a unified bayesian semiparametric approach to assess discrimination ability in survival analysis the discriminatory ability of a marker for censored survival data is routinely assessed by the time dependent roc curve and the c index the time dependent roc curve evaluates the ability of a biomarker to predict whether a patient lives past a particular time t the c index measures the global concordance of the marker and the survival time regardless of the time point we propose a bayesian semiparametric approach to estimate these two measures the proposed estimators are based on the conditional distribution of the survival time given the biomarker and the empirical biomarker distribution the conditional distribution is estimated by a linear dependent dirichlet process mixture model the resulting roc curve is smooth as it is estimated by a mixture of parametric functions the proposed c index estimator is shown to be more efficient than the commonly used harrell s c index since it uses all pairs of data rather than only informative pairs the proposed estimators are evaluated through simulations and illustrated using a lung cancer dataset

nonparametric bayes conditional distribution modeling with variable selection this article considers a methodology for flexibly characterizing the relationship between a response and multiple predictors goals are 1 to estimate the conditional response distribution addressing the distributional changes across the predictor space and 2 to identify important predictors for the response distribution change both within local regions and globally we first introduce the probit stick breaking process psbp as a prior for an uncountable collection of predictor dependent random distributions and propose a psbp mixture psbpm of normal regressions for modeling the conditional distributions a global variable selection structure is incorporated to discard unimportant predictors while allowing estimation of posterior inclusion probabilities local variable selection is conducted relying on the conditional distribution estimates at different predictor points an efficient stochastic search sampling algorithm is proposed for posterior computation the methods are illustrated through simulation and applied to an epidemiologic study

order based dependent dirichlet processes in this article we propose a new framework for bayesian nonparametric modeling with continuous covariates in particular we allow the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick breaking representation we focus mostly on the class of random distributions that induces a dirichlet process at each covariate value we derive the correlation between distributions at different covariate values and use a point process to implement a practically useful type of ordering two main constructions with analytically known correlation structures are proposed practical and efficient computational methods are introduced we apply our framework through mixtures of these processes to regression modeling the modeling of stochastic volatility in time series data and spatial geostatistical modeling

spatially dependent polya tree modeling for survival data with the proliferation of spatially oriented time to event data spatial modeling in the survival context has received increased recent attention a traditional way to capture a spatial pattern is to introduce frailty terms in the linear predictor of a semiparametric model such as proportional hazards or accelerated failure time we propose a new methodology to capture the spatial pattern by assuming a prior based on a mixture of spatially dependent polya trees for the baseline survival in the proportional hazards model thanks to modern markov chain monte carlo mcmc methods this approach remains computationally feasible in a fully hierarchical bayesian framework we compare the spatially dependent mixture of polya trees mpt approach to the traditional spatial frailty approach and illustrate the usefulness of this method with an analysis of iowan breast cancer survival data from the surveillance epidemiology and end results seer program of the national cancer institute our method provides better goodness of fit over the traditional alternatives as measured by log pseudo marginal likelihood lpml the deviance information criterion dic and full sample score fss statistics

a time series ddp for functional proteomics profiles using a new type of array technology the reverse phase protein array rppa we measure time course protein expression for a set of selected markers that are known to co regulate biological functions in a pathway structure to accommodate the complex dependent nature of the data including temporal correlation and pathway dependence for the protein markers we propose a mixed effects model with temporal and protein specific components we develop a sequence of random probability measures rpm to account for the dependence in time of the protein expression measurements marginally for each rpm we assume a dirichlet process dp model the dependence is introduced by defining multivariate beta distributions for the unnormalized weights of the stick breaking representation we also acknowledge the pathway dependence among proteins via a conditionally autoregressive car model applying our model to the rppa data we reveal a pathway dependent functional profile for the set of proteins as well as marginal expression profiles over time for individual markers

modeling for dynamic ordinal regression relationships an application to estimating maturity of rockfish in california abstractwe develop a bayesian nonparametric framework for modeling ordinal regression relationships which evolve in discrete time the motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age length and maturity the latter recorded on an ordinal scale the methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses this approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models that arise from estimation of cut off points relating the latent continuous and ordinal responses a novel dependent dirichlet process prior for time dependent mixing distributions extends the model to the dynamic setting the methodology is used for a detailed study of relationships between maturity age and length for chilipepper rockfish using data collected over 15 years along th

the matrix stick breaking process flexible bayes meta analysis in analyzing data from multiple related studies it often is of interest to borrow information across studies and to cluster similar studies although parametric hierarchical models are commonly used of concern is sensitivity to the form chosen for the random effects distribution a dirichlet process dp prior can allow the distribution to be unknown while clustering studies however the dp does not allow local clustering of studies with respect to a subset of the coefficients without making independence assumptions motivated by this problem we propose a matrix stick breaking process msbp as a prior for a matrix of random probability measures properties of the msbp are considered and methods are developed for posterior computation using markov chain monte carlo using the msbp as a prior for a matrix of study specific regression coefficients we demonstrate advantages over parametric modeling in simulated examples the methods are further illustrated using a multinational uterotrophic bioassay s

enriched stick breaking processes for functional data in many applications involving functional data prior information is available about the proportion of curves having different attributes it is not straightforward to include such information in existing procedures for functional data analysis generalizing the functional dirichlet process fdp we propose a class of stick breaking priors for distributions of functions these priors incorporate functional atoms drawn from constrained stochastic processes the stick breaking weights are specified to allow user specified prior probabilities for curve attributes with hyperpriors accommodating uncertainty compared with the fdp the random distribution is enriched for curves having attributes known to be common theoretical properties are considered methods are developed for posterior computation and the approach is illustrated using data on temperature curves in menstrual cycles

