2018-09-16

Bayes’ theorem explained by Lily Serna

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by Neil Godfrey

Last night I chanced to turn on the TV half way through a program trying to show viewers how interesting maths was. Yeh, okay. But I watched a little as they demonstrated how they do searches at sea for missing persons. Then it suddenly got interesting. Bayes’ theorem was introduced as their way of handling new information that came to them as they conducted their search. And the presenter, a maths wiz (I have seen her magical maths brain at work on another show), Lily Serner, explained it all without the maths. Move the red button forward to the 44:54 mark:

Or a more truncated version is also on youtube

Another simple introduction on The Conversation:

Bayes’ Theorem: the maths tool we probably use every day, but what is it?

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Neil Godfrey

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15 Comments

  • 2018-09-17 16:21:51 UTC - 16:21 | Permalink

    So, from the video, I gleaned that Bayes Theorem teaches us to eliminate what probably isn’t true, so that what we are left with should be the case.

    You know who else said that? Sherlock Holmes!

    • Neil Godfrey
      2018-09-17 20:46:08 UTC - 20:46 | Permalink

      I thought the video further showed that each item of “what we are left with should be” assessed in the light of probability given our background knowledge and updating each hypothesis as that new information comes along.

      • 2018-09-17 21:39:37 UTC - 21:39 | Permalink

        I think Bayes is a useful method, but I am somewhat concerned about Carrier’s method for assigning probabilities for his Bayesian reasoning. Along these lines, if anyone here is interested in Carrier, I wrote a very brief (I promise) blog post called “Conspiracy Thinking In The System of Dr. Richard Carrier’s Thought.” Check it out: http://palpatinesway.blogspot.com/2018/09/conspiracy-thinking-in-system-of-dr.html

        • Neil Godfrey
          2018-09-17 22:54:57 UTC - 22:54 | Permalink

          What probability estimate does Carrier assign the “conspiracy theory/dying for a hoax” explanation for Christian origins?

        • Der Gottesverachter
          2018-09-18 18:21:46 UTC - 18:21 | Permalink

          Quite some acrobatic reasoning there.

        • proudfootz
          2018-09-19 07:52:28 UTC - 07:52 | Permalink

          I think that equating the notion that some people might have lied with the notion that intelligent aliens used sophisticated technology to replace an historical Jesus to hoax his disciples is not a very apt one.

          For example, we know Joseph Smith was martyred. Should we consider that his story about meeting angels and translating golden tablets using a magic hat was true because ‘no one would die for a lie’?

          I’d suggest that it was more likely Smith was a fraud than that he was fooled by alien intelligences trolling humanity.

    • Robert S.
      2018-09-17 21:56:12 UTC - 21:56 | Permalink

      No, it has nothing to do with eliminating what probably isn’t true. This is a very reasonable conclusion from the video, and is therefore a good critique of it. Bleh.

      Let’s say you claim you have a cat. What is the probability you have a cat? We investigate the class of “People Who Claim to Have a Cat”. It turns out that of those who say they have a cat, 95% actually do (5% lie).

      95% becomes our prior probability – our base probability “prior” to examining the evidence. Now this gets evaluated against the evidence:

      – You show up every day with cat hair on your sweater. That’s 100% expected on “Have Cat”, but only 10% expected on “Not Have Cat” (maybe some people pass cats on their way to work and give them a big hug)

      – You have cat pictures on your desk. That’s 100% expected on “Have Cat”, but only 5% expected on “Not Have Cat”.

      – You were overheard in the lunchroom discussing your lifelong hatred of cats. That’s 40% expected on “Have Cat” (maybe spouses sometimes insist on having cats), and 100% expected on “Not Have Cat”.

      Anyway, the theorem weighs all this evidence against the prior probability, to come up with the probability that you Have A Cat. This is where all the difficult under-the-hood math[s] happens. It’s basically complicated fractional weightings of the percentages I listed. This part is what graduate students are for. But it can be spreadsheeted once, then used forever after.

      What’s left for historians to do, is to debate all the percents listed (that is, evaluate the evidence), plugging and re-plugging in the numbers. But curiously they seem to hate committing themselves to that endeavor.

      • Neil Godfrey
        2018-09-17 23:00:59 UTC - 23:00 | Permalink

        I see nothing wrong with the idea that historians would debate/evaluate the evidence. That’s exactly what they love doing. I don’t recognize your historians who “hate committing to” evaluating and debating the evidence.

        They don’t need to use maths, by the way. All they need to do, and do do, is substitute terms like “very likely”, “unlikely”, highly probable” for percentages. It’s the same mental processes.

    • MrHorse
      2018-09-17 22:13:57 UTC - 22:13 | Permalink

      She highlighted not focusing on what is improbable; and focusing on what is probable, especially as new information comes to light.

  • Charles
    2018-09-17 20:58:08 UTC - 20:58 | Permalink

    “The wisdom of the crowd?” The answer would be according to what crowd you asked. Say you asked Christians about the probability of Jesus existing historically. We know the answer to that one. I doubt “the wisdom of the crowd” would even be in the ballpark on that one. Or even asking randomly worldwide it would seem to me there would be way too many variables.

    • Neil Godfrey
      2018-09-17 21:03:55 UTC - 21:03 | Permalink

      I was wondering the same. But I don’t know the theory involved with the wisdom of the crowd ideas. Does it apply to “yes/no” questions? What I was wondering was if we took 100 non-Christians and asked them what they thought.

      • Charles
        2018-09-17 21:07:52 UTC - 21:07 | Permalink

        Wouldn’t that be biased as well? I wouldn’t know how to find an objective crowd for the question. That lady in the video did say, though, “we got lucky on that answer (paraphrasing).”

        • Neil Godfrey
          2018-09-17 21:26:40 UTC - 21:26 | Permalink

          I don’t think non-Christians would necessarily be biased one way or the other. I think most Christians, for example have no problem with the historical existence of the founders of other religions and my experience with Buddhists, the non-religious, Hindus, leads me to think that as a rule they don’t really care if Jesus was historical or not. They have no vested interest either way.

          • Charles
            2018-09-19 20:47:35 UTC - 20:47 | Permalink

            You may be right but a few years back (as a non-believer) if someone had asked me, “Did Jesus exist historically?” I would have probably said, “Do what?” Left the flock years & years ago and it never entered my mind that Jesus might not have even existed historically. But I wasn’t even aware of the debate at that time. Took the Internet, Google, Amazon forums and vridar, etc. to open my brain up to Jesus’ historicity.

    • MrHorse
      2018-09-17 22:20:24 UTC - 22:20 | Permalink

      I presume one ought to assign a value [probability calculation or other value] to ‘the wisdom of the crowd’, relative to other objective information at hand.

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