Stochastic maps - 02 - Composing conditional probabilities

Stochastic maps can be composed and form a category. The composition is given by the Chapman--Kolmogorov equation. This composition rule reproduces the notion of push-forward of a measure (also called the law of a random variable). We will also see how the composition rule is used in the formulation of Bayes' theorem in a later video. The idea of visualizing a measure-preserving function in terms of water droplets came from Gromov's lectures on "Probability, symmetry, linearity," which are available on youtube.

These videos were created during the 2019 Spring/Summer semester at the UConn CETL Lightboard Room.