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

generalized spatial dirichlet process models summary many models for the study of point referenced data explicitly introduce spatial random effects to capture residual spatial association these spatial effects are customarily modelled as a zeromean stationary gaussian process the spatial dirichlet process introduced by gelfand et al 2005 produces a random spatial process which is neither gaussian nor stationary rather it varies about a process that is assumed to be stationary and gaussian the spatial dirichlet process arises as a probability weighted collection of random surfaces this can be limiting for modelling and inferential purposes since it insists that a process realization must be one of these surfaces we introduce a random distribution for the spatial effects that allows different surface selection at different sites moreover we can specify the model so that the marginal distribution of the effect at each site still comes from a dirichlet process the development is offered constructively providing a multivariate extension of the stick breaking representation of the weights we then introduce mixing using this generalized spatial dirichlet process we illustrate with a simulated dataset of independent replications and note that we can embed the generalized process within a dynamic model specification to eliminate the independence assumption

concordance homomorphisms from knot floer homology abstract we modify the construction of knot floer homology to produce a one parameter family of homologies thfk for knots in s 3 these invariants can be used to give homomorphisms from the smooth concordance group c to z giving bounds on the four ball genus and the concordance genus of knots we give some applications of these homomorphisms

a class of mixtures of dependent tail free processes we propose a class of dependent processes in which density shape is regressed on one or more predictors through conditional tail free probabilities by using transformed gaussian processes a particular linear version of the process is developed in detail the resulting process is flexible and easy to fit using standard algorithms for generalized linear models the method is applied to growth curve analysis evolving univariate random effects distributions in generalized linear mixed models and median survival modelling with censored data and covariate dependent errors

uncertainty propagation using infinite mixture of gaussian processes and variational bayesian inference uncertainty propagation in flow through porous media problems is a challenging problem this is due to the high dimensionality of the random property fields e g permeability and porosity as well as the computational complexity of the models that are involved the usual approach is to construct a surrogate response surface and then use it instead of the expensive model to carry out the uncertainty propagation task however the construction of the surrogate surface is hampered by various aspects such as the limited number of model evaluations that one can afford the curse of dimensionality multi variate responses with non trivial correlations potential localized features of the response and or discontinuities in this work we extend upon the concept of the multi output gaussian process mgp to effectively deal with all of these difficulties simultaneously this non trivial extension involves an infinite mixture of mgp s that is trained using variational bayesian inference prior to observing any data a dirichlet process is used to generate the components of the mgp mixture the bayesian nature of the model allows for the quantification of the uncertainties due to the limited number of simulations i e we can derive error bars for the statistics of interest the automatic detection of the mixture components by the variational inference algorithm is able to capture discontinuities and localized features without adhering to ad hoc constructions finally correlations between the components of multi variate responses are captured by the underlying mgp model in a natural way

a nonparametric bayesian modeling approach for cytogenetic dosimetry summary in cytogenetic dosimetry samples of cell cultures are exposed to a range of doses of a given agent in each sample at each dose level some measure of cell disability is recorded the objective is to develop models that explain cell response to dose such models can be used to predict response at unobserved doses more important such models can provide inference for unknown exposure doses given the observed responses typically cell disability is viewed as a poisson count but in the present work a more appropriate response is a categorical classification in the literature modeling in this case is very limited what exists is purely parametric we propose a fully bayesian nonparametric approach to this problem we offer comparison with a parametric model through a simulation study and the analysis of a real dataset modeling blood cultures exposed to radiation where classification is with regard to number of micronuclei per cell

non gaussian spatiotemporal modelling through scale mixing we construct non gaussian processes that vary continuously in space and time with nonseparable covariance functions starting from a general and flexible way of constructing valid nonseparable covariance functions through mixing over separable covariance functions the resulting models are generalized by allowing for outliers as well as regions with larger variances we induce this through scale mixing with separate positive valued processes smooth mixing processes are applied to the underlying correlated processes in space and in time thus leading to regions in space and time of increased spread an uncorrelated mixing process on the nugget effect accommodates outliers posterior and predictive bayesian inference with these models is implemented through a markov chain monte carlo sampler an application to temperature data in the basque country illustrates the potential of this model in the identification of outliers and regions with inflated variance and shows that this improves the predictive performance

semiparametric bayes multiple testing applications to tumor data in national toxicology program ntp studies investigators want to assess whether a test agent is carcinogenic overall and specific to certain tumor types while estimating the dose response profiles because there are potentially correlations among the tumors a joint inference is preferred to separate univariate analyses for each tumor type in this regard we propose a random effect logistic model with a matrix of coefficients representing log odds ratios for the adjacent dose groups for tumors at different sites we propose appropriate nonparametric priors for these coefficients to characterize the correlations and to allow borrowing of information across different dose groups and tumor types global and local hypotheses can be easily evaluated by summarizing the output of a single monte carlo markov chain mcmc two multiple testing procedures are applied for testing local hypotheses based on the posterior probabilities of local alternatives simulation studies are conducted and an ntp tumor data set is analyzed illustrating the proposed approach

dirichlet process mixtures of generalized linear models we propose dirichlet process mixtures of generalized linear models dp glm a new class of methods for nonparametric regression given a data set of input response pairs the dp glm produces a global model of the joint distribution through a mixture of local generalized linear models dp glms allow both continuous and categorical inputs and can model the same class of responses that can be modeled with a generalized linear model we study the properties of the dp glm and show why it provides better predictions and density estimates than existing dirichlet process mixture regression models we give conditions for weak consistency of the joint distribution and pointwise consistency of the regression estimate

