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Bayes’ Theorem – What is it and what is it good for?

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Re: Bayes’ Theorem – What is it and what is it good for?

#11

Post by ubernostrum »

tjradcliffe wrote: post #4

Bayes' Theorem tells us that the quest for certain knowledge, which drove a great deal of science and philosophy in the pre-Bayesian era (before about 1990, when Bayesian methods started to gain real traction in the scientific community) is much like the alchemist's quest for the secret of transmutation: it is simply the wrong goal to have, even though it generated a lot of interesting and useful results. One of the…

For someone who disdains beliefs which are assigned a plausibility of 1, you sure do seem eager to assign that to one of your beliefs.

Re: Bayes’ Theorem – What is it and what is it good for?

#12

Post by dimino »

Houshalter wrote: post #10
dimino wrote: post #6

Earlier quoted context omitted.

How will it make you aware of uncertainty? At some point you do have to guess (called "estimating" here), do you not, and that will have a compounding effect on the outcome. You incorrectly guess a probability somewhere only by a small amount, and it multiplies its way through to the result, and you're looking at a potentially huge difference in resulting probability, which could easily span the "will act" or "won't…

I think it's worth keeping the principles of bayesian reasoning in mind. The idea that you should update hypotheses on evidence, and adding probability in one place takes it from everywhere else slightly, keeping track of prior probability, etc. Not that you should actually do mental calculations on made up probability estimates. I mean you can do that, and if your estimates are at all decent, the result might be bet…

Judging from the content of lesswrong, I actually think literal math is what many people do recommend, and that's what bothers me.

Re: Bayes’ Theorem – What is it and what is it good for?

#14

Post by shoo »

mkramlich wrote: post #2

I'm in the middle of designing and building a system which uses Bayesian models. One thing that struck me early is that while Bayes itself is rock solid, like arithmetic, when you go to apply it the results live or die on the quality of the models, and the relevance/realism of the evidence used to train them. GIGO. But once you do have a good, relevant, signal-producing model, then, using it is a bit like doing a mul…

"all models are wrong, but some are useful" - Box.

I think the Bayesian approach is a good place to start, and provides a coherent way to think about things.

Pragmatically, one might end up needing to introduce a few approximations into the model, to make it computationally tractable, for example, but it is good to be able to view this in the context of what the gold-plated theoretical modelling approach would be.

Instead of doing something ad-hoc that appears to work, say.

Re: Bayes’ Theorem – What is it and what is it good for?

#15

Post by jhallenworld »

I recently started to think about connections between Bayes' Theorem and fuzzy logic:

http://sipi.usc.edu/~kosko/Fuzziness_Vs_Probability.pdf

    (also from wikipedia on fuzzy logic):

    "Bruno de Finetti argues[citation needed] that only one 
    kind of mathematical uncertainty, probability, is 
    needed, and thus fuzzy logic is unnecessary. However, 
    Bart Kosko shows in Fuzziness vs. Probability that 
    probability theory is a subtheory of fuzzy logic, as 
    questions of degrees of belief in mutually-exclusive 
    set membership in probability theory can be represented 
    as certain cases of non-mutually-exclusive graded 
    membership in fuzzy theory. In that context, he also 
    derives Bayes' theorem from the concept of fuzzy 
    subsethood. Lotfi A. Zadeh argues that fuzzy logic is 
    different in character from probability, and is not a 
    replacement for it. He fuzzified probability to fuzzy 
    probability and also generalized it to possibility 
    theory. (cf.[10])"

Re: Bayes’ Theorem – What is it and what is it good for?

#17

Post by pcrh »

dimino wrote: post #3

My biggest issue with Bayes' Theorem as a method of making everyday decisions is that it assumes the ability to accurately assess the underlying likelihoods of events taking place, especially on-the-fly. I would even argue that it's actually providing a false sense of precision because the sig figs are oftentimes not correctly represented.

As you say, Bayesian statistics is not of much use when there is no prior information as to the frequency of certain events. Once any amount of such information is available, then it comes into play.

Re: Bayes’ Theorem – What is it and what is it good for?

#19

Post by TeMPOraL »

dimino wrote: post #12
Houshalter wrote: post #10

Earlier quoted context omitted.

I think it's worth keeping the principles of bayesian reasoning in mind. The idea that you should update hypotheses on evidence, and adding probability in one place takes it from everywhere else slightly, keeping track of prior probability, etc. Not that you should actually do mental calculations on made up probability estimates. I mean you can do that, and if your estimates are at all decent, the result might be bet…

Judging from the content of lesswrong, I actually think literal math is what many people do recommend, and that's what bothers me.

In some cases you might want to actually do that math, even if you have to guesstimate numbers, since it still will beat your intuition.

http://slatestarcodex.com/2013/05/02/if-its-worth-doing-its-...

But in general, no one has enough computing power in their heads to go and do explicit bayesian updates on everything all day long. You have to pick your battles, and use the right tools for the task at hand.

Re: Bayes’ Theorem – What is it and what is it good for?

#20

Post by amelius »

le0n wrote: post #13

“Seeing the world through the lens of Bayes’ Theorem is like seeing The Matrix. Nothing is the same after you have seen Bayes.” I'm pretty sure this is an instance of cognitive bias.

Like when you are holding a hammer, everything looks like a nail.
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