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Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling

  • Trevor Campbell
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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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Cite

BibTeXRIS
BibTeX
@misc{campbell2026optimal,
  title = {{Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling}},
  author = {Trevor Campbell},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08172},
  eprint = {2609.08172},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08172},
}
RIS
TY  - UNPB
TI  - Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling
AU  - Trevor Campbell
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08172
UR  - https://arxiv.org/abs/2609.08172
AB  - 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.
ER  -