PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Concave-Convex Adaptive Rejection Sampling
Dilan Gorur and Yee Whye Teh
Journal of Computational and Graphical Statistics 2010.

Abstract

We describe a method for generating independent samples from univariate density functions using adaptive rejection sampling without the log-concavity requirement. The method makes use of the fact that many functions can be expressed as a sum of con- cave and convex functions. Using a concave-convex decomposition, we bound the log-density by separately bounding the concave and convex parts using piecewise linear functions. The upper bound can then be used as the proposal distribution in rejection sampling. We demonstrate the applicability of the concave-convex approach on a number of standard distributions and describe an application to the efficient construction of sequential Monte Carlo proposal distributions for inference over genealogical trees. Computer code for the proposed algorithms is available online.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:8128
Deposited By:Yee Whye Teh
Deposited On:24 April 2011