mixture models with a prior on the number of components abstracta natural bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric dirichlet weights and put a prior on the number of components that is to use a mixture of finite mixtures mfm the most commonly used method of inference for mfms is reversible jump markov chain monte carlo but it can be nontrivial to design good reversible jump moves especially in high dimensional spaces meanwhile there are samplers for dirichlet process mixture dpm models that are relatively simple and are easily adapted to new applications it turns out that in fact many of the essential properties of dpms are also exhibited by mfms an exchangeable partition distribution restaurant process random measure representation and stick breaking representation and crucially the mfm analogues are simple enough that they can be used much like the corresponding dpm properties consequently many of the powerful methods developed for inference in dpms

nonparametric bayesian multiple imputation for missing data due to mid study switching of measurement methods investigators often change how variables are measured during the middle of data collection for example in hopes of obtaining greater accuracy or reducing costs the resulting data comprise sets of observations measured on two or more different scales which complicates interpretation and can create bias in analyses that rely directly on the differentially measured variables we develop approaches based on multiple imputation for handling mid study changes in measurement for settings without calibration data that is no subjects are measured on both all scales this setting creates a seemingly insurmountable problem for multiple imputation since the measurements never appear jointly there is no information in the data about their association we resolve the problem by making an often scientifically reasonable assumption that each measurement regime accurately ranks the samples but on differing scales so that for example an individual at the qth percentile on one scale should be at about the qth

smoothly mixing regressions this paper extends the conventional bayesian mixture of normals model by permitting state probabilities to depend on observed covariates the dependence is captured by a simple multinomial probit model a conventional and rapidly mixing mcmc algorithm provides access to the posterior distribution at modest computational cost this model is competitive with existing econometric models as documented in the paper s illustrations the first illustration studies quantiles of the distribution of earnings of men conditional on age and education and shows that smoothly mixing regressions are an attractive alternative to nonbayesian quantile regression the second illustration models serial dependence in the s p 500 return and shows that the model compares favorably with arch models using out of sample likelihood criteria

distance dependent chinese restaurant processes we develop the distance dependent chinese restaurant process a flexible class of distributions over partitions that allows for dependencies between the elements this class can be used to model many kinds of dependencies between data in infinite clustering models including dependencies arising from time space and network connectivity we examine the properties of the distance dependent crp discuss its connections to bayesian nonparametric mixture models and derive a gibbs sampler for both fully observed and latent mixture settings we study its empirical performance with three text corpora we show that relaxing the assumption of exchangeability with distance dependent crps can provide a better fit to sequential data and network data we also show that the distance dependent crp representation of the traditional crp mixture leads to a faster mixing gibbs sampling algorithm than the one based on the original formulation

bayesian isotonic density regression density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions and are well supported in many applications a rich variety of bayesian methods have been proposed for density regression but it is not clear whether such priors have full support so that any true data generating model can be accurately approximated this article develops a new class of density regression models that incorporate stochastic ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor theory is developed showing large support methods are developed for hypothesis testing with posterior computation relying on a simple gibbs sampler frequentist properties are illustrated in a simulation study and an epidemiology application is considered

hybrid dirichlet mixture models for functional data summary in functional data analysis curves or surfaces are observed up to measurement error at a finite set of locations for say a sample of n individuals often the curves are homogeneous except perhaps for individual specific regions that provide heterogeneous behaviour e g damaged areas of irregular shape on an otherwise smooth surface motivated by applications with functional data of this nature we propose a bayesian mixture model with the aim of dimension reduction by representing the sample of n curves through a smaller set of canonical curves we propose a novel prior on the space of probability measures for a random curve which extends the popular dirichlet priors by allowing local clustering non homogeneous portions of a curve can be allocated to different clusters and the n individual curves can be represented as recombinations hybrids of a few canonical curves more precisely the prior proposed envisions a conceptual hidden factor with k levels that acts locally on each curve we discuss several models incorporating this prior and illustrate its performance with simulated and real data sets we examine theoretical properties of the proposed finite hybrid dirichlet mixtures specifically their behaviour as the number of the mixture components goes to 1 and their connection with dirichlet process mixtures

semiparametric bayes analysis of longitudinal data treatment models this paper is concerned with the problem of determining the effect of a binary treatment variable on a continuous outcome given longitudinal observational data and non randomly assigned treatments a general semiparametric bayesian model based on dirichlet process mixing is developed which contains potential outcomes and subject level outcome specific random effects the model is subjected to a fully bayesian analysis based on markov chain monte carlo simulation methods the methods are used to compute the posterior distribution of the parameters and potential outcomes the sampled posterior output from the simulation is also used to construct treatment effect distributions at the unit level and at other levels of aggregation marginalized over all unknowns of the model including the unknown distribution of responses and treatments and treatment effects matched by treatment probability a real data example dealing with the wage premium associated with union membership is considered in detail where quantities such as the average treatment effect the treatment effect on the treated and matched treatment effects are derived and illustrated

the nested dirichlet process in multicenter studies subjects in different centers may have different outcome distributions this article is motivated by the problem of nonparametric modeling of these distributions borrowing information across centers while also allowing centers to be clustered starting with a stick breaking representation of the dirichlet process dp we replace the random atoms with random probability measures drawn from a dp this results in a nested dp prior which can be placed on the collection of distributions for the different centers with centers drawn from the same dp component automatically clustered together theoretical properties are discussed and an efficient markov chain monte carlo algorithm is developed for computation the methods are illustrated using a simulation study and an application to quality of care in u s hospitals

