Optimal Learning from the Doob-Dynkin lemma

Abstract

The Doob-Dynkin Lemma gives conditions on two functions $X$ and $Y$ that ensure existence of a function $\varphi$ so that $X=\varphi \circ Y$. This communication proves different versions of the Doob-Dynkin Lemma, and shows how it is related to optimal statistical learning algorithms. Keywords and phrases: Improper prior, Descriptive set theory, Conditional Monte Carlo, Fiducial, Machine learning, Complex data.

References in corpus (2)

• Improper posteriors are not improper
• Nonlinear probability. A theory with incompatible stochastic variables