Barker acceptance rule
Mathematical Methods AIMech:BarkerAcceptanceRule DRAFT
An acceptance-probability rule for reversible Monte Carlo proposals that uses R/(1+R), where R is the target-density ratio times the reverse-to-forward proposal ratio.
Identity Notes & Concept Scope
The record covers Hastings’s s_ij=1 form, which reduces to Barker’s 1965 rule for symmetric proposals. It is a scalar decision rule used inside a sampler, not a complete choice of proposal, a logistic-regression model, or the Metropolis min(1,R) rule. The original 1965 plasma paper was located but its full text has not been inspected for this record. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 153 prior native IDs/names/aliases. Both checkout text searches included ignored and hidden files and returned no matches for the selected exact IDs, full labels, aliases and source titles. Existing HMM and Markov random field records describe probability models, not these sampling or tuning procedures.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
For a current state x and proposed state y with positive finite denominator, compute R=pi(y)q(x|y)/(pi(x)q(y|x)) and accept with alpha=R/(1+R). This follows algebraically by choosing s_ij=1 in Hastings Equation (6). With a symmetric proposal alpha=pi(y)/(pi(x)+pi(y)). Pairing the rule with the proposal and retaining x on rejection yields detailed balance. At equal positive target weights and symmetric q, acceptance is one half rather than the Metropolis value one.
⚠️ Curated Limitations & Negative Results
- The asymmetric-proposal formula is an explicit algebraic restatement of Hastings’s general construction, not a claim that the inspected source is Barker’s original paper.
- The rule alone supplies neither a proposal distribution nor an ergodic or rapidly mixing chain. Support, boundary cases and numerical evaluation still require specification.
- The same ratio generally gives different acceptance probabilities under Barker and Metropolis rules. A lower or higher acceptance probability alone does not prove a universal computational-efficiency ordering.
- No claim is made about newer methods called Barker proposals or gradient-based Barker samplers; those can use different proposal mechanisms and need separate identity review.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:MarkovChain
Markov Chain
|
related_match | The acceptance rule constructs target-invariant Markov transitions when paired with a proposal and rejection self-transition. AIO MarkovChain describes the stochastic process/model, not this scalar acceptance function. This is a rule-to-process related match, not equivalence or an is-a assertion. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
W. K. Hastings
|
primary paper
full_text
|
ID: doi:10.1093/biomet/57.1.97
sha256:dc620d3651d3…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T06:48:02Z
Updated: 2026-10-11T06:48:02Z
Source File:
data/curated/BarkerAcceptanceRule.yaml