A Note on Conditional Expectation for Markov Kernels

TL;DR

This paper extends the concept of conditional expectation to Markov kernels, providing a density-based interpretation and illustrating its application through clinical diagnosis examples.

Contribution

It introduces a novel extension of conditional expectation to Markov kernels, enhancing theoretical understanding and practical applicability.

Findings

Extension of conditional expectation to Markov kernels

Density interpretation of the extended expectation

Application examples in clinical diagnosis

Abstract

A known property of conditional expectation is extended to the framework of Markov kernels. Its meaning in terms of densities is provided. Some examples located in the field of clinical diagnosis are presented to delimit the main result of the paper.