The ideas of statistical independence (videos [indep1], [indepdis]) can be refined to discuss about
the independence of conditional probability distributions (video [prcond]). With this, we
can think of random variables that are “conditionally independent given a certain
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
“common sense” ideas behind it, and it is at the root of the ideas of “state”
in Physics and Control Theory. and “Bayesian networks” in Artificial
Intelligence.
This video discusses the theoretical definition and some “intuitive”
examples to understand the concept (car brand versus fines, height versus
academic qualifications, etc.). A second video [condin2], continuation of this one,
discusses its relationship with dynamic systems models used in control and
Bayesian networks, also used in other areas of computer science and Artificial
Intelligence.
The idea is also discussed in the ‘hidden tiger’ case study that introduces
some probability concepts, see video [tiger4EN]. Further 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.
, Duration: 18:42