The validity of statistical induction

18 Jul, 2019 at 22:59 | Posted in Statistics & Econometrics | 10 Comments

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!

10 Comments

  1. I read this book by Keynes and was astonished. In a way I believe he answered some of the qustestions Khaneman and Tversky tested, the rationality of people cannot be treated irrespective of risk, the probability and effect of the outcome, and regarding the future uncertainty rules, not probability. He as well treats probability for an individual as a judgment with certain sureness/probability/judgment,

    But then, the whole world is full of social constructions (not post modern), organized behaviour and again and again they are tested, reformed, scrapped, outperformed etc. The ability to produce and make and do seems to be the only realistic criteria for understanding the society?

    And Keynes looks explicity on the fact that the whole has other characteristics than the parts. It’s a systems view.

  2. The validity of statistical induction an empirical matter, which cannot be resolved by theoretical philosophy.
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    Armchair philosophers in ivory towers have delusions about their own grandeur if they think that they can ever throw any light on such empirical matters without examining the history of human progress.
    .
    Does statistical induction work most of the time?
    Has it proved to be useful?
    Has it generally helped to advance the welfare of humanity?
    The answer to these questions is obviously “YES”.
    So who cares about the unproductive abstruse scriptures of theoretical philosophers?

    • Statistical induction was wrong in presidential polling. Why should it be right in economics?
      .
      Also, Keynes ignores the trade in options on urn contents. Traders buy and sell derivatives of the measurements made. You can use options to bet on the color of a ball picked from the urn and also bet on other things like whether the ball is the same color as the last pick. By strategically placing bets as options and re-hedging as each new ball is pulled, you can guarantee that you will come out ahead. And all your counterparties can also come out ahead if they are using different hedging strategies.
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      The uncertainty of the color of the next ball pulled remains but the certainty that your hedges will produce a profit can be guaranteed (by the Fed as a last resort).

      • Robert,
        .
        “By strategically placing bets as options and re-hedging as each new ball is pulled, you can guarantee that you will come out ahead. And all your counterparties can also come out ahead if they are using different hedging strategies.”
        .
        This to me sounds like total nonsense. Risk cannot be destroyed it can only be dispersed. If risk is dispersed, returns can only reduce to the riskless rate – if you’re lucky.
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        If you believe the Fed is the protector of last resort why even bother to hedge – take it naked on the chest and if it blows up wait for the Fed bail out.
        .
        “The uncertainty of the color of the next ball pulled remains…”
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        And of course this second statement is at odds with the your first – you can’t have it both ways.

        • You should study options if you think you can’t have it both ways. You can hedge uncertainty about the price using various options such as volatility.
          .
          See a former UBS trader describe how both sides of an options bet made money:
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          “As an experiment once, we set up a diverse portfolio of rate option trades with the gamma trader (me) getting the long and the Vega desk, which managed long dated options, taking the short leg. Over a six month period, both desks made money on their side of the options portfolio.”
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          From https://threadreaderapp.com/thread/1142997842803351552.html
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          Speculators exist but it is possible to hedge perfectly with derivatives.
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          You can think of price as a multi-dimensional surface. Derivatives are like mathematical partial derivatives with respect to volatility or decay or other dimensions of the price. You can smartly choose partial derivatives that go up no matter what the price does.
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          The existence of specials, which are repo that pay you to lend a Treasury, are an example of returns in excess of the riskless rate, since you bought a riskless Treasury at a risk-free rate then lend out the Treasury for additional return.
          .
          Risk is dispersed so that each player can choose the risk he needs to hedge other risks. Speculators exist but big players can play with each other (or against themselves as in the UBS trader’s example) so that the only risks tgey take on are to hedge other risks. No matter what happens, they will come out ahead because the risk has been dispersed so much that each player can hedge perfectly the slices of risk they take on.

          • Robert,
            .
            I wonder if your UBS buddies paper traded their system or was there real money on the line?
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            If you hedge, you pay, reducing your return.
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            I’m sure there are good position pickers out there who consistently make returns above the the price of hedging either that or they’re big enough to manipulate the markets or stitch up their clients.
            .
            If we believe what you say we should all drop what we are doing and trade full time for a living and sit back and watch the money roll in. According to you, all us will consistently make returns above the risk covered return.
            .
            Before I gave any credence to the stories you tell us I would want to see these trader’s account records.

            • As far as I can tell, doing research via twitter trader comments, you need to re-hedge daily or intra-daily to keep your profits risk-free. But, the task should be automatable.
              .
              See Emanuel Dermal, Trading Volatility https://inference-review.com/article/trading-volatility
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              “An option’s value does not depend on the expected future price of its stock.”
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              “Options market makers typically hedge against or bet on changes in future volatility, whereas the retail investors they deal with usually betting on stock price movements alone.”
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              Note that Derman concludes no perfect hedging is ultimately possible, but does acknowledge that extensions of Black-Scholes are in productive use. I think the key is in continuous re-hedging, which Derman calls a “manufacturing cost”. If you keep re-hedging continuously, you can buy and sell options and make risk-free profits; the proof is in the continued profits of Goldman Sachs, JP Morgan, and others (Medallion hedge fund made a 98% return in 2008).

              • “…the proof…”
                .
                Just because the big boys know what to do and have market power doesn’t prove anything.
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                I suggest you get some real time trading experience for a few years and then see what you say.

                • I would like to submit trades to a public bank. I don’t want to trade for myself because I am non-neoliberal, but if I could trade through a public bank with access to money markets and with profits going towards funding a basic income, I just might try out some trading strategies …

  3. In some way Lars, i think this book is my favourite from John Maynard!


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