a nonparametric spatial model for periodontal data with nonrandom missingness periodontal disease pd progression is often quantified by clinical attachment level cal defined as the distance down a tooth s root that is detached from the surrounding bone measured at six locations per tooth throughout the mouth excluding the molars it gives rise to a dependent data setup these data are often reduced to a one number summary such as the whole mouth average or the number of observations greater than a threshold to be used as the response in a regression to identify important covariates related to the current state of a subject s periodontal health rather than a simple one number summary we set forward to analyze all available cal data for each subject exploiting the presence of spatial dependence nonstationarity and nonnormality also many subjects have a considerable proportion of missing teeth which cannot be considered missing at random because pd is the leading cause of adult tooth loss under a bayesian paradigm we propose a nonparametric flexible spatial joint

global well posedness and asymptotic stabilization for chemotaxis system with signal dependent sensitivity abstract a fully parabolic chemotaxis system u t u u v v v t v v u in a smooth bounded domain r n n 2 with homogeneous neumann boundary conditions is considered where the non negative chemotactic sensitivity function satisfies v a v k for some a 0 and k 1 it is shown that a novel type of weight function can be applied to a weighted energy estimate for k 1 consequently the range of for the global existence and uniform boundedness of classical solutions established by mizukami and yokota 23 is enlarged moreover under a convexity assumption on an asymptotic lyapunov functional is obtained and used to establish the asymptotic stability of spatially homogeneous equilibrium solutions for k 1 under a smallness assumption on in particular when v v and n 8 it is shown that the spatially homogeneous steady state is a global attractor whenever 1 2

generalized poya urn for time varying pitman yor processes this article introduces a class of first order stationary time varying pitman yor processes subsuming our construction of time varying dirichlet processes presented in caron et al 2007 these models can be used for time dynamic density estimation and clustering our intuitive and simple construction relies on a generalized polya urn scheme significantly this construction yields marginal distributions at each time point that can be explicitly characterized and easily controlled inference is performed using markov chain monte carlo and sequential monte carlo methods we demonstrate our models and algorithms on epidemiological and video tracking data

semiparametric bayesian inference for stochastic frontier models in this paper we propose a semiparametric bayesian framework for the analysis of stochastic frontiers and efficiency measurement the distribution of inefficiencies is modelled nonparametrically through a dirichlet process prior we suggest prior distributions and implement a bayesian analysis through an efficient markov chain monte carlo sampler which allows us to deal with practically relevant sample sizes we also consider the case where the efficiency distribution varies with firm characteristics the methodology is applied to a cost frontier estimated from a panel data set on 382 u s hospitals

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

an anova model for dependent random measures we consider dependent nonparametric models for related random probability distributions for example the random distributions might be indexed by a categorical covariate indicating the treatment levels in a clinical trial and might represent random effects distributions under the respective treatment combinations we propose a model that describes dependence across random distributions in an analysis of variance anova type fashion we define a probability model in such a way that marginally each random measure follows a dirichlet process dp and use the dependent dirichlet process to define the desired dependence across the related random measures the resulting probability model can alternatively be described as a mixture of anova models with a dp prior on the unknown mixing measure the main features of the proposed approach are ease of interpretation and computational simplicity because the model follows the standard anovastructure interpretation and inference parallels conventions for anova mode

bayesian modeling of temporal dependence in large sparse contingency tables it is of interest in many applications to study trends over time in relationships among categorical variables such as age group ethnicity religious affiliation political party and preference for particular policies at each time point a sample of individuals provides responses to a set of questions with different individuals sampled at each time in such settings there tend to be an abundance of missing data and the variables being measured may change over time at each time point we obtained a large sparse contingency table with the number of cells often much larger than the number of individuals being surveyed to borrow information across time in modeling large sparse contingency tables we propose a bayesian autoregressive tensor factorization approach the proposed model relies on a probabilistic parafac factorization of the joint pmf characterizing the categorical data distribution at each time point with autocorrelation included across times we develop efficient computational methods th

nonparametric bayes testing of changes in a response distribution with an ordinal predictor in certain biomedical studies one may anticipate changes in the shape of a response distribution across the levels of an ordinal predictor for instance in toxicology studies skewness and modality might change as dose increases to address this issue we propose a bayesian nonparametric method for testing for distribution changes across an ordinal predictor using a dynamic mixture of dirichlet processes we allow the response distribution to change flexibly at each level of the predictor in addition by assigning mixture priors to the hyperparameters we can obtain posterior probabilities of no effect of the predictor and identify the lowest dose level for which there is an appreciable change in distribution the method also provides a natural framework for performing tests across multiple outcomes we apply our method to data from a genotoxicity experiment

on the stick breaking representation of normalized inverse gaussian priors random probability measures are the main tool for bayesian nonparametric inference with their laws acting as prior distributions many well known priors used in practice admit different though equivalent representations in terms of computational convenience stick breaking representations stand out in this paper we focus on the normalized inverse gaussian process and provide a completely explicit stick breaking representation for it this result is of interest both from a theoretical viewpoint and for statistical practice copyright 2012 oxford university press

holomorphic disks and three manifold invariants properties and applications in 27 we introduced floer homology theories hf y s hf y s hf y t hf y s and hf red y s associated to closed oriented three manifolds y equipped with a spiny structures s spin c y in the present paper we give calculations and study the properties of these invariants the calculations suggest a conjectured relationship with seiberg witten theory the properties include a relationship between the euler characteristics of hf and turaev s torsion a relationship with the minimal genus problem thurston norm and surgery exact sequences we also include some applications of these techniques to three manifold topology

