Widely applicable information criterion¶
A Bayesian predictive-fit criterion combining log pointwise posterior predictive density with a variance-based effective-complexity penalty.
Core Idea¶
Pointwise factorization, posterior draws and scale convention must be explicit, finite-sample estimates can be unstable and lower deviance-scale WAIC is only comparative. Posterior draws evaluate each observation’s predictive density; summed log averages estimate fit and posterior variance of log likelihood supplies an effective-parameter correction approximating leave-one-out prediction. 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.
The load-bearing residual is not the broad topic of bayesian statistics. It is the domain-specific identity fixed by the observed data and pointwise likelihood units, posterior distribution and draws, log pointwise predictive density, variance penalty and effective parameter count, factor of minus two convention, standard error, model comparison and asymptotic relation and diagnostics for unstable contributions are explicit.
Scope of Application¶
Widely applicable information criterion belongs to bayesian statistics and is useful where the analyst can specify the typed bayesian statistics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the observed data and pointwise likelihood units, posterior distribution and draws, log pointwise predictive density, variance penalty and effective parameter count, factor of minus two convention, standard error, model comparison and asymptotic relation and diagnostics for unstable contributions are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the observed data and pointwise likelihood units, posterior distribution and draws, log pointwise predictive density, variance penalty and effective parameter count, factor of minus two convention, standard error, model comparison and asymptotic relation and diagnostics for unstable contributions are explicit 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 Widely applicable information criterion. Widely applicable information criterion 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 bayesian statistics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the observed data and pointwise likelihood units, posterior distribution and draws, log pointwise predictive density, variance penalty and effective parameter count, factor of minus two convention, standard error, model comparison and asymptotic relation and diagnostics for unstable contributions are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of bayesian statistics because they reuse the typed bayesian statistics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Posterior draws evaluate each observation’s predictive density; summed log averages estimate fit and posterior variance of log likelihood supplies an effective-parameter correction approximating leave-one-out prediction., and type the carrier, state every parameter and convention in the definition, test that the observed data and pointwise likelihood units, posterior distribution and draws, log pointwise predictive density, variance penalty and effective parameter count, factor of minus two convention, standard error, model comparison and asymptotic relation and diagnostics for unstable contributions are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Widely applicable information criterion Domain-specific
Parents (1) — more general patterns this builds on
-
Widely applicable information criterion is a kind of Evaluation Prime
The proposed strict upward parent is
prime:evaluation.
Hierarchy path (1) — routes to 1 parentless root
- Widely applicable information criterion → Evaluation → Comparison → Self Checking
Neighborhood in Abstraction Space¶
Widely applicable information criterion sits in a crowded region of the domain-specific corpus (2nd percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Bayesian Inference & Probabilistic Models (23 abstractions)
Nearest neighbors
- Bayesian model reduction — 0.95
- Bayesian linear regression — 0.95
- Normal-inverse-gamma distribution — 0.94
- Marginal likelihood — 0.94
- Posterior probability — 0.94
Computed from structural-signature embeddings · 2026-09-08