Bayesian programming

Bayesian programming is a formalism and a methodology to specify probabilistic models and solve problems when less than the necessary information is available.

Edwin T. Jaynes proposed that probability could be considered as an alternative and an extension of logic for rational reasoning with incomplete and uncertain information. In his founding book Probability Theory: The Logic of Science he developed this theory and proposed what he called “the robot,” which was not a physical device, but an inference engine to automate probabilistic reasoning—a kind of Prolog for probability instead of logic. Bayesian programming is a formal and concrete implementation of this "robot".

Bayesian programming may also be seen as an algebraic formalism to specify graphical models such as, for instance, Bayesian networks, dynamic Bayesian networks, Kalman filters or hidden Markov models. Indeed, Bayesian Programming is more general than Bayesian networks and has a power of expression equivalent to probabilistic factor graphs.

A Bayesian program is a means of specifying a family of probability distributions.

The constituent elements of a Bayesian program are presented below:

The purpose of a description is to specify an effective method of computing a joint probability distribution on a set of variables ${\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}}$ given a set of experimental data ${\displaystyle \delta }$ and some specification ${\displaystyle \pi }$. This joint distribution is denoted as: ${\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)}$.

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