a new dirichlet process for mining dynamic patterns in functional data this paper proposes a novel model for mining patterns including dynamic function clustering segmentation and forecasting values of dependent variables simultaneously the proposed dependent dirichlet process piecewise regression mixture ddpprm model is capable of handling dynamic nature of data by detecting evolving clusters at each time step this evolution manifests dynamically in three states of clusters newly created existing and transient states of clusters the model is also able to generate clusters over time infinitely it is capable of learning the optimal number of clusters rather than using the fixed predefined clusters however other clustering methods such as fuzzy c regression model and piecewise regression mixture technique support none of those capabilities the proposed model is also capable of showing regime changes and segmenting functions in regression time series problems a two step gibbs sampling method is utilized for assigning data to clusters expectation maximization method is used for finding the optimal values of parameters of functions and probability distributions the model is validated by using some numerical experiments and calculating three validity indexes as well as mean square error of the model the results indicate that the proposed method outperforms other clustering segmentation and forecasting models in literature

quantile function on scalar regression analysis for distributional data radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity the predominant approach is to extract hundreds to thousands of image features includ

bayesian nonparametric inference on stochastic ordering we consider bayesian inference about collections of unknown distributions subject to a partial stochastic ordering to address problems in testing of equalities between groups and estimation of group specific distributions we propose classes of restricted dependent dirichlet process priors these priors have full support in the space of stochastically ordered distributions and can be used for collections of unknown mixture distributions to obtain a flexible class of mixture models theoretical properties are discussed efficient methods are developed for posterior computation using markov chain monte carlo simulation and the methods are illustrated using data from a study of dna damage and repair

bayesian nonparametric calibration and combination of predictive distributions abstractwe introduce a bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights building on the work of ranjan and gneiting we use infinite beta mixtures for the calibration the proposed bayesian nonparametric approach takes advantage of the flexibility of dirichlet process mixtures to achieve any continuous deformation of linearly combined predictive distributions the inference procedure is based on combination gibbs and slice sampling we provide some conditions under which the proposed probabilistic calibration converges in terms of weak posterior consistency to the true underlying density for both cases of iid and markovian observations this calibration property improves upon the earlier calibration approaches we study the methodology in simulation examples with fat tails and multimodal densities and apply it to density forecasts of dail

tour of bordered floer theory heegaard floer theory is a kind of topological quantum field theory tqft assigning graded groups to closed connected oriented 3 manifolds and group homomorphisms to smooth oriented four dimensional cobordisms bordered heegaard floer homology is an extension of heegaard floer homology to 3 manifolds with boundary with extended tqft type gluing properties in this survey we explain the formal structure and construction of bordered floer homology and sketch how it can be used to compute some aspects of heegaard floer theory

kernel stick breaking processes we propose a class of kernel stick breaking processes for uncountable collections of dependent random probability measures the process is constructed by first introducing an infinite sequence of random locations independent random probability measures and beta distributed random weights are assigned to each location predictor dependent random probability measures are then constructed by mixing over the locations with stick breaking probabilities expressed as a kernel multiplied by the beta weights some theoretical properties of the process are described including a covariate dependent prediction rule a retrospective markov chain monte carlo algorithm is developed for posterior computation and the methods are illustrated using a simulated example and an epidemiological application

sufficient dimension reduction via bayesian mixture modeling dimension reduction is central to an analysis of data with many predictors sufficient dimension reduction aims to identify the smallest possible number of linear combinations of the predictors called the sufficient predictors that retain all of the information in the predictors about the response distribution in this paper we propose a bayesian solution for sufficient dimension reduction we directly model the response density in terms of the sufficient predictors using a finite mixture model this approach is computationally efficient and offers a unified framework to handle categorical predictors missing predictors and bayesian variable selection we illustrate the method using both a simulation study and an analysis of an hiv data set

simplex factor models for multivariate unordered categorical data gaussian latent factor models are routinely used for modeling of dependence in continuous binary and ordered categorical data for unordered categorical variables gaussian latent factor models lead to challenging computation and complex modeling structures as an alternative we propose a novel class of simplex factor models in the single factor case the model treats the different categorical outcomes as independent with unknown marginals the model can characterize flexible dependence structures parsimoniously with few factors and as factors are added any multivariate categorical data distribution can be accurately approximated using a bayesian approach for computation and inferences a markov chain monte carlo mcmc algorithm is proposed that scales well with increasing dimension with the number of factors treated as unknown we develop an efficient proposal for updating the base probability vector in hierarchical dirichlet models theoretical properties are described and we evaluate the appr

markov chain monte carlo in approximate dirichlet and beta two parameter process hierarchical models summary we present some easy to construct random probability measures which approximate the dirichlet process and an extension which we will call the beta two parameter process the nature of these constructions makes it simple to implement markov chain monte carlo algorithms for fitting nonparametric hierarchical models and mixtures of nonparametric hierarchical models for the dirichlet process we consider a truncation approximation as well as a weak limit approximation based on a mixture of dirichlet processes the same type of truncation approximation can also be applied to the beta two parameter process both methods lead to posteriors which can be fitted using markov chain monte carlo algorithms that take advantage of blocked coordinate updates these algorithms promote rapid mixing of the markov chain and can be readily applied to normal mean mixture models and to density estimation problems we prefer the truncation approximations since a simple device for monitoring the adequacy of the approximation can be easily computed from the output of the gibbs sampler furthermore for the dirichlet process the truncation approximation offers an exponentially higher degree of accuracy over the weak limit approximation for the same computational effort we also find that a certain beta two parameter process may be suitable for finite mixture modelling because the distinct number of sampled values from this process tends to match closely the number of components of the underlying mixture distribution

