statistical-model

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• information-geometry← DEPENDS_ON

  Information geometry operates exclusively on parametric families of probability distributions (statistical models). Remove the concept of a statistical model and information geometry has no manifold structure to study — the entire framework of statistical manifolds, Fisher metric, and dual connections is defined on the space of statistical models. The removal test passes: X stops operating without Y.

• log-likelihood← DEPENDS_ON

  Log-likelihood is only defined relative to a statistical model: the likelihood function L(θ|data) = P(data|model, θ). Remove the statistical model and log-likelihood has no meaning — the probability function requires a model specification. Constitutive dependency (Law 8).

• prior-distribution← DEPENDS_ON

  Prior distribution is a probability distribution over the parameter space Θ of a statistical model. Remove the statistical model and the parameter space vanishes — the prior has no domain to be defined over. The concept ceases to operate as a distribution over parameters.

• akaike-information-criterion← DEPENDS_ON

  AIC estimates the relative information loss of a statistical model — it is defined as −2·log-likelihood + 2k, where k is the number of parameters in the model. Remove statistical models and AIC has no definition. Constitutive dependency.

• bias-variance-decomposition← DEPENDS_ON

  Bias-variance decomposition is computed on predictions of a statistical model; remove the model and the decomposition has no data to operate on.

• maximum-likelihood-estimation← DEPENDS_ON

  MLE estimates parameters of a statistical model — the model defines the likelihood family p(x|θ). Remove statistical models and MLE has no parameter space, no likelihood family, nothing to estimate. Epoch test confirms: MLE (0.01) newer than statistical-model (0), arrow MLE → statistical-model.

• sufficient-statistic← DEPENDS_ON

  A sufficient statistic captures all information in the data about a parameter of the model. Remove the statistical model (the parameterized family and its structure) and sufficient statistics have no parameter space to be sufficient for — the concept ceases to operate.

• marginal-likelihood← DEPENDS_ON

  Marginal likelihood p(x) = ∫ p(x|θ)π(θ)dθ requires a statistical model p(x|θ) with its parameter space as its core operand. Without the statistical model (the likelihood function and its parameterization), the marginal likelihood integral cannot even be formulated. The model is constitutive to marginal likelihood's definition and computation.

• information-criterion← DEPENDS_ON

  Law 8 removal test, operational not meta: an information criterion scores a fitted statistical model — its input is a model with a maximized log-likelihood and a count of free parameters. Remove statistical models NOW and there is nothing to score: the scoring, comparing, and selecting operations have no object and stop operating, not merely stop being sayable (Law 2b). Not identity (Law 8c): a criterion is not a model, it is a rule that operates on models; the model is an essential argument of the function, as in the parallel AIC and log-likelihood cases.

• fisher-information← DEPENDS_ON

  Fisher information I(θ) = E[(∂/∂θ log p(x|θ))²] is defined from the log-likelihood of a statistical model. Remove the statistical model (the probability family p(x|θ)) and Fisher information has no mathematical object to operate on — it ceases to exist operationally.