Primitive man, aware of his helplessness against the forces of Nature but totally ignorant of their causes, would try to compensate for his ignorance by inventing hypotheses about them [...]  For one who has no comprehension of physical law, but is aware of his own consciousness and volition, the natural question to ask is not: "What is causing it?", but rather: "Who is causing it?"  [...] The error [Mind Projection Fallacy] occurs in two complementary forms, which we might indicate thus: (a) My own imagination => Real Property of Nature, and (b) My own ignorance => Nature is indeterminate.

The philosophical dierence between conventional probability theory and probability theory as logic is that the former allows only sampling distributions, interprets them as physically real frequencies of "random variables", and rejects the notion of probability of an hypothesis as being meaningless. We take just the opposite position: that the probability of an hypothesis is the fundamental, necessary ingredient in all inference, and the notion of "randomness" is a red herring, at best irrelevant. [...] by "probability theory as logic" we mean nothing more than applying the standard product and sum rules of probability theory to whatever propositions are of interest in our problem.

We do not seek to explain "statistical behavior" because there is no such thing; what we see in Nature is physical behavior, which does not conflict in any way with deterministic physical law.

[...] as in any other problem of inference, we never ask, "Which quantities are random?" The relevant question is: "Which quantities are known, and which are unknown?"

E.T. Jaynes, Probability Theory as Logic  

Dilbert

Alguns cartoons do Dilbert relativos a questões estatísticas:

[via http://stats.stackexchange.com/questions/423/what-is-your-favorite-data-analysis-cartoon]

Modelos

What is a random variable? That’s easy. It’s a measurable function on a probability space. What’s a probability space? Easy too. It’s a measure space such that the measure of the entire space is 1. 

Probability theory avoids defining randomness by working with abstractions like random variables. This is actually a very sensible approach and not mere legerdemain. Mathematicians can prove theorems about probability and leave the interpretation of the results to others. 

As far as applications are concerned, it often doesn’t matter whether something is random in some metaphysical sense. The right question isn’t “is this system random?” but rather “is it useful to model this system as random?” Many systems that no one believes are random can still be profitably modeled as if they were random. 

Probability models are just another class of mathematical models. Modeling deterministic systems using random variables should be no more shocking than, for example, modeling discrete things as continuous. For example, cars come in discrete units, and they certainly are not fluids. But sometimes it’s useful to model the flow of traffic as if it were a fluid. (And sometimes it’s not.) 

Random phenomena are studied using computer simulations. And these simulations rely on random number generators, deterministic programs whose output is considered random for practical purposes. This bothers some people who would prefer a “true” source of randomness. Such concerns are usually misplaced. In most cases, replacing a random number generator with some physical source of randomness would not make a detectable difference. The output of the random number generator might even be higher quality since the measurement of the physical source could introduce a bias. John D. Cook 

Mapas

"The central dogma of statistics is that data should be viewed as realizations of random variables. This has been a very fruitful idea, but it has its limits. It’s a reification of the world. And like all reifications, it eventually becomes invisible to those who rely on it." John D. Cook

"Statisticians can get awfully uptight about numerical approximations. They’ll wring their hands over a numerical routine that’s only good to five or six significant figures but not even blush when they approximate some quantity by averaging a few hundred random samples. Or they’ll make a dozen gross simplifications in modeling and then squint over whether a p-value is 0.04 or 0.06. The problem is not accuracy but familiarity. We all like to draw a circle around our approximation of reality and distrust anything outside that circle. After a while we forget that our approximations are even approximations." John D. Cook