Attempt to explain Bayes without much maths, please review

post by David_Gerard · 2011-08-06T09:24:30.349Z · LW · GW · Legacy · 26 comments

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My current favourite waste of time is the concept of Bayesian postmodernism. Just putting those two words together invokes a world of delightful wrangling, as approximately anyone who understands one won't understand or will have contempt for the other. (Though I found at least one person - a programmer who's studied philosophy - who got the idea straight away when I posted it to my blog, which is one more than I was expecting.) It is currently a page of incoherent notes and isn't necessarily actually useful for anything as yet and may never be.

Anyway, that's not my point today. My point today is that as part of this, I have to somehow explain Bayesian thinking in a nutshell to people who are highly intelligent, but have no mathematical knowledge and may actually be dyscalculic - but who can and do get the feel of things. I'm trying to get across that this is how learning works already and I just want to make them aware of it. I've run it past a couple of working artists who seemed to get the idea a bit. So I am posting this here for your technical correction.

If you think it's any good, please do run it past artists or critics of your acquaintance. (I'm glancing in AndrewHickey's direction right now.)

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"The meaning of a thing is the way you should be influenced by it." - Vladimir Nesov

To explain what "Bayesian postmodernism" means, I first have to try to explain Bayesian epistemology.

1. Probability does not exist outside in the world - it exists in your head. Things happen or not in the world; probability measures your knowledge of them.
2. You know certain things, to some degree. New knowledge and experiences come in and affect your knowledge, pulling your degree of certainty of given ideas up or down.
3. Bayes' Theorem is the equation describing precisely how much a new piece of information (on the probability of something holding in the world) must affect your knowledge. This is a mathematical theorem, true in the sense that 2+2=4 is true; this is a mathematical question with one right answer. If you know your "prior probability," and you know what the new information is, you know your new probability (the "posterior probability").
4. The hard part is, of course knowing what the hell your prior actually is, to more useful specificity than "everything you think you know about everything."
5. (Just to make it harder, the prior is not a number, but a probability distribution over a spectrum of possible alternatives.)

Bayesian epistemology is the notion of using this approach to map out the network of your degrees of certainty of your ideas and how they interact, and just how much a new idea should change your existing degrees of certainty.

The application to criticism and understanding of art should be obvious to anyone with even an enthusiast's experience in the field. (And probably not to anyone without.) Postmodernism tells us we can't be certain of anything; Bayesianism tells us precisely how uncertain we should be.

Problems:

1. Assigning meaningful numbers is tricky. It's hard enough having some sort of feel for how certain you feel a given notion is, let alone working out how those certainties should interact with mathematical rigour.
2. The mathematics to build a Bayesian network properly can get quite hairy. Calculus tends not to be a strong point of art critics.
3. The subject matter is subjective internal feelings about art. Two people could build plausible yet utterly incompatible Bayesian networks of subjective feelings, even given that art is intersubjective rather than purely subjective. (There is an interesting result called Aumann's Agreement Theorem which mathematically proves that two Bayesians starting from the same data cannot "agree to disagree", at least one must be wrong - but find two art enthusiasts who start from the same life experiences with the same personal inclinations. Thus, convincing others becomes an argument about bases.)

No human who claims to be a Bayesian actually has a network mapped out in their head. They're just doing their best. But that people (a) do this and (b) get useful results from it - even in number-based fields, rather than subjective feeling-based ones - is promising.

A word on competing approaches: The model that holds that probability exists in the world, which is the version found in common everyday popular usage and which your statistics textbooks probably taught you how to use, is the frequentist approach. This is a grab-bag of tools and statistical methods to apply to the problem. The easy part is you don't have to know your precise prior. The hard part is that different methods can get different answers, of which only one (if that) can be right, so you have to know which one to apply. The entire frequentist toolkit can be mathematically derived from the Bayesian approach. The Bayesian approach is currently increasingly popular in science and economics, because it gives the right answer if you have your prior right.

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If the above only requires minor fixes, I may post-edit based on comments so I can just refer people to this link.

Despite the above section being what I've posted this here for discussion of, this is going to devolve into a thread about postmodernism. So I'll answer some of the obvious here.

• "Postmodernism" is not one coherent thing, but six or seven (so far that I've encountered). Per the name, it's a reaction against something called "modernism" in whatever field is being addressed.
• This also means that a lot of it makes no damn sense to the untrained reader unless you also understand what it's a reaction against.
• The name is given to both the methods and the results. Finding terrible postmodernism is about as hard as finding terrible punk rock, for the same reasons. (e.g. that Sokal pranked some idiots has negligible bearing on Derrida.)
• Science, and the Enlightenment in general, is a modernist project by nature (despite the Modernist movement per se claiming to be a reaction to Enlightenment thinking), so science fans and postmodernists have a natural culture clash.
• It was obvious to me, but I appear to be the first person in the world to explicitly note the Bayes structure of the postmodern approach. I noticed this then I noticed that différance, insofar as Derrida actually admits there's a definition, looks very like how a Bayesian update would feel from the inside. I think. Maybe.
• Cav points out that I'm basically rebuilding PM in the shape of Bayes. I need to learn enough to attempt to do it the other way around too.
• I've either struck gold or I've struck crack.

Post-script: No-one's coughed up their own skull in horror yet, so I assume I haven't made any glaring technical errors and, modulo a few post-edits, this'll do for now. It's still too mathematical, but diagrams may help - maybe the next version will have some.

Nor has anyone started talking about postmodernism, to my surprise.

PPS: And I'm surprised no-one's disputed "No human who claims to be a Bayesian actually has a network mapped out in their head."

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