SMS scnews item created by John Ormerod at Fri 10 May 2013 1327
Type: Seminar
Distribution: World
Expiry: 18 May 2013
Calendar1: 17 May 2013 1400-1500
CalLoc1: Carslaw 373
Auth: jormerod@pjormerod3.pc (assumed)

Statistics Seminar: Bondell -- Consistent high-dimensional Bayesian variable selection via penalized credible regions

For high-dimensional data, selection of predictors for regression
is a challenging problem. Methods such as sure screening, forward
selection, or penalization are commonly used. Instead, Bayesian
variable selection methods place prior distributions over model
space, along with priors on the parameters, or equivalently, a
mixture prior with mass at zero for the parameters in the full
model. Since exhaustive enumeration is not feasible, posterior
model probabilities are often obtained via long MCMC runs. The
chosen model can depend heavily on various choices for priors and
also posterior thresholds. Alternatively, we propose a conjugate
prior only on the full model parameters and to use sparse
solutions within posterior credible regions to perform selection.
These posterior credible regions often have closed form
representations, and it is shown that these sparse solutions can
be computed via existing algorithms. The approach is shown to
outperform common methods in the high-dimensional setting,
particularly under correlation. By searching for a sparse solution
within a joint credible region, consistent model selection is
established. Furthermore, it is shown that the simple use of
marginal credible intervals can give consistent selection up to
the case where the dimension grows exponentially in the sample
size.


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