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Independence Metropolis–Hastings sampling

Algorithms AIMech:IndependenceMetropolisHastings DRAFT

Aliases: Independence Metropolis sampler, IMH

A Metropolis–Hastings sampler whose proposal distribution is fixed independently of the current state, with proposal-density ratios still included in acceptance.

Identity Notes & Concept Scope Independence describes the proposal q(y), not independence of the retained Markov-chain states. This specializes Metropolis–Hastings and differs from estimating an expectation using separately weighted independent importance samples or from a state-centered random-walk proposal. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 153 prior native IDs/names/aliases. Both checkout text searches included ignored and hidden files and returned no matches for the selected exact IDs, full labels, aliases and source titles. Existing HMM and Markov random field records describe probability models, not these sampling or tuning procedures.

Claims & Grounded Evidence

1 Claim

Mechanism #method

Choose a fixed proposal density or mass g and draw each candidate y from g independently of the current state x. Substitute q(y|x)=g(y) into the Metropolis–Hastings ratio, obtaining alpha=min(1,pi(y)g(x)/(pi(x)g(y)))=min(1,w(y)/w(x)) for w=pi/g where defined. Accept y or retain x. Hastings Section 2.5 explicitly chooses q_ij=pi_prime_j while keeping pi, rather than pi_prime, as the chain’s stationary target. The displayed acceptance formula here is the substitution into his Section 2.2 rule.

supports Source: Monte Carlo sampling methods using Markov chains and their applications · Locator: Sections 2.2 and 2.5, Metropolis choice and final paragraph setting q_ij=pi_prime_j, printed pp. 99–101 and 103 / PDF pp. 3–5 and 7

⚠️ Curated Limitations & Negative Results

The proposal must cover the target support required for irreducibility, and its probability or density must be evaluable for the ratio.
Independent candidates do not imply independent retained draws: rejection leaves the chain at the same state.
The ratio shows why a state with very large pi(x)/g(x) can be hard to leave for ordinary candidates. This is an algebraic caution, not a measured mixing rate or a universal convergence theorem.
Unweighted retained-chain averages and importance-weighted independent-sample estimates are different procedures. Validity still requires appropriate chain and integrability conditions.
Adaptive or learned changing proposals are outside this fixed-proposal definition and require their own validity arguments.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:MarkovChain` Markov Chain	related_match	This procedure constructs transitions of a Markov chain to sample a specified target distribution. The exact AIO CLASS describes a stochastic process/model with dependence on the preceding state and is exported beneath Network. The method-to-process relationship is related_match, not equivalence, subclass membership or a claim that the sampler is a trained network.

Evidence Sources & Primary Literature

1 Source

Source ID	Publication / Document	Type / Access	Reference & Checksum
`method-source`	Monte Carlo sampling methods using Markov chains and their applications W. K. Hastings	primary paper full_text	ID: doi:10.1093/biomet/57.1.97 sha256:dc620d3651d3…

Curation Provenance

Curator: Codex

Method: ai_assisted

Model: GPT-6

Created: 2026-10-11T06:48:02Z

Updated: 2026-10-11T06:48:02Z

Source File: data/curated/IndependenceMetropolisHastings.yaml