Sort of. I think the distribution of Θ is the Ap distribution, since it satisfies that formula; Θ=p is Ap. It’s just that Jaynes prefers an exposition modeled on propositional logic, whereas a standard probability textbook begins with the definition of “random variables” like Θ, but this seems to me just a notational difference, since an equation like Θ=p is after all a proposition from the perspective of propositional logic. So I would rather say that Bayesian statisticians are in fact using it, and I was just explaining why you don’t find any exposition of it under that name. I don’t think there’s a real conceptual difference. Jaynes of course would object to the word “random” in “random variable” but it’s just a word, in my post I call it an “unknown quantity” and mathematically define it the usual way.
Sort of. I think the distribution of Θ is the Ap distribution, since it satisfies that formula; Θ=p is Ap. It’s just that Jaynes prefers an exposition modeled on propositional logic, whereas a standard probability textbook begins with the definition of “random variables” like Θ, but this seems to me just a notational difference, since an equation like Θ=p is after all a proposition from the perspective of propositional logic. So I would rather say that Bayesian statisticians are in fact using it, and I was just explaining why you don’t find any exposition of it under that name. I don’t think there’s a real conceptual difference. Jaynes of course would object to the word “random” in “random variable” but it’s just a word, in my post I call it an “unknown quantity” and mathematically define it the usual way.