Multiple-try Metropolis within Gibbs
Algorithms AIMech:MultipleTryMetropolisWithinGibbs DRAFT
Aliases: MTM-Gibbs, Griddy Gibbs multiple-try Metropolis
A coordinate-update sampler that applies a multiple-try Metropolis transition to a conditional target while holding all other coordinates fixed.
Identity Notes & Concept Scope
This is the MTM-Gibbs construction in Liu–Liang–Wong Section 5.2, a specific multiple-candidate Metropolis-within-Gibbs kernel. It need not draw exactly from a full conditional in one update and does not replace that conditional with a gridded interpolation. 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 a chosen coordinate i, fix x_−i and use the unnormalized scalar target pi_i(z)=pi(x_−i,z). Draw k independent yj from T(x_i,·), compute w(yj,x_i)=pi_i(yj)T(yj,x_i)lambda(yj,x_i), and select y in proportion to these weights. Draw k−1 reference values from T(y,·), append the old x_i, and accept using the forward-to-reference total-weight ratio of MTM. On acceptance replace only coordinate i; otherwise keep the full state. T may depend on the fixed remaining coordinates; its forward/reverse support and symmetric lambda requirements hold within that conditional update.
⚠️ Curated Limitations & Negative Results
- This is conditional target invariance, not an exact independent conditional draw or independence of successive full states.
- Use the complete backward-reference correction. Keeping only the weighted candidate selection defines a different procedure.
- Zero forward total weight is handled by retaining the current coordinate; finite, meaningful target/proposal weights are required.
- Support, coordinate scheduling and irreducibility determine whether the full chain can explore the target. No benchmark advantage over Gibbs or other conditional kernels 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 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/MultipleTryMetropolisWithinGibbs.yaml