Home > Uncategorized > The validity of statistical induction

The validity of statistical induction

from Lars Syll

treatprob-2In my judgment, the practical usefulness of those modes of inference, here termed Universal and Statistical Induction, on the validity of which the boasted knowledge of modern science depends, can only exist—and I do not now pause to inquire again whether such an argument must be circular—if the universe of phenomena does in fact present those peculiar characteristics of atomism and limited variety which appear more and more clearly as the ultimate result to which material science is tending …

The physicists of the nineteenth century have reduced matter to the collisions and arrangements of particles, between which the ultimate qualitative differences are very few …

The validity of some current modes of inference may depend on the assumption that it is to material of this kind that we are applying them … Professors of probability have been often and justly derided for arguing as if nature were an urn containing black and white balls in fixed proportions. Quetelet once declared in so many words—“l’urne que nous interrogeons, c’est la nature.” But again in the history of science the methods of astrology may prove useful to the astronomer; and it may turn out to be true—reversing Quetelet’s expression—that “La nature que nous interrogeons, c’est une urne”.

Professors of probability and statistics, yes. And more or less every mainstream economist!

  1. Frank Salter
    July 20, 2019 at 9:57 am

    If is known what the relationships being examined really are then statistical induction may be useful. Otherwise it is not helpful.

    The real problem with conventional economic analysis is that it is akin to building a house of cards. The true scientific method which needs to be used to approach the underlying quantitative reality is dimensional analysis. A fully worked example is found at http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/dimension/node6.html. It is well worth your time to follow the analysis in full. It demonstrates how a seemingly intractable problem is turned into useful analysis.

  2. Ken Zimmerman
    July 25, 2019 at 11:51 am

    In 1912, an American statesman, Elihu Root, won the Nobel Peace Prize. The Nobel laureate was also widely considered as one of the ablest lawyers the United States has ever produced. He once wrote:
    About half the practice of a decent lawyer consists in telling would-be clients that they are damned fools and should stop.

    Many statisticians follow a completely different tactic: They are enthusiastic about promoting the use of statistics and are often reluctant to tell scientists (or would-be scientists) about the severe limitation of statistical inference. Many veteran statisticians are aware of this problem, but they either are busy in producing esoteric articles or simply do not want to rock the boat.

    Professor D.A. Freedman pointed out many of the deficiencies that other statisticians would not or could not in law-like statistical models that rely on regression and/or time-series techniques. Among the dominant research methodologies in econometrics and social science research. Many even lauded as examples of exemplary research techniques. “Despite their popularity, I do not believe that they [the statistical models in question] have in fact created much new understanding of the phenomena they are intended to illuminate. On the whole, they may divert attention from the real issues, by purporting to do what cannot be done-given the limits of our knowledge of the underlying processes. If I am right, it is better to abandon a faulty research paradigm and go back to the drawing boards.” Freedman insists that multiple regression, as commonly employed in social science, “does not license counterfactual claims.” His objections to these models can be summarized as follows. First, the models are devoid of intellectual content. The investigators do not derive the models from substantive knowledge; instead, the models are either data-driven or simply assumed. Second, nobody pays much attention to the stochastic assumptions of the models. In most social-science applications, these assumptions do not hold water. Neither do the resulting models. Some investigators are aware “of the problem of the stochastic assumptions in their models and therefore label the computer outputs as merely descriptive statistics. According to Freedman, “This is a swindle. If the assumptions of the regression model do not hold, the computer outputs do not describe anything.” Third, statistics as a science must deal explicitly with uncertainty. But in practice, complicated statistical models often are the dominant source of uncertainty in a serious investigation. Instead of solving problems in real life, such models sweep the problems under the carpet. Fourth, these models do not render meaningful predictions; they only invite misinterpretations. In comparison to natural science models (e.g., Newtonian mechanics and Mendelian genetics), social science models do not capture the causal relationships being studied. In sharp contrast, the natural science models work “not only by log likelihood criteria, but for real.”

  3. August 4, 2019 at 10:00 am

    To be fair, Whitehead and Russell subsequently reformed mathematics, taking full account of Keynes’ objections to prior practice, and citing him as a source. Turing et al took things much further, as reflected in many public lectures on the subject. (Although these seem to have escaped economists’ attention.)

    • Ken Zimmerman
      August 5, 2019 at 11:54 am

      Dave, but they did not accept it in the way Reuben Hersh recommends, “Dealing with mathematics (or money or religion) is impossible in purely physical terms-inches and pounds-or in purely mental terms- thoughts and emotions, habits and reflexes. It can only be done in social-cultural-historic terms. This isn’t controversial. It’s a fact of life.” But far as I can tell neither Russell or Whitehead treat mathematics in this manner. Include Turing here as well. Russell, Whitehead, and Turing learned mathematics as a formal logic using equations. Some among them linked these equations with others, into arrays which became complex. Some so complex that few others could understand their results of how they came to them. But still they never considered mathematics as a social-cultural-historic creation.

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