09:00 to 09:30 G Yin ([Texas])Bayesian semiparametic cure rate model with an unknown threshold (Venue: GH seminar RM2) We propose a Bayesian semiparametric model for survival data with a cure fraction. We explicitly consider a finite cure time in the model, which allows us to separate the cured and the uncured populations. We take a mixture prior of a Markov gamma process and a point mass at zero to model the baseline hazard rate function of the entire population. We focus on estimating the cure threshold after which subjects are considered cured. We can incorporate covariates through a structure similar to the proportional hazards model and allow the cure threshold also to depend on the covariates. For illustration, we undertake simulation studies and a full Bayesian analysis of a bone marrow transplant data set. INI 2 09:00 to 10:00 R Kohn ([New South Wales])Flexibly modelling conditional distributions in regression A general methodology for nonparametric regression modelling is proposed based on a mixture-of-experts model extended along two important dimensions. First, the experts are allowed to be heteroscedastic. The standard model with homoscedastic experts is shown to give a poor fit to heteroscedastic data in finite samples, especially when the number of covariates is large. Moreover, with heteroscedastic experts we typically need a lot fewer of them, which is beneficial for interpretation and the efficiency of the inference algorithm. The second main extension is the introduction of variable selection among the covariates in the mean, variance, and in the set of covariates that control the mixture probabilities. The variable selection acts as a self-adjusting mechanism which is a very effective guard against overfitting, and makes fitting of high-dimensional nonparametric models feasible. We also point out a certain type of identification problem that arises with nonparametric experts, and we design the variable selection prior to solve this problem. INI 1 09:30 to 10:00 K Yu ([Brunel])Bayesian inference for quantile regression, expectile regression and M-quantile regression (Venue: GH seminar RM2) Quantile regression, expectile regression and M-quantile regression, including time series based these models, have become popular with wide applications recent years. Based on the authors recent work on Bayesian quantile regression, this talk will outline nonparametric Bayesian inference quantile regression, including quantile autoregression. Moreover, this talk will introduce the idea of Bayesian expectile regression and M-quantile regression. INI 2 10:00 to 11:00 E Arjas ([Helsinki])Postulating monotonicity in nonparametric Bayesian regression Strong structural assumptions, such as constant proportionality between hazard rates in analyzing survival data, or similar proportionality between odds when considering binary responses, are often imposed on the form of the regression function describing the effects of the covariates on a response. This is typically done as a modelling convention and without real support from contextual substantive arguments, evidence coming from earlier studies, or careful diagnostics afterwards. Here we consider one particular way of relaxing such assumptions, by postulating that the dependencies between the considered response and at least some of the covariates are monotonic in an assumed direction. We then consider a class of constructing such models, based on an extension of piecewise constant functions into the multivariate case. Applying Bayesian inference and MCMC, we then illustrate the method by an epidemiological study of some risk factors for cardiovascular diseases. INI 1 11:00 to 11:30 Coffee and Poster session 11:30 to 12:30 D Dunson ([Duke])The matrix stick-breaking process: flexible Bayes meta analysis In analyzing data from multiple related studies, it is often of interest to borrow information across studies and to cluster similar studies. Although parametric hierarchical models are commonly used, a 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 MCMC. 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 applications to a multinational bioassay study and to borrowing of information in compressing signals. INI 1 12:30 to 13:30 Lunch at Wolfson Court 14:00 to 15:00 CKI Williams ([Edinburgh])Gaussian processes for machine learning The aim of this talk is to give an overview of the work that has been going on in the Machine Learning community with respect to Gaussian process prediction; this may be of particular interest to statisticians who are less familiar with the machine learning literature. Particular topics to be covered include approximations for inference (e.g. expectation propagation), covariance functions, dealing with hyperparameters, theoretical viewpoints, and approximations for large datasets. Related Links http://www.gaussianprocess.org/gpml/ - Gaussian Processes for Machine Learning book website INI 1 15:00 to 15:30 Tea and Poster session 15:30 to 