Statistical modeling and reality

15 Jan, 2015 at 11:24 | Posted in Statistics & Econometrics | 4 Comments

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 … Kalman_dummiesAs 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.

To 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


  1. Is the problem with the statistical theory, the application, or a confusion about the relationship between the two?

    • I would say both, because a rather widespread confusion about the relation makes for bad applications! I usually have no problem with statistics per se, but when used in science one often forgets that a set of axioms and theorems have to have “bridging warrants” if we are going to be able to “export” them to a, e. g., social science setting. Otherwise we have to — as e. g. Haavelmo — rely on “pure hope”. That’s not enough for this critical realist! As social scientists we ALWAYS should have to argue and justify the use of essentially deductive-axiomatic theories and models if we want to apply them!

      • Lars, as a mathematician I think that the appreciation of what an axiom is is vital. It is never something to be taken for granted, as some suppose. Rather, it is a part of a ready-made theory that may or may not be appropriate. The responsibility is on those seeking to apply the theory to ensure that it is appropriate, and to seek advice where necessary.(Do you agree?)

        Of course, mathematicians and statisticians are only human, and if their livelihood depends on it they may well seek to bamboozle people into accepting some axiom as if it were an iron law of nature. They may even get to deceive themselves, e.g. in an unhealthy group-think. Hence everyone should have a basic appreciation of what mathematics and statistics can and cannot deliver. Keep it up!

  2. Kalman seems to requesting an explanation for variations. In social science, there are generally speaking two methodologies: individualistic and aggregate or non-individualistic. The effect however of the aggregate statistic mathematical models is to remove empirical content and subjective interpretations. The only remedies available are to critique the criteria for validity of mathematical models which requires delving into mathematics and statistics, or to comment critically and reflexively on the findings of these studies. The field of economics has been highly formalized (mathematized and statisticalized) without much predictive power but commentary has therefore been muted; universities prefer nonpolitical or unpoliticized research and they procure this by politically preferring in terms of funding and evaluation those research programmes which are contentless or interpretation free. There is no substitute for addressing anomalies between formal models and visible reality by commentary.

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