Elliptical slice sampling
Algorithms AIMech:EllipticalSliceSampling DRAFT
Aliases: ESS
A Markov-chain update for a target factored into a Gaussian prior and a likelihood, which performs an angular slice search along the ellipse defined by the current state and an independent prior draw.
Identity Notes & Concept Scope
This is the full-circle default algorithm in Murray et al. Figure 2 for a fixed Gaussian prior covariance. It differs from a fixed-angle Gaussian autoregressive Metropolis proposal and from scalar interval stepping-out or doubling. ESS here denotes this sampler, not the effective-sample-size diagnostic. 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
1 Claim
Mechanism
#method
For pi(f) proportional to Normal(f;0,Sigma)L(f), draw nu from Normal(0,Sigma), then log y=log L(f)+log u for independent u uniform on (0,1). Draw theta uniformly on (0,2pi) and initialize [theta_min,theta_max]=[theta−2pi,theta]. Test f_prime=f cos(theta)+nu sin(theta); accept when log L(f_prime)>log y. Otherwise shrink the bracket at theta on the side determined by its sign relative to zero, redraw theta uniformly from that bracket, and repeat with the same nu, f and threshold. The randomly positioned bracket retains the angle zero corresponding to the current state. Gaussian rotational invariance and the reversible bracket construction give the target-invariant transition.
⚠️ Curated Limitations & Negative Results
- A Gaussian prior draw and likelihood evaluation are required. A nonzero prior mean must be handled by centering the ellipse; an arbitrary non-Gaussian prior is outside this formula.
- Fixing the initial bracket deterministically to [−pi,pi] is not the proved algorithm; the paper explicitly explains why its random placement matters.
- The algorithm may reject multiple internal angle trials before returning an update. Its lack of an outer Metropolis rejection is not a claim of one likelihood evaluation or independent retained states.
- The default full-circle algorithm avoids a user-specified proposal scale, but covariance, model hyperparameters and optional narrower angular variants still involve choices.
- Strong offsets, covariance structure and likelihood geometry can impede exploration. No universal mixing rate, finite-run accuracy or timing advantage is asserted.
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
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Iain Murray, Ryan Prescott Adams, David J. C. MacKay
|
primary paper
full_text
|
ID: https://proceedings.mlr.press/v9/murray10a.html
sha256:ad6fbbfb8fb7…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T07:13:10Z
Updated: 2026-10-11T07:13:10Z
Source File:
data/curated/EllipticalSliceSampling.yaml