weighted bootstrap methods for the kaplan meier and nelson aalen estimates using the methods contained in the monograph by barbe and bertail von mises representations up to the third order are established for the weighted bootstrap versions of these estimators it is shown that there exists weights which outperform efron s bootstrap method in terms of coverage accuracy moreover it is shown that this holds for a particular choice of gamma weights which are very easy to use in practice the general weighting schemes are also useful in approximating the posterior distribution of survival function with respect to mixtures of beta neutral process priors

representations of levy processes without gaussian components we consider levy processes without gaussian components known as pure jump processes with a view to simulating such a process in order to implement full bayesian nonparametric analyses involving the modelling of continuous time stochastic processes in particular from practical and theoretical perspectives we investigate a recent representation of wolpert ickstadt 1998

poisson calculus for spatial neutral to the right processes neutral to the right ntr processes were introduced by doksum in 1974 as bayesian priors on the class of distributions on the real line since that time there have been numerous applications to models that arise in survival analysis subject to possible right censoring however unlike the dirichlet process the larger class of ntr processes has not been used in a wider range of more complex statistical applications here to circumvent some of these limitations we describe a natural extension of ntr processes to arbitrary polish spaces which we call spatial neutral to the right processes our construction also leads to a new rich class of random probability measures which we call ntr species sampling models we show that this class contains the important two parameter extension of the dirichlet process we provide a posterior analysis which yields tractable ntr analogues of the blackwell macqueen distribution our analysis turns out to be closely related to the study of regenerative composition structures a new computational scheme which is an ordered variant of the general chinese restaurant processes is developed this can be used to approximate complex posterior quantities we also discuss some relationships to results that appear outside of bayesian nonparametrics

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

canonical and noncanonical equilibrium distribution february 1 2008 we address the problem of the dynamical foundation ofnon canonical equilibrium we consider as a source of di vergence from ordinary statistical mechanics the breakdownof the condition of time scale separation between microscopicand macroscopic dynamics we show that this breakdownhas the e ect of producing a signi cant deviation from thecanonical prescription we also show that while the canoni cal equilibrium can be reached with no apparent dependenceon dynamics the speci c form of non canonical equilibriumis in fact determined by dynamics we consider the specialcase where the thermal reservoir driving the system of interestto equilibrium is a generator of intermittent uctuations weassess the form of the non canonical equilibrium reached bythe system in this case using both theoretical and numericalarguments we demonstrate that l evy statistics are the bestdescription of the dynamics and that the l evy distribution isthe correct basin of attraction we also show that the cor rect path to non canonical equilibrium by means of strictlythermodynamic arguments has not yet been found and thatfurther research has to be done to establish a connection be tween dynamics and thermodynamics i introduction

priors for random count matrices derived from a family of negative binomial processes abstractwe define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns the three distributions we consider are derived from the gamma poisson gamma negative binomial and beta negative binomial processes which we refer to generically as a family of negative binomial processes because the models lead to closed form update equations within the context of a gibbs sampler they are natural candidates for nonparametric bayesian priors over count matrices a key aspect of our analysis is the recognition that although the random count matrices within the family are defined by a row wise construction their columns can be shown to be independent and identically distributed iid this fact is used to derive explicit formulas for drawing all the columns at once moreover by analyzing these matrices combinatorial structure we describe how to sequentially construct a column iid random count matrix one row at a time and derive the predictive d

clustering from categorical data sequences the three parameter cluster model is a combinatorial stochastic process that generates categorical response sequences by randomly perturbing a fixed clustering parameter this clear relationship between the observed data and the underlying clustering is particularly attractive in cluster analysis in which supervised learning is a common goal and missing data is a familiar issue the model is well equipped for this task as it can handle missing data perform out of sample inference and accommodate both independent and dependent data sequences moreover its clustering parameter lies in the unrestricted space of partitions so that the number of clusters need not be specified beforehand we establish these and other theoretical properties and also demonstrate the model on datasets from epidemiology genetics political science and legal studies

pseudospectral delves freeman computations of the radiation coefficient for weakly nonlocal solitary waves of the third order nonlinear schroedinger equation and their relation to hyperasymptotic perturbation theory we revive a strategy of delves to precondition a spectral calculation using an almost diagonal galerkin matrix we also show that hyperasymptotic singular perturbation theory is a specialization of the delves freeman iteration to a single step with a diagonal galerkin matrix we calculate the first three orders in the hyperasymptotic expansion of the radiation coefficient of the weakly nonlocal envelope solitary waves of the third order nonlinear schroedinger tnls equation which is important in fiber optics telecommunications and water waves in a long appendix it was necessary to develop some non numerical but numerically essential additions to the theory of the tnls equation good numerics often requires a much deeper understanding of a problem than the generation of a string of power series coefficients

