Stepping-out slice sampling
Algorithms AIMech:SteppingOutSliceSampling DRAFT
A univariate slice-sampling algorithm that randomly places a width-w interval around the current point, expands it in width-w steps under a randomly divided budget, and samples by slice-aware interval shrinkage.
Identity Notes & Concept Scope
This record specifies Neal’s stepping-out procedure paired with shrinkage, Figures 3 and 5. The interval-search component alone is not a complete sampler. It differs from doubling in expansion increments and in not requiring doubling’s retrospective acceptability test. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 159 prior native IDs/names/aliases. Ignored-inclusive full-checkout searches found prior discovery leads for Gibbs and slice sampling plus unrelated environment substring hits, not existing concept records. Existing HMM/MRF models and general Metropolis–Hastings were inspected to distinguish model, general transition and specialized algorithm scope.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
Draw height y uniformly below f(x0). For w>0 and integer m≥1, set L=x0−wU and R=L+w with U uniform on (0,1); independently choose J uniformly from {0,...,m−1} and K=m−1−J. Extend L left by w while J remains positive and f(L)>y, decrementing J; similarly extend R right using K. From this interval repeatedly propose x1 uniformly: accept if f(x1)>y; otherwise replace the left endpoint by x1 when x1<x0, or the right endpoint otherwise. Shrinkage retains x0. The random placement and random left/right budget split are part of the invariance construction; the resulting interval need not cover every slice component.
⚠️ Curated Limitations & Negative Results
- The finite expansion cap limits the interval length to at most mw. It is not a certificate that all of the slice has been found.
- The width and expansion budget affect computational work and exploration; this method does not remove all tuning choices.
- Shrinking the rejected side relative to the current state is essential. Arbitrary interval placement or budget allocation is not the proven kernel.
- Unimodal shortcuts and tuning width from past draws in Section 4.4 require the source’s additional conditions, including unlimited expansion for that history-based width argument; they are not generalized here.
- Multimodality, constrained supports, numerical density evaluation and finite precision require care. No universal mixing guarantee is asserted.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:MarkovChain
Markov Chain
|
related_match | The procedure constructs Markov transitions for sampling a specified target, with the invariance and convergence qualifications stated in this record. AIO MarkovChain denotes the stochastic process/model and is exported beneath Network. This is a method-to-process related match, not equivalence, subclass membership or a claim that the algorithm is a trained network. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Radford M. Neal
|
author technical report
full_text
|
ID: arxiv:physics/0009028v1
sha256:c6cf46fb834b…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T07:00:31Z
Updated: 2026-10-11T07:00:31Z
Source File:
data/curated/SteppingOutSliceSampling.yaml