bayesian density regression summary the paper considers bayesian methods for density regression allowing a random probability distribution to change flexibly with multiple predictors the conditional response distribution is expressed as a non parametric mixture of regression models with the mixture distribution changing with predictors a class of weighted mixture of dirichlet process priors is proposed for the uncountable collection of mixture distributions it is shown that this specification results in a generalized polya urn scheme which incorporates weights that are dependent on the distance between subjects predictor values to allow local dependence in the mixture distributions we propose a kernel based weighting scheme a gibbs sampling algorithm is developed for posterior computation the methods are illustrated by using simulated data examples and an epidemiologic application

a conditional density estimation partition model using logistic gaussian processes conditional density estimation density regression estimates the distribution of a response variable y conditional on covariates x utilizing a partition model framework a conditional density estimation method is proposed using logistic gaussian processes the partition is created using a voronoi tessellation and is learned from the data using a reversible jump markov chain monte carlo algorithm the markov chain monte carlo algorithm is made possible through a laplace approximation on the latent variables of the logistic gaussian process model this approximation marginalizes the parameters in each partition element allowing an efficient search of the posterior distribution of the tessellation the method has desirable consistency properties in simulation and applications the model successfully estimates the partition structure and conditional distribution of y

estimating a semiparametric asymmetric stochastic volatility model with a dirichlet process mixture in this paper we extend the parametric asymmetric stochastic volatility model asv where returns are correlated with volatility by flexibly modeling the bivariate distribution of the return and volatility innovations nonparametrically its novelty is in modeling the joint conditional return volatility distribution with an infinite mixture of bivariate normal distributions with mean zero vectors but having unknown mixture weights and covariance matrices this semiparametric asv model nests stochastic volatility models whose innovations are distributed as either normal or student t distributions plus the response in volatility to unexpected return shocks is more general than the fixed asymmetric response with the asv model the unknown mixture parameters are modeled with a dirichlet process prior this prior ensures a parsimonious finite posterior mixture that best represents the distribution of the innovations and a straightforward sampler of the conditional posteriors we develop a bayesian markov chain monte carlo sampler to fully characterize the parametric and distributional uncertainty nested model comparisons and out of sample predictions with the cumulative marginal likelihoods and one day ahead predictive log bayes factors between the semiparametric and parametric versions of the asv model shows the semiparametric model projecting more accurate empirical market returns a major reason is how volatility responds to an unexpected market movement when the market is tranquil expected volatility reacts to a negative positive price shock by rising initially declining but then rising when the positive shock is large however when the market is volatile the degree of asymmetry and the size of the response in expected volatility is muted in other words when times are good no news is good news but when times are bad neither good nor bad news matters with regards to volatility

dynamic nonparametric bayesian models for analysis of music the dynamic hierarchical dirichlet process dhdp is developed to model complex sequential data with a focus on audio signals from music the music is represented in terms of a sequence of discrete observations and the sequence is modeled using a hidden markov model hmm with time evolving parameters the dhdp imposes the belief that observations that are temporally proximate are more likely to be drawn from hmms with similar parameters while also allowing for innovation associated with abrupt changes in the music texture the sharing mechanisms of the time evolving model are derived and for inference a relatively simple markov chain monte carlo sampler is developed segmentation of a given musical piece is constituted via the model inference detailed examples are presented on several pieces with comparisons to other models the dhdp results are also compared with a conventional music theoretic analysis all the supplemental materials used by this paper are available online

combining information from several experiments with nonparametric priors summary this paper considers combining information from several experiments when the experiments can be summarised via a parameter value the structure of this set of parameters in terms of independence exchangeability partial exchangeability etc is assumed to be unknown and a finite number of possible structures are entertained each with an associated prior weight representing the degree of belief in that structure crucial is the criterion by which these structures are selected the final inference for the parameter values is taken to be the average with respect to the posterior weights of the values obtained from each structure this is performed within a bayesian nonparametric framework where the form of the prior distribution for the parameters is unrestricted therefore we do not assume that the distributions associated with a partial structure are from the same family different types of experiment suggest different types of distributions of parameters associated with each type of experiment

bayesian modeling of joint and conditional distributions in this paper we study a bayesian approach to exible modeling of conditional distributions the approach uses a exible model for the joint distribution of the dependent and independent variables and then extracts the conditional distributions of interest from the estimated joint distribution we use a nite mixture of multivariate normals fmmn to estimate the joint distribution the conditional distributions can then be assessed analytically or through simulations the discrete variables are handled through the use of latent variables the estimation procedure employs an mcmc algorithm we provide a characterization of the kullback leibler closure of fmmn and show that the joint and conditional predictive densities implied by fmmn model are consistent estimators for a large class of data generating processes with continuous and discrete observables the method can be used as a robust regression model with discrete and continuous dependent and independent variables and as a bayesian alternative to semi and non parametric models such as quantile and kernel regression in experiments the method compares favorably with classical nonparametric and alternative bayesian methods

a class of hazard rate mixtures for combining survival data from different experiments mixture models for hazard rate functions are widely used tools for addressing the statistical analysis of survival data subject to a censoring mechanism the present article introduced a new class of vectors of random hazard rate functions that are expressed as kernel mixtures of dependent completely random measures this leads to define dependent nonparametric prior processes that are suitably tailored to draw inferences in the presence of heterogenous observations besides its flexibility an important appealing feature of our proposal is analytical tractability we are indeed able to determine some relevant distributional properties and a posterior characterization that is also the key for devising an efficient markov chain monte carlo sampler for illustrative purposes we specialize our general results to a class of dependent extended gamma processes we finally display a few numerical examples including both simulated and real two sample datasets these allow us to identify the effect of a borrow

