Abstract
SummaryThe availability of datasets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these datasets has proved difficult since available Markov chain Monte Carlo methods do not perform well in typical problem sizes of interest. We propose new adaptive Markov chain Monte Carlo algorithms to address this shortcoming. The adaptive design of these algorithms exploits the observation that in large-$p$, small-$n$ settings, the majority of the $p$ variables will be approximately uncorrelated a posteriori. The algorithms adaptively build suitable nonlocal proposals that result in moves with squared jumping distance significantly larger than standard methods. Their performance is studied empirically in high-dimensional problems and speed-ups of up to four orders of magnitude are observed.
Highlights
The availability of large data sets has led to an increasing interest in variable selection methods applied to regression models with many potential variables but few observations, so-called large 25 p, small n problems
Markov chain Monte Carlo methods are typically used to sample from the posterior distribution (George and McCulloch, 1997; O’Hara and Sillanpaa, 2009; Clyde et al, 2011)
The exploratory individual adaptation algorithm is described in Algorithm 1 and we indicate its transition kernel at time i as PηE(IiA)
Summary
The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain Monte Carlo methods do not perform well in typical problem sizes of interest. The algorithms adaptively build suitable non-local proposals that result in moves with squared jumping distance significantly larger than standard methods. Their performance is studied empirically in high-dimensional problems and speedups of up to 4 orders of magnitude are observed. Some key words: variable selection; spike-and-slab priors; high-dimensional data; large p, small n problems; linear regression: expected squared jumping distance; optimal scaling
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
