Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling

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 $w$.

Computation (stat.CO); Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2609.08172 [stat.CO]

(or arXiv:2609.08172v1 [stat.CO] for this version)

https://doi.org/10.48550/arXiv.2609.08172 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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