Hidden tiger (3): marginal, conditional, Bayes rule, graphical interpretation

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 21:20

*Enlace a Spanish version

Summary:

This video continues the discussion about marginal and conditional probabilities that we started in the video [tiger2EN]. A quick recap of such video is made in the first minutes of the present one.

In particular, the relationship between marginals and conditionals will be graphically represented as a function of the a priori probability... If the a priori probability of the condition is 1, marginal and conditional coincide; if it is not 1, then the marginal is a kind of “interpolation” of the conditional.

The second part of the video discusses the Bayes formula to obtain the “backward” conditional probability (cause given effect) from the joint table or, better, as it is usually written, from the “forward” conditional ( effect given cause) and the a priori probability of the cause.

The backward conditional probability of a cause given a certain effect is also called “a posteriori” if it is evaluated after actually observing said effect in a practical situation.

Various a priori and a posteriori probability plots are plotted for different conditional tables representing different levels of “precision” in the observation of tiger roaring noise.

Extensions to two roaring events are discussed in the continuation video [tiger4EN], and to any number of roarings in [tiger5EN].

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