Construction and properties of Bayesian nonparametric regression models

Workshop theme

Modern Bayesian nonparametric analysis was introduced by Ferguson with the development of the Dirichlet process in the 1970s. Since then there has been rapid progress in both theoretical and applied work, the latter usually relying on Markov chain Monte Carlo simulation methods. The outstanding challenges include the construction and properties, such as consistency issues, of Bayesian nonparametric regression models. This is the theme of the workshop.

Bayesian nonparametric inference relies on the construction of an infinite dimensional probability distribution on function spaces. Typically this is a space of density functions, but could also be hazard rate functions, distribution functions or some other function related to modelling observations. The probability models have traditionally been adapted from stochastic process; such as Lévy processes. These probabilities act as the prior distribution and combine with the data to provide the posterior distribution.

Another strand of Bayesian nonparametric inference involves the construction of regression functions. This is concerned with how observables relate to each other, where one type of observable (the predictor observable) is used to predict another type (the dependent observable). To date the functions used to do this have been quite different to those used for modeling density functions. For example, splines and wavelets are recent popular choices, and these have been used to model means and variances sitting within a class of parametric density functions.

Recent attempts have been made to strengthen the connections between these two area of Bayesian nonparametric research. The ultimate goal is obtain suitable classes of fully Bayesian nonparametric regression models. The current standard is semi-parametric; where if density functions are modeled nonparametrically, the regression function is modeled parametrically, and if the regression model is nonparametric then the density function which carries it is modeled parametrically.

The full Bayesian nonparametric regression model would involve the construction of a collection of density functions; one for each distinct predictor variable. The key question is how to connect up all the density functions to provide suitable interactions.

Leading international researchers in Bayesian nonparametric methods, both theory and applied, will be brought together to discuss and tackle this outstanding issue in Bayesian research.

The application is closed

Timetable

Monday 6th August 2007
08:00 to 09:00	Registration	No Room Required
09:00 to 10:30	Subhashis Ghoshal North Carolina State University Dirichlet process, related priors and posterior asymptotics	Room 1
10:30 to 11:00	Coffee	No Room Required
11:00 to 12:30	Antonio Lijoi Models beyond the Dirichlet process	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:30	David Dunson Duke University Applications to biostatistics	Room 1
15:30 to 16:00	Tea	No Room Required
16:00 to 17:30	Applications to machine learning	Room 1
17:30 to 18:30	Welcome Wine Reception and Poster session	No Room Required
18:45 to 19:30	Dinner at Wolfson Court (Residents only)	No Room Required

Tuesday 7th August 2007
09:00 to 09:30	Bhramar Mukherjee University of Michigan Bayesian semiparametric analysis of gene-environment interactionn unde conditional gene-environment independence (Venue: GH seminar RM2)	Room 2
09:00 to 10:00	Yongdai Kim Seoul National University Posterior consisteny of logistic random effect models	Room 1
09:30 to 10:00	Matteo Ruggiero Università degli Studi di Torino Bayesian countable representation of some population genetics diffusions (Venue: GH seminar RM2)	Room 2
10:00 to 11:00	Luis Enrique Nieto-Barajas Saitama University Some good news about nonparametric priors in density estimation	Room 1
11:00 to 11:30	Coffee and Poster session	No Room Required
11:30 to 12:30	Wes Johnson Semi-parametric survival analysis with time dependent covariates	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Prakash Laud Medical College of Wisconsin Genetic association studies in the presence of population structure and admixture	Room 1
15:00 to 15:30	Tea and Poster session	No Room Required
15:30 to 16:30	Dennis Cox Rice University Useful priors for covariance operators	Room 1
16:30 to 17:00	Maria Kalli University of Kent Bayesian nonparametrics and variance regression-: mixtures of Dirichlet processes and the slice sampler	Room 1
17:00 to 17:30	Dario Spano University of Oxford Canonical representations for dependent Dirichlet populations	Room 1
17:30 to 18:30	Steven MacEachern Ohio State University Minimally informative nonparametric Bayesian procedures	Room 1
18:45 to 19:30	Dinner at Wolfson Court (Residents only)	No Room Required

