Random-walk Metropolis–Hastings sampling
Algorithms AIMech:RandomWalkMetropolisHastings DRAFT
Aliases: RWMH
A Metropolis–Hastings sampler that proposes a new state by adding an increment drawn from a fixed distribution independent of the current state.
Identity Notes & Concept Scope
The random walk describes the proposal Y=x+Z, not an assertion that accepted chain increments are independent or target-free. The increment density may be asymmetric; the common symmetric random-walk Metropolis case is included. This differs from a fixed independence proposal g(Y), which does not center on x, and from gradient-directed Langevin proposals. 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
At state x draw Z from a fixed increment density f and set y=x+Z, so q(y|x)=f(y−x). Accept with min(1,pi(y)f(x−y)/(pi(x)f(y−x))) where the ratio is defined; retain x on rejection. For f(z)=f(−z), the increment-density terms cancel and acceptance is min(1,pi(y)/pi(x)). The formula is the substitution of Tierney’s random-walk proposal into his general Metropolis ratio. The proposal scale and shape determine which candidate movements are attempted.
⚠️ Curated Limitations & Negative Results
- The simplification to the target-density ratio requires a symmetric increment law, not merely an additive proposal.
- Proposal and target support determine irreducibility. An invariant kernel is not a guarantee of rapid convergence or movement between separated modes.
- Accepted-state increments and retained draws are generally dependent. Rejected states remain in the chain.
- This definition uses a fixed increment distribution; adaptive scales and state-dependent covariance require their own proposal ratios and validity analysis.
- No universal acceptance-rate target, optimal scale, dimension-scaling law or benchmark advantage 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
|
Luke Tierney
|
author technical report
full_text
|
ID: https://conservancy.umn.edu/server/api/core/bitstreams/f87bc468-91ac-45bc-a1cf-5d4b0f8fbcd6/content
sha256:cfde8fc2fa3c…
|
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/RandomWalkMetropolisHastings.yaml