Hidden tiger (5): Bayes formula for any number of roars (non-recursive)

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 16:18

*Enlace a Spanish version

Summary:

This video is part of the “hidden tiger” case study in the collection. Here we generalize the Bayes formula that was seen for the case of one roar in the video [tiger3EN] and for two roars in [tiger4EN].

Specifically, it is generalized to an arbitrary number of roars, say $N$. Two possible conditional probability tables are introduced: an expanded one where the order in which the roars are received does matter, and another compressed one where only the number of roars heard through each of the doors matters; The second table has a “binomial” distribution.

Applying the Bayes formula in both cases produces an identical result. The video ends with a numerical example in which it is shown that if we wait for, say, 15 roaring events, then we are pretty sure on which side the tiger lies.

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