Statistics Papers
Document Type
Conference Paper
Date of this Version
2014
Publication Source
Seventeenth International Conference on Artificial Intelligence and Statistics
Volume
33
Start Page
448
Last Page
456
Abstract
We develop a new sampling strategy that uses the hit-and-run algorithm within level sets of a target density. Our method can be applied to any quasi-concave density, which covers a broad class of models. Standard sampling methods often perform poorly on densities that are high-dimensional or multi-modal. Our level set sampler performs well in high-dimensional settings, which we illustrate on a spike-and-slab mixture model. We also extend our method to exponentially-tilted quasi-concave densities, which arise in Bayesian models consisting of a log-concave likelihood and quasiconcave prior density. We illustrate our exponentially-tilted level-set sampler on a Cauchy-normal model where our sampler is better able to handle a high-dimensional and multi-modal posterior distribution compared to Gibbs sampling and Hamiltonian Monte Carlo.
Recommended Citation
Jensen, S. T., & Foster, D. P. (2014). A Level-Set Hit-And-Run Sampler for Quasi-Concave Distributions. Seventeenth International Conference on Artificial Intelligence and Statistics, 33 448-456. Retrieved from https://repository.upenn.edu/statistics_papers/143
Date Posted: 27 November 2017
This document has been peer reviewed.