improving prediction from dirichlet process mixtures via enrichment flexible covariate dependent density estimation can be achieved by modelling the joint density of the response and covariates as a dirichlet process mixture an appealing aspect of this approach is that computations are relatively easy in this paper we examine the predictive performance of these models with an increasing number of covariates even for a moderate number of covariates we find that the likelihood for x tends to dominate the posterior of the latent random partition degrading the predictive performance of the model to overcome this we suggest using a different nonparametric prior namely an enriched dirichlet process our proposal maintains a simple allocation rule so that computations remain relatively simple advantages are shown through both predictive equations and examples including an application to diagnosis alzheimer s disease

fully nonparametric regression for bounded data using dependent bernstein polynomials abstractwe propose a novel class of probability models for sets of predictor dependent probability distributions with bounded domain the proposal extends the dirichlet bernstein prior for single density estimation by using dependent stick breaking processes a general model class and two simplified versions are discussed in detail appealing theoretical properties such as continuity association structure marginal distribution large support and consistency of the posterior distribution are established for all models the behavior of the models is illustrated using simulated and real life data the simulated data are also used to compare the proposed methodology to existing methods supplementary materials for this article are available online

bayesian nonparametric spatial modeling with dirichlet process mixing customary modeling for continuous point referenced data assumes a gaussian process that is often taken to be stationary when such models are fitted within a bayesian framework the unknown parameters of the process are assumed to be random so a random gaussian process results here we propose a novel spatial dirichlet process mixture model to produce a random spatial process that is neither gaussian nor stationary we first develop a spatial dirichlet process model for spatial data and discuss its properties because of familiar limitations associated with direct use of dirichlet process models we introduce mixing by convolving this process with a pure error process we then examine properties of models created through such dirichlet process mixing in the bayesian framework we implement posterior inference using gibbs sampling spatial prediction raises interesting questions but these can be handled finally we illustrate the approach using simulated data as well as a dataset involving precipitati

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

semiparametric bayesian inference in autoregressive panel data models this paper develops bayesian methods for inference in dynamic panel data models with individual effects and applies them to study longitudinal data on earnings from the panel study of income dynamics psid we study semiparametric versions of commonly used random effects autoregressive models in which the distribution of the disturbances is not restricted to fall in a parametric class to model the unknown distributions without resorting to strong parametric assumptions we draw upon recent advances in the theory and computation of nonparametric bayesian models using dirichlet process priors the overall approach can be viewed as an application of the general semiparametric bayesian approach of west muller and escobar 1994 which in turn makes use of results on bayesian density estimation by escobar 1994 and escobar and west 1995 most conventional panel data methods e g anderson and hsiao 1981 macurdy

bayesian regression with heteroscedastic error density and parametric mean function abstract in this paper we consider bayesian estimation of restricted conditional moment models with the linear regression as a particular example a common practice in the bayesian literature for linear regression and other semi parametric models is to use flexible families of distributions for the errors and to assume that the errors are independent from covariates however a model with flexible covariate dependent error distributions should be preferred for the following reason assuming that the error distribution is independent of predictors might lead to inconsistent estimation of the parameters of interest when errors and covariates are dependent to address this issue we develop a bayesian regression model with a parametric mean function defined by a conditional moment condition and flexible predictor dependent error densities sufficient conditions to achieve posterior consistency of the regression parameters and conditional error densities are provided in experiments the proposed method compares favorably with classical and alternative bayesian estimation methods for the estimation of the regression coefficients and conditional densities

a bayesian nonparametric regression model with normalized weights a study of hippocampal atrophy in alzheimer s disease hippocampal volume is one of the best established biomarkers for alzheimer s disease however for appropriate use in clinical trials research the evolution of hippocampal volume needs to be well understood recent theoretical models propose a sigmoidal pattern for its evolution to support this theory the use of bayesian nonparametric regression mixture models seems particularly suitable due to the flexibility that models of this type can achieve and the unsatisfactory predictive properties of semiparametric methods in this article our aim is to develop an interpretable bayesian nonparametric regression model which allows inference with combinations of both continuous and discrete covariates as required for a full analysis of the dataset simple arguments regarding the interpretation of bayesian nonparametric regression mixtures lead naturally to regression weights based on normalized sums difficulty in working with the intractable normalizing constant is overcome thanks to recent advances in mcmc

latent factor models for density estimation although discrete mixture modelling has formed the backbone of the literature on bayesian density estimation there are some well known disadvantages as an alternative to discrete mixtures we propose a class of priors based on random nonlinear functions of a uniform latent variable with an additive residual the induced prior for the density is shown to have desirable properties including ease of centring on an initial guess large support posterior consistency and straightforward computation via gibbs sampling some advantages over discrete mixtures such as dirichlet process mixtures of gaussian kernels are discussed and illustrated via simulations and an application

holomorphic disks and topological invariants for closed three manifolds the aim of this article is to introduce certain topological invariants for closed oriented three manifolds y equipped with a spiny structure given a heegaard splitting of y u 0o u u 1 these theories are variants of the lagrangian floer homology for the g fold symmetric product of relative to certain totally real subspaces associated to u 0 and u 1

bayesian regression with nonparametric heteroskedasticity abstract this paper studies large sample properties of a semiparametric bayesian approach to inference in a linear regression model the approach is to model the distribution of the regression error term by a normal distribution with the variance that is a flexible function of covariates the main result of the paper is a semiparametric bernstein von mises theorem under misspecification even when the distribution of the regression error term is not normal the posterior distribution of the properly recentered and rescaled regression coefficients converges to a normal distribution with the zero mean and the variance equal to the semiparametric efficiency bound

regression analysis using dependent polya trees many commonly used models for linear regression analysis force overly simplistic shape and scale constraints on the residual structure of data we propose a semiparametric bayesian model for regression analysis that produces data driven inference by using a new type of dependent polya tree prior to model arbitrary residual distributions that are allowed to evolve across increasing levels of an ordinal covariate e g time in repeated measurement studies by modeling residual distributions at consecutive covariate levels or time points using separate but dependent polya tree priors distributional information is pooled while allowing for broad pliability to accommodate many types of changing residual distributions we can use the proposed dependent residual structure in a wide range of regression settings including fixed effects and mixed effects linear and nonlinear models for cross sectional prospective and repeated measurement data a simulation study illustrates the flexibility of our novel semiparametric regression model to accurately capture evolving residual distributions in an application to immune development data on immunoglobulin g antibodies in children our new model outperforms several contemporary semiparametric regression models based on a predictive model selection criterion copyright 2013 john wiley sons ltd

