Racket wrote:(1) ...Probability densities are not subjective. They are rigorously defined. It'd be akin to saying the real number line is in the eye of the beholder.
(2) Appropriateness of a fitted model can be tested through residual diagnostics (for stochastic processes).
(3) You entire argument seems to suggest that all models are equal and none are better than any others ...
(1) Since you use the expression "rigorously defined" I presume you are talking about about probability density functions, which are mathematical constructs, rather than probability distributions, which are a mathematical representation of a set of observations (or a window into some part of reality). Perhaps you conflate the two? The functions are convenient simplifications, and our best effort to represent reality, or fit functions to data. But they are not reality itself. The distributions (which we may attempt to fit PDFs to) are our best effort to inventory reality, subject to whatever uncertainties affect the accuracy of the individual observations. Some probability distributions can be reasonably well represented by probability density functions, from which we can derive some important practical meaning. Others, not so much. Or at least the important parts of the distribution (e.g., the tails for chaotic phenomena) can be devilishly hard to capture meaningfully. I think Igy understands this better than you
(2) I defy you to show this for a model that has accurately (whatever you would like that to mean) forecast / predicted financial markets or asset classes. I'm very interested to see how well you can do this. That would be the pot of gold at the end of the rainbow.
(3) Nonsense. Utter rubbish. I never said that; if you've inferred that, it may begin to explain where our communication is failing.