Hidden tiger 6: RECURSIVE Bayes formula, any number of roars (proof)

This video reviews the theory behind the recursive Bayes formula for the N "hidden tiger roar" problem.
The NON-recursive formula was discussed in the video • Hidden tiger 5: Bayes ... . Here, we verify that applying N times the Bayes formula with the `1 roar conditional table' gives the same final posterior probability as applying the `N roar table' just one single time.
In both cases, `conditional independence' must be assumed for the results to be correct.
Simulation of several realizations of the tiger setup and how belief (posterior probability) is updated is carried out in video • Hidden tiger 7: recurs... .
Ideas similar to the ones here are behind some `recursive Bayes filters'.
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#bayes #filtering #probability #statistics
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Antonio Sala
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