I do not really understand your statement. First you say "True values are only *theoretical *according to Frequentist statistical theory." then you say that "true values do exist [...]". What exactly to you challenge in my statement?

There is no challenge! Briefly The foundation of Frequentist statistics hinges on the concepts of there being a hypothetical ensemble of possible measurements of

*something*; Bayesian analysis (more-or-less) starts with a prior belief in what the actual value of the

*something *is.

In other words: Frequentists (more-or-less, from the first principles of frequentist analysis) believe "if you repeat a measurement an infinite number of times, that's the answer you get for the

*measurement* *of the value*"...so it isn't the

*value *that is real it is the

*measurement of the value*. Bayesian's will (more-or-less) start with "I believe the

*value *is some range of allowable values (the prior degree-of-belief); do the

*measurement *and we can answer with a calculated degree-of-belief what the

*actual value *is (for the prior belief)." There is a famous (apocryphal?) story about Laplace's wager about the mass of planets (he used a 'Bayesian' methodology). The planets must

*have *mass, independent of any measurements.

The point about Andrew Gellman is odd... I don't think I wrote precisely what you think I did... I certainly don't think he would have written (what was attributed to me?) about Bayesian analysis.

We could just ask him if he ever wrote such a thing, but that seems pointless.

I would be *slightly* embarrassed to have AG critique my (over-)simplification of the Bayesian method... the guy has generated a lot of his professional output on the many subtleties of choices-of-priors! I'm a pure dilettante compared to him, as I've almost always stuck to a simple scale-invariant prior and if wanted to make sure I wasn't too crazy with that choice I'd do the same analysis using a flat prior (to make sure results were not radically different).