hierarchical generalized linear models and frailty models with bayesian nonparametric mixing summary this paper proposes bayesian nonparametric mixing for some well known and popular models the distribution of the observations is assumed to contain an unknown mixed effects term which includes a fixed effects term a function of the observed covariates and an additive or multiplicative random effects term typically these random effects are assumed to be independent of the observed covariates and independent and identically distributed from a distribution from some known parametric family this assumption may be suspect if either there is interaction between observed covariates and unobserved covariates or the fixed effects predictor of observed covariates is misspecified another cause for concern might be simply that the covariates affect more than just the location of the mixed effects distribution as a consequence the distribution of the random effects could be highly irregular in modality and skewness leaving parametric families unable to model the distribution adequately this paper therefore proposes a bayesian nonparametric prior for the random effects to capture possible deviances in modality and skewness and to explore the observed covariates effect on the distribution of the mixed effects

bayesian nonparametric inference for random distributions and related functions in recent years bayesian nonparametric inference both theoretical and computational has witnessed considerable advances however these advances have not received a full critical and comparative analysis of their scope impact and limitations in statistical modelling many aspects of the theory and methods remain a mystery to practitioners and many open guestions remain in this paper we discuss and illustrate the rich modelling and analytic possibilities that are available to the statistician within the bayesian nonparametric and or semiparametric framework

negative binomial process count and mixture modeling the seemingly disjoint problems of count and mixture modeling are united under the negative binomial nb process a gamma process is employed to model the rate measure of a poisson process whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an nb process for count modeling a draw from the nb process consists of a poisson distributed finite number of distinct atoms each of which is associated with a logarithmic distributed number of data samples we reveal relationships between various count and mixture modeling distributions and construct a poisson logarithmic bivariate distribution that connects the nb and chinese restaurant table distributions fundamental properties of the models are developed and we derive efficient bayesian inference it is shown that with augmentation and normalization the nb process and gamma nb process can be reduced to the dirichlet process and hierarchical dirichlet process respectively these relationships highlight theoretical structural and computational advantages of the nb process a variety of nb processes including the beta geometric beta nb marked beta nb marked gamma nb and zero inflated nb processes with distinct sharing mechanisms are also constructed these models are applied to topic modeling with connections made to existing algorithms under poisson factor analysis example results show the importance of inferring both the nb dispersion and probability parameters

bayesian estimation of the spectral density of a time series this article describes a bayesian approach to estimating the spectral density of a stationary time series a nonparametric prior on the spectral density is described through bernstein polynomials because the actual likelihood is very complicated a pseudoposterior distribution is obtained by updating the prior using the whittle likelihood a markov chain monte carlo algorithm for sampling from this posterior distribution is described that is used for computing the posterior mean variance and other statistics a consistency result is established for this pseudoposterior distribution that holds for a short memory gaussian time series and under some conditions on the prior to prove this asymptotic result a general consistency theorem of schwartz is extended for a triangular array of independent nonidentically distributed observations this extension is also of independent interest a simulation study is conducted to compare the proposed method with some existing methods the method is illustrated with

microscopic origins of irreversible macroscopic behavior time asymmetric behavior as embodied in the second law of thermodynamics is observed in individual macroscopic systems it can be understood as arising naturally from time symmetric microscopic laws in accord with the ideas of thompson maxwell and boltzmann alternative explanations based on equating irreversible macroscopic behavior with the mixing type of behavior already present in the time evolution of ensembles probability distributions of certain systems having only a few degrees of freedom are in my opinion unnecessary misguided and misleading

the indian buffet process an introduction and review the indian buffet process is a stochastic process defining a probability distribution over equivalence classes of sparse binary matrices with a finite number of rows and an unbounded number of columns this distribution is suitable for use as a prior in probabilistic models that represent objects using a potentially infinite array of features or that involve bipartite graphs in which the size of at least one class of nodes is unknown we give a detailed derivation of this distribution and illustrate its use as a prior in an infinite latent feature model we then review recent applications of the indian buffet process in machine learning discuss its extensions and summarize its connections to other stochastic processes

a hyperasymptotic perturbative method for computing the radiation coefficient for weakly nonlocal solitary waves we offer a new computational method to calculate the radiation coefficient of a weakly nonlocal solitary wave in the limit that the amplitude e of the core of the structure tends to zero a weakly nonlocal solitary wave is a finite amplitude nondissipative wave which decays to a sinusoidal oscillation of amplitude at large distance from the core the multiple scales series for the solitary wave in powers of e is asymptotic but divergent when truncated at optimal order superasymptotic approximation the series gives no information about the radiation coefficient except order of magnitude because the absolute error is o we describe two hyperasymptotic approximations which add a second different asymptotic series to the multiple scales expansion so as to compute itself the zeroth order hyperasymptotic approximation has a relative error of o e in the sequence of approximations may be extrapolated to give the proportionality constant in the limiting asymptotic expression for as e 0 the first order hyperasymptotic approximation has a relative error of only o e2 its extrapolation gives the o e correction to the limit as e 0

bayesian analysis of proportional hazard models this paper is concerned with bayesian analysis of the proportional hazard model with left truncated and right censored data we use a process neutral to the right as the prior of the baseline survival function and a finite dimensional prior is placed on the regression coefficient we then obtain the exact form of the joint posterior distribution of the regression coefficient and the baseline cumulative hazard function as a by product we prove the propriety of the posterior distribution with the constant prior on the regression coefficient