A1324
Title: Adaptive neighborhood methods for Bayesian variable selection and structure learning
Authors: Jim Griffin - University College London (United Kingdom) [presenting]
Abstract: Some Bayesian methods lead to posterior distributions defined on large discrete spaces. Bayesian variable selection for regression models with p variables leads to a posterior distribution defined on a space with $2^p$ possible models. Bayesian structure learning in Gaussian graphical models leads to a posterior distribution on all possible DAGs. It is well understood that sampling from these posterior distributions is very challenging. The purpose is to review recent work on the use of adaptive random neighborhood with informed proposal (ARNI) samplers. These combine adaptive proposals with informed proposals. Informed proposals allow the methods to converge more quickly and mix better than vanilla MCMC methods and the adaptive proposal allows scaling to large p settings. The use of these methods is illustrated in generalized linear models and Gaussian graphical models.
