A New Definition of Conditional Expectation for Finite Uncertainty Spaces
Document Type
Conference Proceeding
Publication Date
1-24-2024
Abstract
This paper continues the authors' previous work on developing a theory of conditional expectations in uncertainty spaces. In a previous paper, they adopted the standard definition from classical probability by defining the conditional expectation E[X|G] of an uncertain variable X with respect to a σ-algebra G as a G-measurable function provided by a version of the Radon-Nikodym Theorem for uncertainty spaces. In this current work, a definition is provided by minimizing the expected mean squared error (X .Y)2 among G -measurable functions Y. The development, adopted from an existing work on non-additive probability spaces and repurposed for the current setting, similarly assumes a finite sample space and hence finitely many atoms for G. It also justifies the existence of conditional expectations and discusses some of their properties.
Recommended Citation
Michael Frondoza, Richard Eden, Elvira de Lara-Tuprio; A new definition of conditional expectation for finite uncertainty spaces. AIP Conf. Proc. 24 January 2024; 3016 (1): 060002. https://doi.org/10.1063/5.0193426