16:30 G Karabatsos ([Illinois at Chicago])Bayesian nonparametric single-index regression The single-index model provides a flexible approach to nonlinear regression, and unlike many nonparametric regression models, this model is interpretable, easily handles high-dimensional covariates, and readily incorporates interactions among individual covariates. The model is defined by y = g(w'x) + e, where g is an unspecified univariate (ridge) function, x is a p-dimensional covariate, and the regression errors e[1],...,e[n] are assumed to be iid Normal with common variance. Previous research on the single-index model has mainly been limited to issues of point-estimation, where specifically, the focus is to estimate the function g by maximizing a penalized likelihood, with the function defined by splines having a fixed number of knots located at fixed locations of the predictor space. In this talk I will discuss a novel, Bayesian nonparametric approach to the single-index model, where the function g is modeled by linear splines with the number and locations of knots treated as unknown parameters, where random-effect parameters are added to the model to describe the effects of different clusters of observations, and where the variance of the regression error is allowed to change nonparametrically with the value of the covariate. In particular, the random-effects are modeled by a Dirichlet Process centered on a Normal distribution, and the error variances are modeled by a Dirichlet Process centered on a inverse-gamma distribution. Moreover, this new single-index model can readily handle observed dependent variables that are either continuous, binary, ordered-categories, or counts. I will illustrate Bayesian nonparametric single-index models through the analysis of real data of students from secondary schools. Related Links http://tigger.uic.edu/~georgek/HomePage/ - Homepage INI 1 16:30 to 17:00 MW Ho ([Singapore])A Bayes method for a monotone hazard rate via ${S}$-paths A class of random hazard rates, which is defined as a mixture of an indicator kernel convoluted with a completely random measure, is of interest. We provide an explicit characterization of the posterior distribution of this mixture hazard rate model via a finite mixture of $\mathbf{S}-paths. A closed and tractable Bayes estimator for the hazard rate is derived to be a finite sum over$\mathbf{S}-paths. The path characterization or the estimator is proved to be a Rao-Blackwellization of an existing partition characterization or partition-sum estimator. This accentuates the importance of $\mathbf{S}-path in Bayesian modeling of monotone hazard rates. An efficient Markov chain Monte Carlo method is proposed to approximate this class of estimates. It is shown that$\mathbf{S}-path characterization also exists in modeling with covariates by a proportional hazard model, and the proposed algorithm again applies. Related Links http://www.stat.nus.edu.sg/~stahmw/AOS0125.pdf INI 1 17:00 to 17:30 T Choi ([Maryland])Alternative posterior consisteency results in nonparametric binary regression using Gaussian process priors We establish consistency of posterior distribution when a Gaussian process prior is used as a prior distribution for the unknown binary regression function. Specifically, we take the work of Ghosal and Roy (2007) as our starting point, and then weaken their assumptions on the smoothness of the Gaussian process kernel while retaining a stronger yet applicable condition about design points. Furthermore, we extend their results to multi-dimensional covariates under a weaker smoothness condition on the Gaussian process. Finally, we study the extent to which posterior consistency can be achieved under a general model structure, when additional hyperparameters in the covariance function of a Gaussian process are involved. INI 1 19:30 to 23:00 Conference Dinner at Christ's College (Dining Hall)
 09:00 to 09:30 P De Blasi ([Turin])Asymptotics for posterior hazards (Venue: GH seminar RM2) A popular Bayesian nonparametric approach to survival analysis consists in modeling hazard rates as kernel mixtures driven by a completely random measure. A comprehensive analysis of the asymptotic behaviour of such models is provided. Consistency of the posterior distribution is investigated and central limit theorems for both linear and quadratic functionals of the posterior hazard rate are derived. The general results are then specialized to various specific kernels and mixing measures, thus yielding consistency under minimal conditions and neat central limit theorems for the distribution of functionals. INI 2 09:00 to 10:00 FA Quintana ([Catolica de Chile])Bayesian clustering with regression We consider clustering with regression, i.e., we develop a probability model for random clusters that is indexed by covariates. The two motivating applications are inference for a clinical trial and for survival of patients with breast cancer. As part of the desired inference we wish to define