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Bayesian statistics, in a small (drunken) nutshell

Discussion in 'Other Health News and Research' started by Simon, Nov 11, 2015.

  1. Simon

    Simon

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    Monmouth, UK
    I found this a really helpful explanation about the central Bayesian idea of prior probablilities, illustrated by a drunk, and a musician.
    Comwell's rule in Bayesian statistics

    I've probably already quoted more than is fair, but the basic idea is that according to normal statistical approaches, we should have as much confidence in the drunk as the musician. But with Bayesian statistics, you would probably (ha) start off the with prior confidence (probablility) that the musician was much more likely to be right than the drunk. After the experiment the claims of both would have more credibility, but the musician would still be rated as more likely to be right than the drunk.

    That's it. Did it for me, hope it helps someone.

    Actually, that's not even the main point of the article (Oliver Cromwell comes into it)
    Full blog
     
  2. barbc56

    barbc56 Senior Member

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    @Simon

    I don't think you have ever written a post I haven't liked. Just don't let it go to your head!:)

    I've taken several statistics courses and once dated a statistics professor for five years (true)*, but both are in the distant past. It always helps to read these type of articles as sometimes I cant remember past mean median and mode.

    I particularly liked the following as it shows the difference between Evidence Based Medicine where you could theoretically have a study to determine whether jumping out of an airplane with a patachute is safer than jumping out of an airplane without one and Science Based Medicine where you consider a priori .

    .
    Again thanks.

    Barb

    *I I added this as an example. Which event has more weight as far as my knowledge about statistics? A teachable moment, so to speak!
     
    Last edited: Nov 11, 2015
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  3. anciendaze

    anciendaze Senior Member

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    In the case of the drunk, I'd like to know if the experimenter was also drinking. I've encountered reports of remarkable happenings with similar evidence, like the hurricane party which deposited a number of sailors in Tampa Bay during a hurricane. Reasoning must have been impaired to choose that time to go sailing.

    Prior probability distributions can be abused. I have seen examples where Bayesian methods have been abused to "weight the dice" so that you would need an endless series of experiments to reject an hypothesis the experimenter preferred. Unfortunately, the frequentist alternative can also be abused to set prior probability to zero while claiming objectivity.

    The classic medical application of Bayesian methods took place when Bradford Hill investigated the linkage between smoking and lung cancer in the 1950s. His opponent was smoker, and consultant for tobacco companies, R.A. Fisher. Fisher had been part of the "new synthesis" of Darwinian evolution based on population genetics, and was a formidable force in applied statistics. Fisher delayed official recognition of health dangers of smoking by about 10 years. Sir Austin Bradford Hill turned out to be right, and not by accident.

    Bayesian methods were already in use during WWII in methods Turing developed to break German ciphers, using what he called "the weight of evidence". This technique was eventually published in an academic paper by a surviving colleague, but public revelations of the importance of cryptanalysis had to wait 30 years. (Similar methods were used in less-classified work by Abraham Wald on sequential testing.) The critical insight is that probabilities are measures of information, and will change when available information changes. This confounds people indoctrinated with Fisher's approach, as happened with The Monty Hall Problem.

    There are some very sophisticated ways of applying Bayesian methods, as in biochemical cascades where it is hard to detect some chemicals before they are converted to others. (The same thing happens in particle physics, where you have real trouble detecting things like neutrinos.) What I have to impress on people is that the logic involved is completely inflexible. These assumptions should not be under test. If, however, you have an independent basis for knowing that x->y->z, you can use this to deduce that finding y or z means x must have been present earlier. This can save you from using up large numbers of laboratory animals -- or patients.
     
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  4. barbc56

    barbc56 Senior Member

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  5. Simon

    Simon

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    Thanks! Nice to know someone else shares my obsession with research and statistics.
    And too late...

    upload_2015-11-12_12-19-25.png
    (source)​

    You've obviously been closer to a real statistician than me too (I've learnnt mainly from online courses run by US universities).

    Will check out those pdfs another time

    And thanks, @anciendaze, for the bits I understood.
     
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