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Adaptive sampling for Bayesian variable selection
| Content Provider | Semantic Scholar |
|---|---|
| Author | Nott, David J. |
| Abstract | Bayesian methods for variable selection and for dealing with model uncertainty have become increasingly popular in recent years, mostly due to advances in Markov chain Monte Carlo computational algorithms. In this paper we consider adaptive Markov chain Monte Carlo schemes for Bayesian variable selection in Gaussian linear regression models which improve on standard Metropolis-Hastings algorithms by making use of accumulated information about the posterior distribution during sampling for the construction of proposal distributions. Adaptation needs to be done very carefully to ensure that sampling is from the correct ergodic distribution. We give conditions for the validity of an adaptive sampling scheme in this problem, and for simulating from a distribution on a finite state space in general, and suggest a class of adaptive proposal densities which uses best linear prediction to approximate the Gibbs sampler. Our sampling scheme is computationally much faster per iteration than the Gibbs sampler, and when this is taken into account the efficiency gains when using our sampling scheme compared to alternative approaches are substantial in terms of precision of estimation of posterior quantities of interest for a given amount of computation time. We compare our method with other sampling schemes for examples involving both real and simulated data. The methodology developed in the article can be extended to variable selection in more general problems. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.researchgate.net/profile/Robert_Kohn/publication/5207408_Adaptive_sampling_for_Bayesian_variable_selection/links/0fcfd51267f006d03d000000.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Adaptive sampling Approximation algorithm Computation Ergodicity Feature selection Finite-state machine Gibbs sampling Iteration Markov chain Monte Carlo Metropolis Metropolis–Hastings algorithm Monte Carlo method Normal Statistical Distribution Quantity Sampling (signal processing) Sampling - Surgical action Simulation State space Time complexity density |
| Content Type | Text |
| Resource Type | Article |
