Symmetric delayed rejection
Algorithms AIMech:SymmetricDelayedRejection DRAFT
Aliases: Symmetric delaying rejection algorithm
The delayed-rejection specialization using the same symmetric proposal kernel at every stage, centered through the last rejected candidate, with acceptance determined by the largest previous rejected target density.
Identity Notes & Concept Scope
This record is the fixed-kernel specialization in Mira Section 3. The next proposal depends on the last rejected point rather than being recentered on the unchanged chain state. Stage-dependent variances and generic symmetric proposals do not automatically satisfy the cancellations used by this simplified rule. No normalized match was found across all 442 pinned AIO labels/scoped synonyms and 175 prior native IDs/names/aliases. Full-checkout searches included ignored and hidden files in both worktrees; the only text hit was an unrelated installed-package checksum substring. Existing general Metropolis-Hastings, Metropolis-within-Gibbs and random-walk records were inspected to resolve these specialization boundaries.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
Let q(a,b)=q(b,a) be the same kernel at every stage. Starting from x, propose y1 from q(x,·) and accept with min(1,pi(y1)/pi(x)). After i−1 rejections, propose yi from q(y(i−1),·), set M=max_{j<i} pi(yj), and accept with min(1,max(0,(pi(yi)−M)/(pi(x)−M))). On a reachable rejection path, M<pi(x). If a chosen finite stage limit is exhausted, retain x. Accepted candidates end the transition; rejected candidates do not become chain states. The formula follows cancellation of the forward and reverse path terms under the fixed symmetric-kernel assumption.
⚠️ Curated Limitations & Negative Results
- Figure 1 prints pi(x)/pi(y1) for its first-stage nontrivial acceptance region, reversing the correct pi(y1)/pi(x) in the preceding text. This record uses the text and general Metropolis formula; the figure discrepancy was visually inspected.
- The later suggestion to decrease variance by stage is not treated as permission to use this simplified acceptance with arbitrary changing q. Such proposals need the general delayed-rejection correction.
- A candidate whose target density is no larger than the maximum target density among previous rejected candidates is rejected. No finite-time eventual-acceptance or universal efficiency guarantee is asserted.
- Detailed balance is not a substitute for support, irreducibility and numerical-stability checks.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:MarkovChain
Markov Chain
|
related_match | The procedure defines target-invariant Markov transitions under its stated assumptions. AIO MarkovChain describes a stochastic process/model and is exported beneath Network. This method-to-process related match is not equivalence, an is-a assertion or a claim of independent samples or a trained network. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Antonietta Mira
|
primary paper
full_text
|
ID: https://www.dss.uniroma1.it/RePec/mtn/articoli/2001-LIX-3_4-16.pdf
sha256:cd857ff8d7f7…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T07:26:59Z
Updated: 2026-10-11T07:27:21Z
Source File:
data/curated/SymmetricDelayedRejection.yaml