Bayesianism — the new positivism

12 Jan, 2022 at 23:21 | Posted in Theory of Science & Methodology | 6 Comments

Fact and Method: Miller, Richard W.: 9780691020457: Amazon.com: BooksNo matter how atheoretical their inclination, scientists are interested in relations between properties of phenomena, not in lists of readings from dials of instruments that detect those properties …

Here as elsewhere, Bayesian philosophy of science obscures a difference between scientists’ problems of hypothesis choice and the problems of prediction that are the standard illustrations and applications of probability theory. In the latter situations, such as the standard guessing games about coins and urns, investigators know an enormous amount about the reality they are examining, including the effects of different values of the unknown factor. Scientists can rarely take that much knowledge for granted. It should not be surprising if an apparatus developed to measure degrees of belief in situations of isolated and precisely regimented uncertainty turns out to be inaccurate, irrelevant or incoherent in the face of the latter, much more radical uncertainty.

For all scholars seriously interested in questions on what makes up a good scientific explanation, Richard Miller’s Fact and Method is a must read. His incisive critique of Bayesianism is still unsurpassed.

Given that we study processes that are adequately captured by our statistical models (think of urns, cards, coins, etc), Bayesian reasoning works. The problem, however, is that when we choose among scientific hypotheses, we standardly lack that kind of knowledge. As a consequence — as Miller puts it — “Bayesian inference to the preferred alternative has not resolved, even temporarily, a single fundamental scientific dispute.”

Assume you’re a Bayesian turkey/chicken and hold a nonzero probability belief in the hypothesis H that “people are nice vegetarians that do not eat turkeys/chickens and that every day I see the sun rise confirms my belief.” For every day you survive, you update your belief according to Bayes’ Rule

P(H|e) = [P(e|H)P(H)]/P(e),

where evidence e stands for “not being eaten” and P(e|H) = 1. Given that there do exist other hypotheses than H, P(e) is less than 1 and a fortiori P(H|e) is greater than P(H). Every day you survive increases your probability belief that you will not be eaten. This is totally rational according to the Bayesian definition of rationality. Unfortunately — as Bertrand Russell famously noticed — for every day that goes by, the traditional Christmas dinner also gets closer and closer …

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  1. The story of Russell’s Bayesian turkey illustrates misunderstandings which lead to Miller’s spurious claim that “Bayesian inference to the preferred alternative has not resolved, even temporarily, a single fundamental scientific dispute”.
    .
    Inductive inference and science can never be 100% certain about any hypothesis. It follows that unfulfilled expectations cannot disprove any hypothesis.
    .
    The scientific issue in turkey’s case was whether he would survive another day.
    On every day throughout the turkey’s life, with the sole exception of the last day, Bayesian inference gave the correct answer, namely that the turkey was likely to survive.
    The sad fact that the turkey died on the last day of his life does not in any way invalidate the turkey’s scientific reasoning on previous days.
    .
    This was well explained by Bertrand Russell:
    “This knowledge [of the turkeys death] would be a fresh datum, by no means proving that the probability relatively to our previous data had been wrongly estimated. The fact, therefore, that things often fail to fulfil our expectations is no evidence that our expectations will not probably be fulfilled in a given case or a given class of cases. Thus our inductive principle is at any rate not capable of being disproved by an appeal to experience.”
    Bertrand Russell – The Problems of Philosophy 1912, chapter 6: On Induction.

    • So if another bird wanted to escape because he had an intuition, the inductive principle would correctly dismiss him as a crank? What good is the inductive principle, then?

      • Prof. Syll’s turkey is a highly intelligent scientist, capable of Bayesian inference regarding hypotheses. This fantasy has no resemblance to Russell’s account.
        .
        Russell argued that turkeys are incapable of Bayesian or any other kind of inductive inference.
        “Domestic animals expect food when they see the person who usually feeds them”.
        Such “crude expectations of uniformity are liable to be misleading … more refined views as to the uniformity of nature would have been useful to the chicken”.
        .
        But let us enter Prof. Syll’s imaginary world of turkey scientists.
        Induction then has the following uses:
        The farmer learns by experiment and experience which techniques for producing and marketing turkeys are likely to be the most profitable.
        Turkeys which stay at the farm learn how to get regular food which enables them to survive and reproduce.
        Turkeys which escape soon learn that due to food scarcities and predators their life expectancy, quality of life and mating prospects are far less certain and probably much worse than on the farm.
        .
        What type of turkey are you, rsm?