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

bayesian nonparametric functional data analysis through density estimation in many modern experimental settings observations are obtained in the form of functions and interest focuses on inferences on a collection of such functions we propose a hierarchical model that allows us to simultaneously estimate multiple curves nonparametrically by using dependent dirichlet process mixtures of gaussians to characterize the joint distribution of predictors and outcomes function estimates are then induced through the conditional distribution of the outcome given the predictors the resulting approach allows for flexible estimation and clustering while borrowing information across curves we also show that the function estimates we obtain are consistent on the space of integrable functions as an illustration we consider an application to the analysis of conductivity and temperature at depth data in the north atlantic

bayesian semiparametric modeling of realized covariance matrices this paper introduces several new bayesian nonparametric models suitable for capturing the unknown conditional distribution of realized covariance rcov matrices existing dynamic wishart models are extended to countably infinite mixture models of wishart and inverse wishart distributions in addition to mixture models with constant weights we propose models with time varying weights to capture time dependence in the unknown distribution each of our models can be combined with returns to provide a coherent joint model of returns and rcov the extensive forecast results show the new models provide very significant improvements in density forecasts for rcov and returns and competitive point forecasts of rcov

absolutely graded floer homologies and intersection forms for four manifolds with boundary abstract in ozsvath and szabo holomorphic triangles and invariants for smooth four manifolds math sg 0110169 2001 we introduced absolute gradings on the three manifold invariants developed in ozsvath and szabo holomorphic disks and topological invariants for closed three manifolds math sg 0101206 ann of math 2001 to appear coupled with the surgery long exact sequences we obtain a number of three and four dimensional applications of this absolute grading including strengthenings of the complexity bounds derived in ozsvath and szabo holomorphic disks and three manifold invariants properties and applications math sg 0105202 ann of math 2001 to appear restrictions on knots whose surgeries give rise to lens spaces and calculations of hf for a variety of three manifolds moreover we show how the structure of hf constrains the exoticness of definite intersection forms for smooth four manifolds which bound a given three manifold in addition to these new applications the techniques also provide alternate proofs of donaldson s diagonalizability theorem and the thom conjecture for cp 2

posterior simulation in countable mixture models for large datasets mixture models or convex combinations of a countable number of probability distributions offer an elegant framework for inference when the population of interest can be subdivided into latent clusters having random characteristics that are heterogeneous between but homogeneous within the clusters traditionally the different kinds of mixture models have been motivated and analyzed from very different perspectives and their common characteristics have not been fully appreciated the inferential techniques developed for these models usually necessitate heavy computational burdens that make them difficult if not impossible to apply to the massive data sets increasingly encountered in real world studies this paper introduces a flexible class of models called generalized polya urn gpu processes many common mixture models including finite mixtures hidden markov models and dirichlet processes are obtained as special cases of gpu processes other important special cases include finite dimensional

khovanov homology and the slice genus we use lee s work on the khovanov homology to define a knot invariant s we show that s k is a concordance invariant and that it provides a lower bound for the smooth slice genus of k as a corollary we give a purely combinatorial proof of the milnor conjecture

stick breaking autoregressive processes this paper considers the problem of defining a time dependent nonparametric prior for use in bayesian nonparametric modelling of time series a recursive construction allows the definition of priors whose marginals have a general stick breaking form the processes with poisson dirichlet and dirichlet process marginals are investigated in some detail we develop a general conditional markov chain monte carlo mcmc method for inference in the wide subclass of these models where the parameters of the marginal stick breaking process are nondecreasing sequences we derive a generalised polya urn scheme type representation of the dirichlet process construction which allows us to develop a marginal mcmc method for this case we apply the proposed methods to financial data to develop a semi parametric stochastic volatility model with a time varying nonparametric returns distribution finally we present two examples concerning the analysis of regional gdp and its growth

latent stick breaking processes we develop a model for stochastic processes with random marginal distributions our model relies on a stick breaking construction for the marginal distribution of the process and introduces dependence across locations by using a latent gaussian copula model as the mechanism for selecting the atoms the resulting latent stick breaking process lasbp induces a random partition of the index space with points closer in space having a higher probability of being in the same cluster we develop an efficient and straightforward markov chain monte carlo mcmc algorithm for computation and discuss applications in financial econometrics and ecology this article has supplementary material online

semiparametric regression for count data we introduce a class of bayesian semiparametric models for regression problems in which the response variable is a count our goal is to provide a flexible easy to implement and robust extension of generalised linear models for datasets of moderate or large size our approach is based on modelling the distribution of the response variable using a dirichlet process whose mean distribution function is itself random and is given a parametric form such as a generalised linear model the effects of the explanatory variables on the response are modelled via both the parameters of the mean distribution function of the dirichlet process and the total mass parameter we discuss modelling options and relationships with other approaches we derive in closed form the marginal posterior distribution of the regression coefficients and discuss its use in inference and computing we illustrate the benefits of our approach with a prognostic model for early breast cancer patients