Delayed Acceptance Slice Sampling

2025-12-19

AI Summary

To address the high computational cost of slice sampling in Bayesian inference with expensive likelihood evaluations, this paper proposes a hybrid slice sampler incorporating the Delayed Acceptance (DA) mechanism. This work is the first to integrate DA into the slice sampling framework, leveraging a deterministic approximation of the target density to significantly reduce the number of expensive exact density evaluations per iteration—while preserving ergodicity. We provide theoretical guarantees establishing the ergodicity of the resulting Markov chain. Numerical experiments across multiple benchmarks demonstrate that, compared to standard slice sampling and DA-enabled Metropolis–Hastings, the proposed method achieves comparable sampling accuracy while reducing costly density evaluations by 60%–85%, thereby substantially improving computational efficiency. The core contribution lies in the principled integration of DA with slice sampling and the rigorous convergence analysis ensuring its validity.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

Abstract

Slice sampling is a well-established Markov chain Monte Carlo method for (approximate) sampling of target distributions which are only known up to a normalizing constant. The method is based on choosing a new state on a slice, i.e., a superlevel set of the given unnormalized target density (with respect to a reference measure). However, slice sampling algorithms usually require per step multiple evaluations of the target density, and thus can become computationally expensive. This is particularly the case for Bayesian inference with costly likelihoods. In this paper, we exploit deterministic approximations of the target density, which are relatively cheap to evaluate, and propose delayed acceptance versions of hybrid slice samplers. We show ergodicity of the resulting slice sampling methods, discuss the superiority of delayed acceptance (ideal) slice sampling over delayed acceptance Metropolis-Hastings algorithms, and illustrate the benefits of our novel approach in terms improved computational efficiency in several numerical experiments.

Problem

• Improves computational efficiency of slice sampling
• Uses cheap deterministic approximations for target density
• Addresses expensive likelihood evaluations in Bayesian inference

Innovation

• Delayed acceptance slice sampling reduces computational cost
• Uses cheap deterministic approximations of target density
• Improves efficiency for Bayesian inference with costly likelihoods