Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling

2026-09-08

AI Summary

该研究通过分析不同切片查找方案下混合切片采样的平均目标密度评估次数，提出了自动适应性调优方案，解决了切片采样中初始设置依赖问题。

Abstract

Slice sampling is a Markov chain Monte Carlo algorithm that draws its next state uniformly from a"slice"---a super-level set of the target density function---at each iteration, thereby providing automatic local adaptivity to the scale of the target. In practice the exact slice is not known, so general-purpose implementations use an approximate slice that is grown from a starting interval of length $w>0$, with a computational cost that depends on $w$. This work presents an analysis of the average per-iteration number of target density evaluations, as a function of $w$, of hybrid slice sampling with various slice-finding schemes for targets with contiguous slices. The paper uses the results of the analysis to develop automated, slice-adaptive tuning schemes along with suboptimality bounds and asymptotic convergence guarantees. Simulations demonstrate that the tuning schemes reliably yield near-optimal slice-adaptive tuning with essentially no dependence on the initial setting of $w$.

Problem

• slice sampling
• target density evaluation
• adaptive tuning

Innovation

• Hybrid Slice Sampling
• Slice-Adaptive Tuning
• Target Density Evaluation
• Automatic Adaptivity
• Asymptotic Convergence