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Bayesian analysis for beginners

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  • Bayesian analysis for beginners

    Could somebody point me in the direction of a good resource to learn the basics about Bayesian analysis, particularly as it may be applied to history? I'd like to be able to keep up here, mostly, and while I do know how to use Google , I figured I might need some help separating the wheat from the chaff.
    "I am not angered that the Moral Majority boys campaign against abortion. I am angry when the same men who say, "Save OUR children" bellow "Build more and bigger bombers." That's right! Blast the children in other nations into eternity, or limbless misery as they lay crippled from "OUR" bombers! This does not jell." - Leonard Ravenhill

  • #2
    Originally posted by KingsGambit View Post
    Could somebody point me in the direction of a good resource to learn the basics about Bayesian analysis...as it may be applied to history?
    1. Assert that certain probabilities have certain values
    2. Plug them into Bayes' formula
    3. Voila, you get your desired final probability!

    Comment


    • #3
      Originally posted by KingsGambit View Post
      Could somebody point me in the direction of a good resource to learn the basics about Bayesian analysis, particularly as it may be applied to history? I'd like to be able to keep up here, mostly, and while I do know how to use Google , I figured I might need some help separating the wheat from the chaff.
      Some would suggest that any input from me is chaff by definition. For what it's worth, though . . . .

      You can find a mathematical derivation of Bayes' theorem here: http://www.inf.ed.ac.uk/teaching/cou.../bayes-Ch7.pdf.

      The Stanford Encyclopedia of Philosophy has a discussion of its relevance to epistemology: http://plato.stanford.edu/entries/ep...logy-bayesian/.

      Some historical perspective on the theorem itself: http://lesswrong.com/lw/774/a_history_of_bayes_theorem/

      Comment


      • #4
        Originally posted by Doug Shaver View Post
        Some would suggest that any input from me is chaff by definition. For what it's worth, though . . . .

        You can find a mathematical derivation of Bayes' theorem here: http://www.inf.ed.ac.uk/teaching/cou.../bayes-Ch7.pdf.

        The Stanford Encyclopedia of Philosophy has a discussion of its relevance to epistemology: http://plato.stanford.edu/entries/ep...logy-bayesian/.

        Some historical perspective on the theorem itself: http://lesswrong.com/lw/774/a_history_of_bayes_theorem/
        This is helpful, thanks.
        "I am not angered that the Moral Majority boys campaign against abortion. I am angry when the same men who say, "Save OUR children" bellow "Build more and bigger bombers." That's right! Blast the children in other nations into eternity, or limbless misery as they lay crippled from "OUR" bombers! This does not jell." - Leonard Ravenhill

        Comment


        • #5
          Found a good overview on it:

          Originally posted by Mencius Moldbug
          One new, and very popular (among the smart set) algorithmist automatism is Bayesianism. Bayesians are followers of Bayes' theorem, a result in probability theory. The Bayesians tend to congregate at the group blog Overcoming Bias, where they get together and figure out how many blue balls are in the white urn.

          Here is a good intuitive explanation of Bayes' theorem by one prominent Bayesian. Please take my word for it: this level of hubris is not at all atypical. When they say things like "in cognitive science, Bayesian reasoner is the technically precise codeword that we use to mean rational mind," they really do mean it. Move over, Aristotle!

          Of course, in Catholicism, Catholic is the technically precise codeword that they use to mean rational mind. I am not a Catholic or even a Christian, but frankly, I think that if I had to vote for a dictator of the world and the only information I had was whether the candidate was an orthodox Bayesian or an orthodox Catholic, I'd go with the latter.

          Let's take a slightly closer look at Bayes' theorem, and see why these people are on crack.

          Bayes' theorem is a pure product of mathematics. It is extremely true and extremely reasonable. If A and B are stochastic events, P(A|B) really does equal P(A) * P(B|A) / P(B).

          The only problem is that this little formula is not a complete, drop-in replacement for your brain. If a reservationist is skeptical of anything on God's green earth, it's people who want to replace his (or her) brain with a formula.


          We can see this by looking for cases of cogitation for which Bayes' theorem is about as relevant as tits on a boar hog. Believe it or not, there turn out to be one or two such cases.

          First, what Bayes' theorem gives us is a way of constructing one value from three others. We know: X = W * (Y/Z). Therefore, if we know W, Y, and Z, we can know X. Or if we know X, W and Z, we can know Y. And so on. Algebra! Do it yourself at home!

          Now, there are certainly plenty of cases in which it is actually useful to calculate P(A|B) from P(A), P(B) and P(B|A). Spam filtering is one. P(Am) is the probability that message M is spam, P(Bs) is the probability that it contains some string S, P(Bs|Am) is the probability that if it's spam it contains S, and P(Am|Bs) is the probability that if it contains S it's spam. If we keep a database of past messages, we can estimate P(Bs|Am) and P(Bs) by assuming that spam messages are similar to other spam messages, and likewise for non-spam. Then we can construct P(Am) iteratively by starting with the percentage of all messages that are spam, and reapplying this algorithm for various S.

          Note how interesting and special a case this is. It is precisely a case in which we have good estimates for Y and Z, and a crappy estimate for W which can be improved by iterating with a large set of Y's and Z's. Thus it makes sense to use Bayes' theorem.

