Perturbation stability of slice sampling under noisy target evaluations

Establish perturbation-stability results for slice sampling algorithms, including standard and elliptical slice sampling, quantifying how noise or error in target density evaluations affects ergodicity, convergence rates, and bias, and derive conditions guaranteeing robustness under such perturbations.

Background

Slice sampling methods often serve as near–black-box procedures requiring minimal tuning and avoiding random-walk behavior, and are widely used in practice.

Despite their popularity, the authors state that stability with respect to errors in target evaluations has not been explored, highlighting a gap in perturbation theory for these samplers.