Delayed-rejection Metropolis
Algorithms AIMech:DelayedRejectionMetropolis DRAFT
Aliases: Delayed rejection Metropolis-Hastings
A Metropolis-Hastings sampling procedure that can propose another candidate after rejection within the same transition, correcting acceptance for the probabilities of the forward and reversed rejected paths.
Identity Notes & Concept Scope
This is the path-reversal delayed-rejection construction in Mira Sections 2–3. Rejected internal candidates are auxiliary information; the chain remains at its original state until a candidate is accepted or the transition ends. It differs from across-iteration adaptive Metropolis and from independent repeated accept-reject generation. 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
For current x with pi(x)>0, propose y1 from q1(x,·) and use a1(x,y1)=min(1,pi(y1)q1(y1,x)/(pi(x)q1(x,y1))). If rejected, draw y2 from q2(x,y1,·). Accept y2 with min(1, [pi(y2)q1(y2,y1)q2(y2,y1,x)(1−a1(y2,y1))]/[pi(x)q1(x,y1)q2(x,y1,y2)(1−a1(x,y1))]). The zero reverse-path case has acceptance zero. A fixed two-stage implementation retains x if both tests reject. Higher stages require the corresponding reversed-path proposal and previous-rejection products; simply applying ordinary Metropolis to each retry omits those factors.
⚠️ Curated Limitations & Negative Results
- Proposal support and well-defined forward-path probabilities are required; formulas apply to reachable rejection paths. Irreducibility and convergence need further conditions beyond detailed balance.
- The record gives the explicit two-stage rule and identifies the higher-stage construction, not a claim that every history-dependent retry is valid.
- Extra stages cost proposal and target evaluations. Per-transition asymptotic-variance comparisons do not guarantee faster estimates per unit computation.
- A finite stage cap retains the original state after all rejections. Eventual acceptance is not guaranteed for unrestricted retry schemes.
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/DelayedRejectionMetropolis.yaml