          But fundamentally, we are calculating one variable from three. The Rev. Bayes was a great man, no doubt, but his theorem does not contradict the Garbage Theorem. If there is garbage in W, Y or Z, there will be garbage in X. If we can iterate the computation for a wide variety of reliable Y and Z, we may be able to dilute the garbage in W to oblivion, but without reliable Y and Z, what we have is a magic box that turns garbage into fresh, tasty food.

          To make this more concrete, let's look at how fragile Bayesian inference is in the presence of an attacker who's filtering our event stream. By throwing off P(B), any undetected pattern of correlation can completely foul the whole system. If the attacker, whenever he pulls a red ball out of the urn, puts it back and keeps pulling until he gets a blue ball, the Bayesian "rational mind" will conclude that the urn is entirely full of blue balls. And Bayesian inference certainly does not offer any suggestion that you should look at who's pulling balls out of the urn and see what he has up his sleeves.
          Did you think Civics had nothing to say in Apologetics?

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          • #6
            Originally posted by KingsGambit View Post
            Could somebody point me in the direction of a good resource to learn the basics about Bayesian analysis, particularly as it may be applied to history? I'd like to be able to keep up here, mostly, and while I do know how to use Google , I figured I might need some help separating the wheat from the chaff.
            Depends on how familiar you are with Bayes
            You can check out here
            http://commonsenseatheism.com/?p=13156
            Its an explanation focusing more on giving you an intuitive understanding of Bayes.
            he links to Yudkowsky's tutorial on lesswrong which is supposed to be good as well.
            My introduction to Bayesian reasoning was in Swinburne's "The Existence of God". Its great in terms of methods.

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            • #7
              If there is any worthwhile application in history, it's for cases in which plenty of statistical data is available for relevant and meaningful analysis.
              The greater number of laws . . . , the more thieves . . . there will be. ---- Lao-Tzu

              [T]he truth Iím after and the truth never harmed anyone. What harms us is to persist in self-deceit and ignorance -ó Marcus Aurelius, Meditations

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              • #8
                Originally posted by Truthseeker View Post
                If there is any worthwhile application in history, it's for cases in which plenty of statistical data is available for relevant and meaningful analysis.
                I don't think so. I mean , William Lane Craig ,Swinburne and the McGrews have done a Bayesian analysis of the resurrection of Jesus. All good inductive reasoning is in some sense Bayesian , so I think it has some good application. Of course there are the cranks (like Carrier ) who will abuse the method to support their fringe theory and its difficult to get a precise number in come cases, but it is helpful.

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                • #9
                  Originally posted by LaplacesDemon View Post
                  I mean , William Lane Craig ,Swinburne and the McGrews have done a Bayesian analysis of the resurrection of Jesus.
                  That they've used it doesn't validate the methodology.
                  I'm not here anymore.

                  Comment


                  • #10
                    Originally posted by Carrikature View Post
                    That they've used it doesn't validate the methodology.
                    Not a fan of it eh?

                    Comment


                    • #11
                      Originally posted by Cerebrum123 View Post
                      Not a fan of it eh?
                      Not in this usage, no. Don't get me wrong, I don't have a problem with the theorem itself. My issue is with its application to the realm of apologetics and historicity. It looks like a working mathematical system being borrowed to imply some semblance of robust justification to a position one already holds. Neither side escapes this accusation.
                      I'm not here anymore.

                      Comment


                      • #12
                        Originally posted by Carrikature View Post
                        Not in this usage, no. Don't get me wrong, I don't have a problem with the theorem itself. My issue is with its application to the realm of apologetics and historicity. It looks like a working mathematical system being borrowed to imply some semblance of robust justification to a position one already holds. Neither side escapes this accusation.
                        Undeerstood. I figured it was something like that.

                        Comment


                        • #13
                          Originally posted by Carrikature View Post
                          Not in this usage, no. Don't get me wrong, I don't have a problem with the theorem itself. My issue is with its application to the realm of apologetics and historicity. It looks like a working mathematical system being borrowed to imply some semblance of robust justification to a position one already holds. Neither side escapes this accusation.
                          Agreed. I posted this in the other thread, and I might as well post it here too. Its from the blog of a mathematician named Ian, and I think it makes a pretty good case for why Bayes' Theorem is unhelpful when applied to history.

                          An Introduction to Probability Theory and Why Bayesís Theorem is Unhelpful in History

                          Error in Bayesís Theorem

                          Comment


                          • #14
                            Originally posted by Cerebrum123 View Post
                            Undeerstood. I figured it was something like that.
                            The main problem is two-fold. Firstly, that of quantifying the prior probabilities, which basically boils down to "I assert that it is so". For the second, let's assume for the sake of argument that there's an 'objective' way to quantify them. The precise values will be determined by what evidence and background knowledge is being used, so it will boil down again to a very 'subjective' argument about what is the evidence and how it should be interpreted.

                            Comment


                            • #15
                              Originally posted by Paprika View Post
                              basically boils down to "I assert that it is so".
                              For the moment, let's assume that that is the case. In this respect, does Bayesian analysis differ from any alternative method of historical inquiry?

                              Comment

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