Likelihood principle¶
The proposition that, for a fixed statistical model, all sample evidence about its parameters is contained in the observed-data likelihood up to proportionality.
Core Idea¶
Two experiments or outcomes with proportional likelihood functions carry the same evidential content about the parameter under the likelihood principle, irrespective of unobserved stopping or sampling possibilities. Conditioning on the observed sample produces a function of the parameter; proportional functions preserve every relative support ratio, so inference that depends on tail areas or stopping rules can conflict with the principle. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Likelihood principle belongs to statistical foundations and is useful where the analyst can specify the typed statistical foundations carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the model and parameter are fixed, likelihoods are based on the observed data, proportionality is parameter-independent, and the claim concerns evidential equivalence rather than a complete decision rule. The scope is broad within that domain but bounded by the need for the model and parameter are fixed, likelihoods are based on the observed data, proportionality is parameter-independent, and the claim concerns evidential equivalence rather than a complete decision rule. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the model and parameter are fixed, likelihoods are based on the observed data, proportionality is parameter-independent, and the claim concerns evidential equivalence rather than a complete decision rule the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Likelihood principle. Likelihood principle compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed statistical foundations carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the model and parameter are fixed, likelihoods are based on the observed data, proportionality is parameter-independent, and the claim concerns evidential equivalence rather than a complete decision rule independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of statistical foundations because they reuse the typed statistical foundations carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Conditioning on the observed sample produces a function of the parameter; proportional functions preserve every relative support ratio, so inference that depends on tail areas or stopping rules can conflict with the principle., and type the carrier, state every parameter and convention in the definition, test that the model and parameter are fixed, likelihoods are based on the observed data, proportionality is parameter-independent, and the claim concerns evidential equivalence rather than a complete decision rule, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Likelihood principle Domain-specific
Parents (1) — more general patterns this builds on
-
Likelihood principle is a kind of Evidence Prime
The proposed strict upward parent is
prime:evidence.
Hierarchy paths (4) — routes to 4 parentless roots
- Likelihood principle → Evidence → Provenance → Traceability → Observability
- Likelihood principle → Evidence → Provenance → Attestation → Authentication
- Likelihood principle → Evidence → Provenance → Traceability → Transformation → Function (Mapping)
- Likelihood principle → Evidence → Provenance → Custody Transfer → State and State Transition → Phase Space
Neighborhood in Abstraction Space¶
Likelihood principle sits in a crowded region of the domain-specific corpus (13th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Statistical Estimation & Hypothesis Testing (35 abstractions)
Nearest neighbors
- Empirical likelihood — 0.94
- Maximum likelihood estimation — 0.93
- Nuisance parameter — 0.92
- Sequential analysis — 0.92
- Observed information — 0.91
Computed from structural-signature embeddings · 2026-09-08