I'm not the poster you're responding to, but your observation about the distinction between P and p is crucial. The version of Bayes' rule that is relevant for

I'm not the poster you're responding to, but your observation about the distinction between P and p is crucial. The version of Bayes' rule that is relevant for the Kalman filter is the third one here: https://en.wikipedia.org/wiki/Bayes'_theorem#Random_variables https://en.wikipedia.org/wiki/Bayes'_theorem#Random_variable... ("if both X and Y are continuous").