Multiple-try Metropolis
Algorithms AIMech:MultipleTryMetropolis DRAFT
Aliases: MTM
A Metropolis sampling algorithm that selects a candidate from several weighted forward proposals, draws a backward reference set containing the original state, and corrects acceptance using the ratio of their total weights.
Identity Notes & Concept Scope
This record covers Liu–Liang–Wong Section 2 finite-k MTM with one proposal kernel and a symmetric weight factor. It is not simple selection of the highest-density candidate, importance resampling without a correction, or the general auxiliary-variable extension in Section 3.1. 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
Choose k≥1, a proposal T with T(a,b)>0 iff T(b,a)>0, and nonnegative symmetric lambda positive wherever T is positive. Define w(a,b)=pi(a)T(a,b)lambda(a,b). From current x, draw k independent yj from T(x,·), and select y with probabilities proportional to w(yj,x). Draw k−1 independent xj* from T(y,·), and append xk*=x. Accept y with min(1,sum_j w(yj,x)/sum_j w(xj*,y)); otherwise retain x. For k=1 the symmetric lambda cancels, recovering Metropolis-Hastings. Selection and the backward reference set are essential to this correction.
⚠️ Curated Limitations & Negative Results
- Weight sums must be finite and usable. If all forward candidates have zero target weight, the transition can be completed by retaining x; weighted selection is not performed with a zero denominator.
- The number of proposals and target evaluations grows with k. Larger k does not imply universal improvement per unit computation or independent retained draws.
- The auxiliary-variable extension in Section 3.1 prints selection weights with an argument order inconsistent with Section 2 and its own acceptance expression. That extension is not asserted by this record.
- Target invariance under the stated construction does not alone establish irreducibility or a mixing rate.
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
|
Jun S. Liu, Faming Liang, Wing Hung Wong
|
primary paper
full_text
|
ID: doi:10.1080/01621459.2000.10473908
sha256:5329c50b3760…
|
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/MultipleTryMetropolis.yaml