Independent random elements

Depends on

• Random elements and real random variables
• The sigma-algebra generated by a function
• Independent sigma-algebras and independent events

Used by

• Aalen–Johansen cumulative-incidence estimator Algorithm
• Dominating thinning for bounded time-varying propensities Algorithm
• Finite-candidate Gaussian-process acquisition search with explicit statuses Algorithm
• Gillespie direct method with horizon and budget statuses Algorithm
• Identity-corrected random-permutation Monte Carlo p-value Algorithm
• Minimum-intensity coupling of reaction networks Algorithm
• Next-reaction method by internal Poisson clocks Algorithm
• Coordinate random elements of a countable product are independent Corollary
• Finite-sample exactness under equal distributions Corollary
• A last exit time need not be a stopping time Counterexample
• Kolmogorov extension alone does not give a continuous version Counterexample
• Marginal split coverage need not give rare-subgroup coverage Counterexample
• The uncorrected Monte Carlo permutation fraction can be zero and invalid Counterexample
• A simple Markovian mediation model Definition
• Additive measurement error and categorical misclassification models Definition
• Batch and measurement-process variation Definition
• Binary instrumental-variable potential-outcome setup Definition
• Biological and technical replication model Definition
• d-dimensional Brownian motion Definition
• Density targets and the kernel density estimator Definition
• Empirical, centered, and Rademacher processes Definition
• Explicit exponential-family response contracts Definition
• Finite product-law polynomial-chaos input data Definition
• Finite-dimensional linear mixed model with explicit longitudinal roles Definition
• Full-orbit and tie-randomized permutation p-values Definition
• Gaussian sequence model with sparse means Definition
• Identical distribution and IID families Definition
• L2-m-approximable causal Bernoulli shifts Definition
• Linear-Gaussian state-space models with independent noises Definition
• Minimax squared operator risk Definition
• Orbit upper-tail rank p-values Definition
• Poisson and Cox point processes Definition
• Poisson random measure on a standard Borel space Definition
• Randomized conditional upper-tail p-values Definition
• Recursive structural causal models on finite DAGs Definition
• Row-wise independent centered triangular array Definition
• Tail sigma-algebra of a sequence Definition
• A binary SCM where front-door adjustment works Example
• A confounder and a conditioned collider Example
• A Gaussian process retains uncertainty at an independent index Example

…and 116 more results.

Dependency tree · two levels

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Sources

• S. R. S. Varadhan, Probability Theory, Definitions 3.2 and 3.4 (standard reference, not scraped)
• Rick Durrett, Probability: Theory and Examples, 5th ed., Section 2.1 (standard reference, not scraped)