What is a statistical model?

15 Nov, 2014 at 13:14 | Posted in Statistics & Econometrics | Comments Off on What is a statistical model?

My critique is that the currently accepted notion of a statistical model is not scientific; rather, it is a guess at what might constitute (scientific) reality without the vital element of feedback, that is, without checking the hypothesized, postulated, wished-for, natural-looking (but in fact only guessed) model against that reality. To be blunt, as far as is known today, there is no such thing as a concrete i.i.d. (independent, identically distributed) process, not because this is not desirable, nice, or even beautiful, but because Nature does not seem to be like that … As Bertrand Russell put it at the end of his long life devoted to philosophy, “Roughly speaking, what we know is science and what we don’t know is philosophy.” In the scientific context, but perhaps not in the applied area, I fear statistical modeling today belongs to the realm of philosophy.

science_medal9_hTo make this point seem less erudite, let me rephrase it in cruder terms. What would a scientist expect from statisticians, once he became interested in statistical problems? He would ask them to explain to him, in some clear-cut cases, the origin of randomness frequently observed in the real world, and furthermore, when this explanation depended on the device of a model, he would ask them to continue to confront that model with the part of reality that the model was supposed to explain. Something like this was going on three hundred years ago … But in our times the idea somehow got lost when i.i.d. became the pampered new baby.

Rudolf Kalman

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