A Fast, Robust Elliptical Slice Sampling Implementation for Linearly Truncated Multivariate Normal Distributions
This work provides a more efficient and robust method for statistical inference and Bayesian analysis in fields like machine learning and computational statistics, though it is incremental as it builds on existing elliptical slice sampling techniques.
The paper tackled the problem of efficiently sampling from linearly truncated multivariate normal distributions by developing an algorithm that computes ellipse-polytope intersections in O(m log m) time, resulting in improved numerical stability, faster running times, and easy parallelization for multiple Markov chains.
Elliptical slice sampling, when adapted to linearly truncated multivariate normal distributions, is a rejection-free Markov chain Monte Carlo method. At its core, it requires analytically constructing an ellipse-polytope intersection. The main novelty of this paper is an algorithm that computes this intersection in $\mathcal{O}(m \log m)$ time, where $m$ is the number of linear inequality constraints representing the polytope. We show that an implementation based on this algorithm enhances numerical stability, speeds up running time, and is easy to parallelize for launching multiple Markov chains.