Sampling from Constrained Gibbs Measures: with Applications to High-Dimensional Bayesian Inference
受约束 Gibbs 测度采样及其高维贝叶斯推断应用
This paper considers a non-standard problem of generating samples from a low-temperature Gibbs distribution with \emph{constrained} support, when some of the coordinates of the mode lie on the boundary. These coordinates are referred to as the non-regular part of the model. We show that in a ``pre-asymptotic'' regime in which the limiting Laplace approximation is not yet valid, the low-temperature Gibbs distribution concentrates on a neighborhood of its mode. Within this…