Rejection-driven independence Metropolis sampling
Algorithms AIMech:RejectionDrivenIndependenceMetropolis DRAFT
An independence Metropolis sampler whose proposals are generated by a rejection procedure with a fixed possibly non-dominating envelope, followed by a Metropolis correction for the resulting clipped proposal law.
Identity Notes & Concept Scope
This is Tierney’s rejection sampling chain in Section 2.3.4. It specializes independence Metropolis by an inner proposal generator; it is not ordinary rejection sampling unless the envelope dominates everywhere. It is distinct from adaptive rejection Metropolis sampling, because h and c are fixed here. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 167 prior native IDs/names/aliases. Full-checkout searches in both worktrees included ignored and hidden files; the 15 lines in each were shared Tierney source-title references or an adaptive-rejection discovery lead, not matching records. Existing Gibbs, Metropolis-within-Gibbs, random-walk and independence Metropolis mechanisms were inspected to resolve specialization boundaries.
Claims & Grounded Evidence
2 Claims
Mechanism
#method
For a proper target pi and a normalized proposal density h covering its support, fix c>0. Repeatedly draw z from h and u uniformly on (0,c h(z)) until u<pi(z). This yields a proposal y with density f proportional to min(pi,c h). At current state x apply independence Metropolis acceptance min(1,pi(y)f(x)/(pi(x)f(y))); retain x if rejected. Let C={x:pi(x)≤c h(x)}. The published acceptance cases are 1 when x is in C; c h(x)/pi(x) when x is outside C and y is in C; and min(1,pi(y)h(x)/(pi(x)h(y))) when both are outside C. Normalizing constants of f cancel. When c h dominates pi everywhere, this reduces to independent rejection sampling.
Scope
#earlier-report-discrepancy
The inspected 1991 technical report prints pi(x)/(c h(x)) in the mixed acceptance case and an uncapped ratio in the both-outside case. The 1994 published Section 2.3.4 instead gives c h(x)/pi(x) and a minimum with one, matching the independence Metropolis ratio used in this record.
⚠️ Curated Limitations & Negative Results
- The inner proposal must have positive acceptance mass and cover the target support required for irreducibility. A poor choice of h or c can make either stage inefficient.
- The inner rejected trials are discarded, while rejection by the outer Metropolis test repeats the chain state; these two rejection events have different roles.
- A non-dominating envelope without the outer correction generally gives the clipped density rather than pi. Correcting it does not guarantee fast mixing.
- The inspected 1991 technical report prints the reciprocal of the mixed-case factor and omits the minimum with one in the final case. This record uses the visually verified 1994 published expressions, consistent with the general independence ratio; no separate erratum is asserted.
- Adapting h or c from chain history is outside the fixed-proposal definition and needs its own validity argument.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:MarkovChain
Markov Chain
|
related_match | This algorithm constructs target-invariant Markov transitions under its stated assumptions. The exact AIO CLASS denotes a stochastic process/model and is exported beneath Network. This is a method-to-process related match, not equivalence, subclass membership, independence of retained draws or a claim that the algorithm is a trained network. |
Evidence Sources & Primary Literature
2 Sources| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Luke Tierney
|
primary paper
full_text
|
ID: https://www.ma.imperial.ac.uk/~das01/MyWeb/SCBI/Papers/Tierney94.pdf
sha256:91155ffee0e3…
|
earlier-report-discrepancy
|
Luke Tierney
|
author technical report
full_text
|
ID: https://conservancy.umn.edu/server/api/core/bitstreams/f87bc468-91ac-45bc-a1cf-5d4b0f8fbcd6/content
sha256:cfde8fc2fa3c…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T07:13:10Z
Updated: 2026-10-11T07:13:36Z