        • Wild?
          .
          Also, does the following Fischer Black quotation from Noise remind you of the posts by lesdomes on bayesianism etc. in another thread?
          .
          《I think that noise is a major reason for the use of decision rules that seem to violate the normal axioms of expected utility. Because there is so much noise in the world, people adopt rules of thumb. They share their rules of thumb with each other, and very few people have enough experience with interpreting noisy evidence to see that the rules are too simple. Over time, I expect that the transmission through the media and through the schools of scientific ways of interpreting evidence will gradually make the rules of thumb more sophisticated, and will thus make the expected utility model more valid.
          .
          Even highly trained people, though, seem to make certain kinds of errors consistently. For example, there is a strong tendency in looking at data to assume that when two events frequently happen together, one causes the other. There is an even stronger tendency to assume that the one that occurs first causes the one that occurs second. These tendencies are easy to resist in the simplest cases. But they seem to creep back in when econometric studies become more complex. Sometimes I wonder if we can draw any conclusions at all from the results of regression studies.
          .
          Because there is so much noise in the world, certain things are essentially unobservable.》

          • @rsm
            Wild turkeys don’t fall prey to inept predators like Fischer Black.
            In order to survive and reproduce you must redirect yourself back to the farmyard whence you escaped.
            .
            Fischer Black’s “Noise”
            ==================
            Black’s article is a dog’s dinner, a lazy mish-mash of second hand ideas, muddles and confusions.
            .
            Econometrics
            ——————
            Black briefly mentions a few well known problems encountered in econometrics but he has nothing new to say on these matters.
            Then, contradicting his earlier skepticism, he concedes that “Correlations among economic and financial variables do give us some information of value. Experimental studies in economics and finance have value.”

            New Classical Real Business-Cycle (RBC) theory
            ————————————————————-
            Black subscribes to the Classical Dichotomy, the theory that in the long run relative prices and real variables are unaffected by the money supply, ie that money supply is neutral in the long run.
            However, this idea is defective because it assumes continuous full employment levels of aggregate demand. It neglects a variety of hysteresis effects which periodic recessions and slumps can have on the real economy in the medium term and thence into the longer term.
            .
            Black outlines a version of RBC theory, namely that business cycles are caused by noise in the form of “unanticipated shifts in the entire pattern of tastes and technologies across sectors”.
            Black says that this theory is impregnable: “I cannot think of any conventional econometric tests that would shed light on the question of whether my business cycle theory is correct or not.”
            However, RBC theory has been widely discredited.
            Moreover, Black asserts that according to his theory “real wages will be procyclical”.
            This is patently false as shown in:
            https://fred.stlouisfed.org/series/LES1252881600Q
            and

            .
            Theory of Prices and Inflation
            —————————————
            Black produces no evidence regarding his assertion that “monetary policy doesn’t cause changes in inflation”.
            He seems to think that if money has no effect on RELATIVE prices (as in his New Classical RBC theory) then monetary policy can’t have any effect of the GENERAL LEVEL of prices. This is a non sequitur.
            .
            His theory is that:
            (a) Inflation and the general level of prices are determined by expectations of future prices;
            (b) Expectations are “irrational and arbitrary”.
            He concludes that “noise causes changes in the rate of inflation”.
            .
            This theory appears to stem from Black’s peculiar understanding of speculation on the Stock Exchange. However, financial markets differ hugely from the markets for real goods and services.
            Regarding (a), Black gives no details or evidence of how expectations influence the prices of goods and services, and he completely ignores the numerous other far more important considerations taken into account by businesses.
            Regarding (b), Black gives no evidence supporting his theory that business expectations are completely irrational.
            .
            While it is true that economists are not able to fully explain or agree about the causes of inflation, there is general agreement and masses of evidence that inflation is not entirely caused by unknown uncertainties as per Black’s ridiculous theory.

            • Kingsley,
              .
              Can you provide any evidence that inflation is not simply noisy expectations?
              .
              《This theory appears to stem from Black’s peculiar understanding of speculation on the Stock Exchange. However, financial markets differ hugely from the markets for real goods and services.》
              .
              When you start from a position that acknowledges the huge volume of transactions in financial markets that dwarf real transactions by an order of magnitude (evidence: daily repo transactions alone are several trillion dollars, while real goods traded is … what? A few hundred billion dollars at most?), do you end up realizing that supply chains are just payment chains in reverse? And since every trader knows price is a liar, from experience, aren’t prices plausibly at least as noisy as Black claimed?
              .
              Wikipedia says:
              .
              《A boom is a period when technology matches well with demand. A bust is a period of mismatch. This view made Black an early contributor to real business cycle theory.》
              .
              If money demand was met by financial innovation from, say, 2001 to 2007, can you see that an irrational financial panic caused the Great Depression by causing a sudden loss of liquidity? (Are your other criticisms of RBC irrelevant because they were subsequent to Black? Doesn’t Black say in “Noise” that monetary policy is passive, not really neutral as you claim?)
              .
              Regarding your FRED graph: how much statistical uncertainty is unreported? Are the error bars so wide, you could tell any story?
              .
              Quoting from “Noise”:
              .
              《Most generally, noise makes it very difficult to test either practical or academic theories about the way that financial or economic markets work […] research will be seen as a process leading to reliable and relevant conclusions only very rarely, because of the noise that creeps in at every step.》
              .
              Does the “rarely” in the above explain why Black wrote that some studies have value? Is it really so confusing that most studies are noisy, but some can have value?
              .
              《Black’s article is a dog’s dinner, a lazy mish-mash of second hand ideas, muddles and confusions.》
              .
              Can you imagine an appropriate personal insult I might easily respond with?


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