clusters of patients. Defining a prior probability model for cluster memberships should include a regression on patient baseline covariates. We build on product partition models (PPM). We define an extension of the PPM to include the desired regression. This is achieved by including in the cohesion a new factor that increases the probability of experimental units with similar covariates to be included in the same cluster. We discuss implementations suitable for continuous, categorical, count and ordinal covariates. INI 1 09:30 to 10:00 R Mena ([IIMAS, UNAM])Bayesian nonparametric methods for prediction in EST analysis (Venue: GH seminar RM2) Expressed sequence tags (ESTs) analyses are an important tool for gene identification in organisms. Given a preliminary EST survey from a certain cDNA library, various features of a possible additional sample have to be predicted. For instance, interest may rely on estimating the number of new genes to be detected and the gene discovery rate at each additional read. We propose a Bayesian nonparametric approach for prediction in EST analysis based on nonparametric priors inducing Gibbs-type exchangeable random partitions and derive estimators for the relevant quantities. Several EST datasets are analysed by resorting to the two parameter Poisson-Dirichlet process, which represents the most remarkable Gibbs-type prior. Our proposal has appealing properties over frequentist nonparametric methods, which become unstable when prediction is required for large future samples. INI 2 10:00 to 11:00 S Basu ([Northern Illinois])Double Dirichlet process mixtures In this work we consider a new class of Dirichlet process mixtures, that we call the double and multple DPM class, which generates a clustering structure in the data that is different from those generated by simple DPM or other DPM models. Fitting of double and related DPM models is possible by MCMC methods by multiple applications of the standard Polya urn and blocked Gibbs samplers within each sweep of the sampling. Based on experimental investigations we show that the proposed model performs reasonably well when the model is correctly specified and when the model is misspecified. We also investigate the similarity between the clustering produced by the model fit and the true clustering. Finally, we consider model comparison and model diagnostics, and illustrate the implementation, performance and applicability of the proposed class of DPM models in regressions for survival data and clustered longitudinal data. INI 1 11:00 to 11:30 Coffee 11:30 to 12:30 J Griffin ([Warwick])Normalised kernel-weighted random measures This talk discusses a wide class of probability measure-valued processes to be used as nonparametric priors for problems with time-varying, spatially-varying or covariate-dependent distributions. They are constructed by normalizing correlated random measures, which are stationary and have a known marginal process. Dependence is modelled using kernels (a method that has become popular in spatial modelling). The ideas extend Griffin~(2007), which used an exponential kernel in time series problems, to arbitrary kernel functions. Computational issues will be discussed and the ideas will be illustrated by examples in financial time series. Griffin, J. E. (2007): The Ornstein-Uhlenbeek Dirichlet Process and other measure valued processes for Bayesian inference,'' Technical Report, University of Warwick. INI 1 12:30 to 13:30 Lunch at Wolfson Court 14:00 to 15:00 G Kokolakis ([Athens])Convexification and multimodality of random probability measures In this work we develop and describe a new class of nonparametric prior distributions on the subspace of the random multivariate distributions. Our methodology is based on a variant of Khinchin's representation theorem for unimodal distributions extended to multimodal multivariate cases. Results using our approach in a bivariate setting with a random draw from a Dirichlet process are presented. Related Links http://ba.stat.cmu.edu/journal/2007/vol02/issue01/kokolakis.pdf - Bayesian Analysis INI 1 15:00 to 15:30 Tea 15:30 to 16:30 J Lee ([Seoul])Posterior consistency of species sampling priors Recently there have been increasing interests on species sampling priors, the nonparametric priors defined as the directing random probability measures of the species sampling sequences. In this paper, we show that not all of the species sampling priors produce consistent posteriors. In particular, in the class of Pitman-Yor process priors, the only priors rendering posterior consistency are essentially the Dirichlet process priors. For the general species sampling priors, we also give a necessary and sufficient condition for the posterior consistency. INI 1 16:30 to 17:30 L James ([Hong Kong])Some new identities for Dirichlet means and implications We present some new identities for Dirichlet Mean funcitonal and discuss some applications. INI 1 18:45 to 19:30 Dinner at Wolfson Court (Residents only)