Transdimensional methods for variable selection in large p, small n problems
Speaker: Jim Griffin (University of Kent)
Date: Thu 11th March 2010
Location: Statistics Seminar Room- Library building
Model search in probit regression is often conducted by simultaneously exploring the model and parameter space, using a reversible jump MCMC sampler. The chain moves around model space using random walk proposals. In large p, small n problems these samplers often have high acceptance rates for between model moves which are associated with poorly mixing chains. In this talk, a more general model proposal is discussed that allows us to propose models ''further'' from our current model. This proposal can be tuned to achieve a suitable acceptance rate for good mixing. The effectiveness of this proposal is linked to the form of the marginalisation scheme when updating the model and we propose a new efficient implementation of the automatic generic transdimensional algorithm of Green~(2003). The development of a tuneable proposal allows us to develop adaptive MCMC schemes using the idea of diminishing adaptation. The methods will be illustrate by applications to gene expression data.
(This talk is part of the Statistics and Actuarial Science series.)