Dominated statistical experiments

Depends on

• Statistical experiments
• Measures on sigma-algebras
• Finite, sigma-finite, and semifinite measures
• Absolute continuity of a signed or complex measure with respect to a positive measure

Used by

• A full-rank local Hessian does not capture both posterior modes Counterexample
• Identifiability and KL support do not replace testability Counterexample
• A dominated differentiable-in-quadratic-mean submodel Definition
• Evidence normalizer and fiberwise posterior update Definition
• Explicit exponential-family response contracts Definition
• Families with a monotone likelihood ratio Definition
• Ideal and finite-simulation synthetic likelihood Definition
• KL projection sets and relative KL neighborhoods Definition
• Likelihood densities Definition
• Likelihood-ratio tests with boundary randomization Definition
• Marginal likelihoods, proper model evidence, and Bayes factors Definition
• Quadratic-mean differentiability at a parameter Definition
• Root-L2 Hellinger distance for dominated laws Definition
• Score and Fisher information Definition
• A finite identifiable model with posterior consistency Example
• Bernoulli likelihood ratio and change of measure Example
• Countably partitioned sieves yield posterior contraction by weighted entropy Lemma
• KL prior mass gives a posterior denominator lower bound in probability Lemma
• Local KL and log-square mass bounds a non-IID posterior denominator Lemma
• Observed-data likelihood under a response model Lemma
• Compact models admit tests at a unique KL projection under fractional-moment continuity Proposition
• A countable mixture dominates a sigma-finite dominated family Theorem
• A sufficient summary preserves the Bayesian posterior Theorem
• Asymptotic linearity and normality of a regular MLE Theorem
• Compact-uniform LAN and rate contraction imply a total-variation BvM limit Theorem
• Dirichlet normal-mixture posterior contraction Theorem
• Finite-window spatial Poisson likelihood relative to unit rate Theorem
• Gaussian-process posterior contraction in density and regression models Theorem
• Hellinger invariance and comparison with library total variation Theorem
• IID posterior contraction by entropy and prior mass Theorem
• Likelihood contributions under censoring, truncation, and delayed entry Theorem
• Mean-zero score and the information identity Theorem
• Neyman–Pearson lemma with singular alternative mass Theorem
• Posterior consistency at a KL projection Theorem
• Posterior consistency from KL support and uniformly summable tests Theorem
• Right-censored exponential likelihood and its boundary maximum Theorem
• Standard Borel dominated factorization criterion Theorem
• The Gaussian covariance likelihood ratio has its fixed-dimensional Wilks limit Theorem

Dependency tree · two levels

15 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• Ryan Martin, Lecture Notes on Advanced Statistical Theory, §2.2, PDF pp. 30–33 (standard reference, not scraped)