Wednesday 8th August 2007
09:00 to 10:00	Alessandra Guglielmi Semiparametric inference for the accelerated failure time model using hierarchical mixtures with generalised gamma processes	Room 1
09:00 to 09:30	Igor Pruenster On the posterior structure of NRMI (Venue: GH seminar RM2)	Room 2
09:30 to 10:00	Amy Herring Semiparametric bayes joint modeling with functional predictors (Venue: GH seminar RM2)	Room 2
10:00 to 11:00	Maria De Iorio Imperial College London A DDP model for survival regression	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Sonia Petrone Hybrid Dirichlet processes for functional data	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Anna Simoni Regularised posteriors in linear ill-posed inverse problems	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Elmira Popova Bayesian semiparametric analysis for a single item maintenance optimis	Room 1
16:30 to 17:30	Functional data analysis using a levy random fields model for multi-spectra peak identification and classification	Room 1
17:30 to 18:30	Mark Steel University of Warwick Bayesian nonparametric modelling with the Dirichlet process regression smoother	Room 1
18:45 to 19:30	Dinner at Wolfson Court (Residents only)	No Room Required

Thursday 9th August 2007
09:00 to 09:30	Guosheng Yin Bayesian semiparametic cure rate model with an unknown threshold (Venue: GH seminar RM2)	Room 2
09:00 to 10:00	Robert Kohn University of New South Wales Flexibly modelling conditional distributions in regression	Room 1
09:30 to 10:00	Keming Yu Brunel University Bayesian inference for quantile regression, expectile regression and M-quantile regression (Venue: GH seminar RM2)	Room 2
10:00 to 11:00	Elja Arjas University of Helsinki Postulating monotonicity in nonparametric Bayesian regression	Room 1
11:00 to 11:30	Coffee and Poster session	No Room Required
11:30 to 12:30	David Dunson Duke University The matrix stick-breaking process: flexible Bayes meta analysis	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Gaussian processes for machine learning	Room 1
15:00 to 15:30	Tea and Poster session	No Room Required
15:30 to 16:30	George Karabatsos University of Illinois at Chicago Bayesian nonparametric single-index regression	Room 1
16:30 to 17:00	Man-Wai Ho National University of Singapore A Bayes method for a monotone hazard rate via ${S}$-paths	Room 1
17:00 to 17:30	Taeryon Choi University of Maryland, College Park Alternative posterior consisteency results in nonparametric binary regression using Gaussian process priors	Room 1
19:30 to 23:00	Conference Dinner at Christ's College (Dining Hall)	No Room Required

Friday 10th August 2007
09:00 to 09:30	Pierpaolo De Blasi Asymptotics for posterior hazards (Venue: GH seminar RM2)	Room 2
09:00 to 10:00	Fernando Andres Quintana Pontificia Universidad Católica de Chile Bayesian clustering with regression	Room 1
09:30 to 10:00	Ramses Mena Bayesian nonparametric methods for prediction in EST analysis (Venue: GH seminar RM2)	Room 2
10:00 to 11:00	Sanjib Basu Double Dirichlet process mixtures	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Jim Griffin University of Warwick Normalised kernel-weighted random measures	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	George Kokolakis National Technical University of Athens Convexification and multimodality of random probability measures	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Jaeyong Lee Posterior consistency of species sampling priors	Room 1
16:30 to 17:30	Lancelot James Hong Kong University of Science and Technology Some new identities for Dirichlet means and implications	Room 1
18:45 to 19:30	Dinner at Wolfson Court (Residents only)	No Room Required

Construction and properties of Bayesian nonparametric regression models

Speakers

Elja Arjas University of Helsinki
Sanjib Basu
Taeryon Choi University of Maryland, College Park
Dennis Cox Rice University
Pierpaolo De Blasi
Maria De Iorio Imperial College London
David Dunson Duke University
Subhashis Ghoshal North Carolina State University
Jim Griffin University of Warwick
Alessandra Guglielmi
Amy Herring
Man-Wai Ho National University of Singapore
Lancelot James Hong Kong University of Science and Technology
Wes Johnson
Maria Kalli University of Kent
George Karabatsos University of Illinois at Chicago
Yongdai Kim Seoul National University
Robert Kohn University of New South Wales
George Kokolakis National Technical University of Athens
Prakash Laud Medical College of Wisconsin
Jaeyong Lee
Antonio Lijoi
Steven MacEachern Ohio State University
Ramses Mena
Bhramar Mukherjee University of Michigan
Luis Enrique Nieto-Barajas Saitama University
Sonia Petrone
Elmira Popova
Igor Pruenster
Fernando Andres Quintana Pontificia Universidad Católica de Chile
Matteo Ruggiero Università degli Studi di Torino
Anna Simoni
Dario Spano University of Oxford
Mark Steel University of Warwick
Guosheng Yin
Keming Yu Brunel University

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Construction and properties of Bayesian nonparametric regression models

Workshop theme

The application is closed

Timetable

Speakers

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