Bayesian Reasoning

Hot on the heels of our discussion of hypotheses comes this: a discussion of Bayesian reasoning.

Bayesian (pronounced "bays-ian") reasoning is named after Bayes' theorem. In the 18th century, the Reverend Thomas Bayes derived a theorem that tells us how to update our beliefs in light of new evidence. The theorem remained in obscurity for much of the 20th century, partly because many of its most astounding successes involved classified military projects (breaking the WWII German Enigma code, and locating sunken submarines and thermonuclear weapons). In recent years, Bayesian reasoning has gained prominence, and it's now regarded as the gold standard of rational inference.

For philosophers, Bayes' theorem is relevant in many ways. First, it's conceptual scheme allows us to think very clearly about any inference from experience. The theorem shows us what it is about a hypothesis that makes it relevant to what we experience, and it suggests a criterion for calling something an explanation.

Second, Bayes' theorem helps us see the interrelationship between deduction, induction and abduction. We also gain insight into the difference between intelligence, creativity and rationality.

Finally, Bayesian reasoning is relevant to some important philosophical claims, such as Hume's position on miracles, design arguments for god, Occam's razor, and the principle that extraordinary claims require extraordinary evidence. 

The meeting will open with a 30-40 minute presentation to give us an intuitive understanding of Bayes' theorem. 

There will be handouts for those who can attend, and I'll try to post a copy here ahead of time.

Here are some discussion notes:

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  • Ivan

    Richard Carrier's new book, Proving History, has a very good, in-depth treatment of Bayes' Theorem. He also argues that all good historical reasoning is Bayesian. He argues that the Inference from Evidence and the Inference to the Best Explanation are imprecise approximation to Bayes.

    2 · February 14

  • Chad Beck

    I enjoyed the discussion and wish I could have stayed later. One thing that I would have liked to hear addressed more is the notion of "noise" (which is a kind of coping with cognitive dissonance) and what essentially becomes a "choice of law" problem (sorry for another legal reference). E.g., when the 14 is rolled, we could either choose to use deduction, or we could discredit the new evidence and yield to Bayesian inference. Each approach yields opposite results. It seems to me that deduction (when available) is preferable (perhaps only after sufficient confirmation), but isn't this a potential locus of bias? From "how reliable is the theory?" we get "how reliable is the evidence which disturbs the theory?" Overall (outside of laboratory conditions) it seems easy to abuse and misuse (arbitrarily assigning probabilities and possibilities, etc.).

    1 · February 7

    • Ivan

      I should add that we should really take this measurement uncertainty into our calculations at each stage in Bayes' theorem. Basically, the probability of seeing a 14 given the D4 is 1 in 1m.

      February 10

    • Ivan

      Dan, the chance of a mistake is not purely calculated. It's an empirical fact that we would have to measure (and set using Bayes' theorem in another context). That is, we use video cameras to record dice rolls, and get multiple people (or better yet, computers) to review the data. For example, if our dice are rolled on a scanner, a computer can flag the errors that the players make.

      BTW, I just estimated the error rate by a back of the envelope calculation. 1m games is like playing this game 40 hours a week for 4 years. I figure people will make at least one mistake over that time period.

      February 10

  • Chad Beck

    Any thoughts on how Bayesian principles could be implemented in a courtroom setting? Currently bias is compensated for by e.g., excluding prejudicial jurors, excluding certain categories of (misleading or irrelevant) evidence, adversarial presentation, etc., but the problem is so deep-seating that simply accusing someone can have a prejudicial effect. What would a Bayesian legal system look like? A police lineup-style of trial? No juries?

    1 · February 4

    • jerry

      Just found an interview of Morgenbesser, who has some wonderful things to say about how to approach inquiry/problems as a community of mind.

      From 2:40 to 5:20­

      1 · February 6

  • Steve

    Among Kevin Kelly's recent insights, were a few related to the Scientific Method...­

    "So the scientific method is still changing over time. It's an invention that we're still evolving and refining. It's a technology. It's a process technology, but it's probably the most important process and technology that we have, but that is still undergoing evolution refinement and advancement and we are adding new things to this invention. We're adding things like a triple blind experiment or multiple authors or quantified self where you have experiment of N equals one. We're doing things like saving negative results and transmitting those. There's many, many things happening with the scientific method itself—as a technology—that we're also improving over time, and that will affect all the other technologies that we make."

    February 4

    • jerry

      But no brilliant talent for mathematics is at all necessary for the study of logic.

      I next take up syllogism, the lowest and most rudimentary of all forms of reasoning, but very fundamental because it is rudimentary.

      February 5

    • Steve

      I'm sorry to say that I won't be able to attend the meeting after all this evening. Gotta work...

      February 6

  • jerry

    Hi Steve,

    I don't want to seem like I'm talking around you. Have you seen this Edge question? It asks what single scientific concept would improve everybody's cognitive toolkit. They asked 167 thinkers and got 166 different responses, I think...So, why should we take Kelly's proposal...not that it isn't worthy...­

    February 5

  • jerry

    Plug in Bayes Theorem for A, but you still have to be clearly define C, deduce, induce, infer to the best explanation and repeat...

    February 4

  • Ivan

    I've written up some notes to guide our discussion:­

    5 · February 4

  • Steve

    Ivan... Thanks for initiating this meeting. Thanks also for preparing a presentation about the topic before the discussion begins.

    I've been thinking that this session would be a great introduction to also considering the work of Karl Popper and Thomas Kuhn and how these ideas in the Philosophy of Science relate to each other.

    1 · February 3

  • Adina Bianchi

    Any recommended reading for this? Looks fun, looking forward to it!

    February 1

    • Jim

      Nate Silver's description should be qualified just a bit. http://www.newyorker....­

      1 · February 2

    • Micah Norman

      I had not seen this. I like the way he immediately applied it. Often, I here it explained overly abstract (I think object oriented programming has this same problem) before it is actually applied to task world problems. I should have looked into this prior to recommending the book. Based on this article, I retract my earlier recommendation

      February 2

  • jerry

    How do you substantiate the following: "In recent years, Bayesian reasoning has gained prominence, and it's now regarded as the gold standard of rational inference"

    ...when others say things such as, "As many philosophers agree, the frame problem is concerned with how an agent may efficiently filter out irrelevant information in the process of problem-solving...However, traditional approaches to relevance—as for example, relevance logic, the Bayesian approach, as well as Description Logic—have failed to do justice to the foregoing constraints ("semantic relevance"- e.g., inferential relations such as insufficiency of knowledge, the limitation of time budget, etc ), and in this sense, they are not proper tools for solving the frame problem/relevance problem." Pei Wang,

    1 · February 1

    • Ivan

      Good point, Jerry!

      Let's discuss this at some point in our meeting. I don't think that Bayesian reasoning solves all problems or solves them all unambiguously. However, I think that once we select a frame, Bayes' Theorem must still apply. It may also be helpful to distinguish Bayes' Theorem from Bayesian reasoning.

      2 · February 2

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