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Nice you just provided the solution to Homework 1, Problem 3.1 (https://davidrosenberg.github.io/mlcourse/Homework/hw1.pdf).

My solution never mentioned Bayes! So, don't have to "be a Bayesian" to use what I wrote.

I just used conditional expectation which, of course, with full details, is from the Radon-Nikodym theorem in measure theory as in, say, Rudin, Real and Complex Analysis with a nice, novel proof from von Neumann.

Yes, of course. A “Bayes prediction function” has nothing to do with Bayesian. Bayes had a lot of things named after him ;)

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