Standard Borel spaces

Depends on

• Measurable spaces and measurable sets
• Polish spaces are separable completely metrizable spaces

Used by

• ABC Metropolis–Hastings on simulator-augmented states Algorithm
• Full-resampling fixed-level SIR splitting with invariant mutations Algorithm
• Metropolis-adjusted Langevin algorithm (MALA) Algorithm
• Metropolis–Hastings kernel Algorithm
• Particle marginal Metropolis–Hastings Algorithm
• Sequential ABC importance-resampling with tolerance populations Algorithm
• Posterior RCD exists for a standard-Borel parameter Corollary
• A curved normal family can make a sufficient statistic incomplete Counterexample
• A nonconstant summary can lose an identifiable parameter Counterexample
• A nontransitive system with two orbits is not classified by one stabilizer Counterexample
• An external dominating law need not be a valid sufficiency reference Counterexample
• An identifiable model can have persistent ABC summary distortion Counterexample
• An open action set need not contain a posterior-risk minimizer Counterexample
• Pointwise continuity alone does not guarantee the zero-tolerance limit Counterexample
• Positive ABC tolerance changes an identity-summary target Counterexample
• A simple Markovian mediation model Definition
• Approximate Bayesian computation and the tolerance-conditioned target Definition
• Assumptions for identifying natural effects Definition
• Augmented ABC tolerance target Definition
• Conditional KL for supplied probability kernels Definition
• Conditional mutual information by a same-marginal product law Definition
• Conditionally linear-Gaussian state-space model Definition
• Controlled and natural mediation effects Definition
• Direct integrals of unitary representations Definition
• Dirichlet process Definition
• Event-time observation, censoring, and truncation schemes Definition
• Exponential families and full rank Definition
• Feynman–Kac path targets and normalizers Definition
• Filtering, predictive, and smoothing laws in a finite-horizon state-space model Definition
• Finite-alphabet conditional entropy given an observation Definition
• Finite-budget stopped-event kernel with a cemetery outcome Definition
• Finite-group hierarchical Bayesian model Definition
• General finite-horizon state-space models by kernels Definition
• General single-letter information rate-distortion function Definition
• Generalized Bayes loss update and temperature Definition
• Likelihood-ratio equivalence on common discrete support Definition
• Location-shift pattern-mixture sensitivity function Definition
• Measurable fields of von Neumann algebras and their direct integrals Definition
• Measurable Hilbert field from a countable fundamental family Definition
• Mutual information for standard-Borel random elements Definition

…and 95 more results.

Dependency tree · two levels

5 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

• Biskup, MATH 275D notes, Definition 2.3 (standard reference, not scraped)