Hidden tiger (4): conditional and Bayes rule for TWO roars

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 13:44

*Enlace a Spanish version

Summary:

This video is part of the “tiger” case study that began in the video [tiger1EN], which continues the inference using Bayes formula discussed in the video [tiger3EN], the one immediately preceding this one in the recommended sequence.

This video addresses the problem of estimating the posterior probability of locating a “hidden tiger” after hearing TWO roaring events (without allowing the tiger to switch cages between roars), while in previous videos it was only assumed that a single roar could be heard.

The problem will be addressed by building the conditional probability table of the four possible observations (LL, LR, RL, RR) conditional on the position at the left or right cage of the hidden tiger.

To conform said conditional table, we will assume “conditional independence” which will allow us to multiply conditional probabilities; Its meaning is briefly discussed in the context of the tiger problem (if the condition that the tiger does not change sides is met, then successive roars are asumed independent), but please refer to the videos [condin1EN] and [condin2EN] for a detailed analysis of the concept and further examples.

Once this new conditional table has been formed, the application of the Bayes formula is identical to previous cases. The video [tiger5EN] will discuss the general case of an arbitrary number of roars, and the video [tiger6brEN] will propose a recursive Bayes formula to solve the same problem.

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