Bayesian Methods for Variable Selection with Applications to High-dimensional Data
Dal 17/06/2013 ore 14.00 al 21/06/2013 ore 13.00
Villa del Grumello
Via per Cernobbio, 11 - 22100 Como
www.villadelgrumello.it
The school ABS13 (2013 Applied Bayesian Statistics School) , organised by CNR IMATI (Milano) and Dipartimento di Scienze Statistiche, Università Cattolica, Milano, aims to present state-of-the-art Bayesian applications, inviting leading experts in their field. Each year a different topic is chosen.
The topic chosen for the 2013 school is "Bayesian Methods for Variable Selection with Applications to High-dimensional Data".
The lecturer will be Prof. Marina Vannucci (Rice University, Houston, USA). She will be assisted by Raffaele Argiento (CNR IMATI, Italy) for the practical sessions.
This course will cover Bayesian methods for variable selection and applications. Various modeling settings will be considered, starting with the widely used linear regression models. Bayesian methods for variable selection have been successfully employed in linear setting models, making problems with hundreds of regressor variables and a few samples quite feasible. These methods use mixing priors on the regression coefficients to do the selection and fast Markov Chain Monte Carlo stochastic search approaches to sample from posterior distributions. Extensions of the methodologies to other linear settings will also be considered, in particular to handle categorical responses, via probit models, and survival data, via accelerated failure time models. Applications of the methodologies will focus on high-dimensional data from genomic studies that use high-throughtput expression levels of thousands of genes. For such applications, models and inferential algorithms will be modified to incorporate specific information, such as data substructure and biological knowledge on gene functions. The last part of the course will address variable selection for a different modeling setting, that is mixture models, both unsupervised (for sample clustering) and supervised (for discriminant analysis). In mixture models variable selection is achieved via latent binary vectors that identify the discriminating variables and are updated via a Metropolis algorithm. In the clustering setting, inference on the sample allocations is obtained either via reversible jump MCMC or split-merge MCMC techniques. Performances of the methodologies will be illustrated on simulated data and on DNA microarray data. The course will end with a brief description of additional topics, such as the use of variable selection priors in nonlinear settings, via Gaussian processes, and for the analysis of functional data.
The school will make use of lectures, practical sessions, software demonstrations, informal discussion sessions and presentations of research projects by school participants. The slides and background reading material will be distributed to the students before the start of the course.
Organizzato da:
CNR IMATI -Sede di Milano
Università Cattolica, Milano
Referente organizzativo:
Fabrizio Ruggeri
CNR - Istituto di matematica applicata e tecnologie informatiche
Via Bassini 15
20133 Milano
abs13@mi.imati.cnr.it
0223699522
Modalità di accesso: a pagamento
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