Some Examples on Conditional Expectation of Markov Kernels

A. García Nogales, P. Perez Fernandez

A well-known property of conditional expectation states that if X,Y,Z are random variables such that Z is independent of (X,Y), then E(X∣Y,Z)=E(X∣Y). A Markov kernel can be considered as an extension of the concept of a random variable (and of a sub-sigma-algebra), and the authors have studied in previous works extensions to Markov kernels of certain probabilistic or statistical concepts (including independence and conditional expectation) and their properties. The main result of this communication considers the extension of the aforementioned result. Thinking about applications, a version in terms of densities is also presented. Finally, some examples from the field of clinical diagnosis are included with the intention of illustrating and delimiting this theorem.

Keywords: Conditional expectation, Markov kernels.

Pósters session II
June 13, 2025  3:30 PM
Foyer principal (coffe break)

M. Úbeda Flores

E. García Gómez, D. Morales

C. Patino Alonso, M. Gómez Sánchez, L. Gómez Sánchez, S. González Sánchez, C. Agudo Conde

L. Acosta, X. Espuña, J. A. Sanchez-Espigares

D. L. Tarruella Hernández, A. García Molina, J. B. Salom Sanvalero, M. M. Dolcet Negre, M. J. Rivas Lopez

A. F. Antivilo Bruna, C. Patino Alonso

Á. de Prado Saborido, M. Mirás Calvo, I. Núñez Lugilde, C. Quinteiro Sandomingo, E. Sánchez Rodríguez

C. A. Ávila-Zarza, S. Sánchez-Monreal, T. Cocho, N. Rodríguez-Iglesias, C. Escudero, L. A. de Castro, J. R. Alonso, J. Valero

N. González García, A. B. Nieto Librero

D. Corrales Alonso, D. Ríos Insua

A. Olivares Canal, V. Peña Pizarro, M. Jauch

K. Díaz Arias, I. Albarran Lozano, A. Grané Chávez

P. Gargallo Valero, L. Lample Gracia, J. Miguel Álvarez, M. Salvador Figueras

M. Anciones Polo, A. Queiruga-Dios, P. Vicente Galindo, E. Benéitez-Andrés, M. Rodríguez-Rosa