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Slice sampling

Algorithms AIMech:SliceSampling DRAFT

An auxiliary-variable Monte Carlo method that augments a target density with a uniform height below its graph and updates the state using a transition preserving the uniform distribution on the resulting density slice.

Identity Notes & Concept Scope This is the single-height construction and its valid within-slice transitions, not a claim that every implementation draws independently and uniformly from an entire slice. Univariate stepping-out and doubling algorithms are distinct concrete variants. Multiple-auxiliary-variable, reflective and overrelaxed extensions require their own mechanism descriptions. 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

For nonnegative unnormalized density f with finite positive integral Z, introduce y and the joint density 1/Z on {(x,y):0<y<f(x)}. Its x marginal is f(x)/Z. At a current supported x draw y uniformly from (0,f(x)), then update x with a kernel leaving uniform measure on S_y={x:f(x)>y} invariant. An independent uniform draw from S_y is one option but is often unavailable; a valid Markov update within the slice can replace it. Discarding y recovers a chain with the desired x marginal under the construction’s invariance conditions.

supports Source: Slice Sampling · Locator: Section 3, The idea of slice sampling, Equations (1)–(2), PDF/printed p. 6; Section 4.3 correctness argument, pp. 12–16

⚠️ Curated Limitations & Negative Results

The target must be proper, and the density and slice updates must be implemented on their valid support. A random move that merely stays inside the slice need not preserve its uniform distribution.
Local interval search need not find the entire slice, especially when it has disconnected components. Its acceptance and shrinkage rules determine validity and exploration.
Target invariance does not alone establish ergodicity or efficient movement between modes. The retained states need not be independent.
Neal’s 2000 report is the inspected version. A later 2003 journal publication was located, but no equivalence of all version details is asserted.
No universal advantage over Gibbs or Metropolis, automatic elimination of every tuning parameter, or numerical benchmark result is claimed.

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`	Slice Sampling 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/SliceSampling.yaml