# Generalized Elliptical Slice Sampling with Regional Pseudo-priors

## TL;DR

This paper introduces a generalized elliptical slice sampling algorithm that uses regional pseudo-priors and mixture models to improve sampling efficiency, especially in multi-modal distributions, with proven ergodicity and demonstrated advantages in experiments.

## Contribution

It proposes a novel elliptical slice sampling method incorporating regional pseudo-priors and mixture models, with theoretical proof of ergodicity and enhanced performance in mode detection.

## Key findings

- More distant modes are found with the same starting points.
- Lower rejection rates compared to traditional methods.
- More accurate estimations for uni-modal posteriors and effective mode detection in multi-modal cases.

## Abstract

In this paper, we propose a MCMC algorithm based on elliptical slice sampling with the purpose to improve sampling efficiency. During sampling, a mixture distribution is fitted periodically to previous samples. The components of the mixture distribution are called regional pseudo-priors because each component serves as the pseudo-prior for a subregion of the sampling space. Expectation maximization algorithm, variational inference algorithm and stochastic approximation algorithm are used to estimate the parameters. Meanwhile, parallel computing is used to relieve the burden of computation. Ergodicity of the proposed algorithm is proven mathematically. Experimental results on one synthetic and two real-world dataset show that the proposed algorithm has the following advantages: with the same starting points, the proposed algorithm can find more distant modes; the proposed algorithm has lower rejection rates; when doing Bayesian inference for uni-modal posterior distributions, the proposed algorithm can give more accurate estimations; when doing Bayesian inference for multi-modal posterior distributions, the proposed algorithm can find different modes well, and the estimated means of the mixture distribution can provide additional information for the location of modes.