Conditional Independence (II): control-relevant examples (Markov hypothesis), Bayesian Networks

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 15:27

*Enlace a Spanish version

Summary:

The video [condin1EN] defined the concept of random variables which were “conditionally independent given some value of another third variable”. Although it may seem like a useless refinement of interest to very few people, this is not the case: there are very relevant ideas behind it, and it is the cornerstone of the idea of “state”, fundamental in multivariable control theory, and “Bayesian networks” in Artificial Intelligence.

This video complements the “intuitive” examples in the above-mentioned video with more abstract examples on measurement and process noise, the concept of state, Markov hypothesis, and the associated Bayesian network diagrams. It is recommended to watch the video [state2] for more discussions about the importance of the concept of state and Markov in the modeling of physical systems.

The video ends presenting some conclusions about the importance of the concept of conditional independence in scientific methods in general.

Further numerical examples (well, actually particularized to the case of conditional correlation or lack thereof) are discussed in the video [condnocoEN], recommending its viewing to consolidate the concepts. The idea is also discussed in the ‘hidden tiger’ case study that introduces some probability concepts, see video [tiger4EN].

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.