Gibbs sampling
Algorithms AIMech:GibbsSampling DRAFT
Aliases: Gibbs sampler
A Markov chain Monte Carlo algorithm that repeatedly draws a coordinate or block from its full conditional distribution given the current values of the remaining coordinates.
Identity Notes & Concept Scope
This record denotes exact conditional resampling, including fixed coordinate cycles and fixed random-scan mixtures. It is a sampling procedure, not a Gibbs distribution, Markov random field, annealing schedule or conditional maximization method. Metropolis-within-Gibbs replaces some exact conditional draws by invariant transitions and is represented separately. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 159 prior native IDs/names/aliases. Ignored-inclusive full-checkout searches found prior discovery leads for Gibbs and slice sampling plus unrelated environment substring hits, not existing concept records. Existing HMM/MRF models and general Metropolis–Hastings were inspected to distinguish model, general transition and specialized algorithm scope.
Claims & Grounded Evidence
2 Claims
Mechanism
#method
Partition the state into coordinates or blocks. Select a block, draw its new value from the target conditional distribution given all other current values, and leave those other values unchanged. Each conditional-resampling kernel preserves the joint target. Composing these kernels in a fixed sweep, or mixing them with fixed selection probabilities, also preserves that target. Later steps in a sweep use the values already updated earlier in that sweep. Exact conditional draws do not make the resulting successive joint states independent.
Scope
#finite-image-gibbs
Geman and Geman update one image site by drawing from its Gibbs conditional using current neighboring states. Their fixed-temperature sampling construction is distinct from the later cooling procedure for minimum-energy configurations. The finite-state convergence discussion assumes strictly positive configuration probabilities and repeated site visits.
⚠️ Curated Limitations & Negative Results
- The full conditional distributions must be compatible with a proper joint target and be sampled correctly. An approximate conditional draw is not automatically an exact Gibbs step.
- Target invariance alone does not establish irreducibility, aperiodicity, convergence from every start or rapid mixing. Coordinate dependence and disconnected support can obstruct exploration.
- The finite positive-state convergence theorem in Geman and Geman has explicit site-visit and positivity assumptions; it is not a theorem for every continuous, constrained or parallel Gibbs implementation.
- Simultaneously updating dependent coordinates using stale neighbors is outside the stated sequential mechanism; valid parallel or adaptive scan schemes need separate arguments.
- Fixed-temperature posterior sampling and a cooling schedule for optimization are different procedures. No universal convergence rate or image-restoration performance 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 constructs Markov transitions for sampling a specified target, with the invariance and convergence qualifications stated in this record. AIO MarkovChain denotes the stochastic process/model and is exported beneath Network. This is a method-to-process related match, not equivalence, subclass membership 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
|
author technical report
full_text
|
ID: https://conservancy.umn.edu/server/api/core/bitstreams/f87bc468-91ac-45bc-a1cf-5d4b0f8fbcd6/content
sha256:cfde8fc2fa3c…
|
finite-image-gibbs
|
Stuart Geman, Donald Geman
|
primary paper
full_text
|
ID: doi:10.1109/TPAMI.1984.4767596
sha256:6adab117ea49…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T07:00:31Z
Updated: 2026-10-11T07:00:31Z
Source File:
data/curated/GibbsSampling.yaml