Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling

• URL: http://arxiv.org/abs/2609.08172v1
• Date: Tue, 08 Sep 2026 03:01:25 GMT
• Title: Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling
• Abstract summary: Slice sampling is a Markov chain Monte Carlo algorithm that draws its next state uniformly from a "slice"<n>The paper uses the results of the analysis to develop automated, slice-adaptive tuning schemes along with suboptimality and convergence guarantees.
• Score: 14.61162620616131
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $w$.

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