h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I think the article should at least mention fuzzy logic, which is another method of dealing with uncertainty often compared with Bayesian probability (though in reality Bayesian probability is totally encompassed by fuzzy logic, as fuzzy logic is a superset of traditional logic).

But then, most Bayesians were hostile to fuzzy logic in the past, and that may still be the case...

- KefX

It was in-again-out-again in the article; but at least it's now in one of the conversations.

Tell me, is fuzzy logic to Bayesian Stats as logic is to classical stats?

Okay, let me describe fuzzy logic (to the best of my ability, since I won't take all day to explain it). Fuzzy logic is a superset of classical (boolean) logic that goes all the way back to the ancient Greeks. By boolean logic I don't mean boolean algebra, I mean the idea all things are either true are false. Is the object (imagine I'm pointing at a chair here) a chair, or not a chair? In other words: object = chair, true or false? (To which we'd say true, assuming we're not Plato.)

Fuzzy logic asks, how MUCH of a chair is it? A chair might have a rating of 1.0 (100%), but a stone that can kind of looks like a chair and might be used as one may have a small rating of, say, 0.2. Are these numbers subjective? Yes. That does not necessarily mean that it causes inaccuracy (as many claims it does), it just means some time needs to be taken to ensure that the system is balanced - something you ought to do anyway, since you should test any programming code you write (fuzzy logic is used mainly for programming).

For a long time, Bayesians have totally rejected fuzzy logic, saying that probability was the be-all and end-all of handling uncertainty. (This strikes me as just plain closed-mindedness. This reminds me of the time the patent office shut down around 1900 because the moron who ran it thought everything had been invented already.) They would say that the proper question to ask is not HOW much of a chair it is, but the PROBABILITY of somebody describing it as a chair. This is misleading, however, because these numbers are two different things.

(allow me to digress with an example)
For instance, say we have a kinda tall person, such as myself (I'm about 6'2"). Let's assume I'm not a basketball player, as I'm not, in which case I wouldn't be considered that tall. Now, I might be described as 0.9 tall. However, if I took a poll of a zillion people asking "Am I tall?", most likely everybody would say "yes". That would be 1.0, which is decidedly not 0.9. Now let's take the giant Douglas Adams, since he's just a convenient example of a tall person. He might be 0.95 tall (there are taller people), but if you ask people if Douglas Adams is tall (assuming they know how tall he is), they would UNDOUBTEDLY ALL respond "yes", so the probability of saying Douglas Adams is tall would be 100%, or 1.0 again, which decidedly isn't 0.95 either.

So Bayesian probability can't replace fuzzy logic, but this doesn't mean that the Bayesians are always wrong. Sometimes a Bayesian probability system might be better. It all depends on your circumstances, and I feel the Bayesian bias against fuzzy has been unfair.

Use the right tool for the job.

- KefX

P.S. This post only scratches the surface of fuzzy logic, by the way. I just wanted to discuss the basic principles - I didn't go into fuzzy variables, fuzzy set theory, the magnificent Combs Method, et cetera...

Interesting...

It all depends on what you consider the 'correct' value to be, for your purpose. From what you wrote, you imply that this 'chairness' doesn't necessarily have to run from 0 to 1. I think one reason Bayesians like their way round is that probability has a definite, concrete, meaning. Arbitrary ratings based on characteristics (like in some spam filtering) sometimes lack a true meaning.

There should be a way to reconcile the two (after all, very few Bayesians would take the asking people method of establishing tallness).