(no subject)

[dr_tectonic]

I beat Dynasty Tactics 2 tonight! W00t!

On the last day of the seminar today, we did a (fictitious) case study about hurricane rebuilding: government agency develops reconstruction plan that involves letting some areas return to nature instead of being rebuilt; some local prefer a plan to put it all back the way it was. Given uncertainties in future storm damage, tax revenues lost, construction cost overruns, lawsuit being brought and possibly lost, and delays during a trial, what's the best plan to go with, which of these things matter, and how much would it be worth to know the outcomes before making your decision? We found the answers and got them right. It was pretty cool!

Also cool: I learned a graphical technique for Bayesian probability calculations that is (for me, at least) about eight million times easier to understand and get right than the standard formulas. Yay for new mental tools!

Comments

[melted-snowball.livejournal.com]

What's the bayesian trick? I tend to think in terms of likelihood ratios nowadays as a way to remember these sorts of things.

[dr-tectonic.livejournal.com]

It's basically just drawing out the tree of possible outcomes, assigning the probabilities you know, and then rearranging it. Let me see if I can do it in ascii...

              ___B__
      __A____/
     /       \__!B__
____/      
    \         ___B__
     \_!A____/
             \__!B__

So the problem is that we know P(A), P(B|A), and P(B|!A) (or some equivalent combination) but we want to know P(A|B), right? Given those values, we can multiply out and assign probabilities to each of the endpoints in this tree: P(AB), P(A!B), P(!AB), and P(!A!B).

The graphical trick is that we can then take the tree and rearrange it:

              ___A__
      __B____/
     /       \__!A__
____/      
    \         ___A__
     \_!B____/
             \__!A__

The endpoint values remain the same, since P(BA) is the same as P(AB). Which means that we can then fill in P(B), since it's just P(BA) + P(B!A), and then the intermediate branch values, P(A|B) and P(!A|B) are easy, because P(B)*P(A|B) = P(AB), so we just divide P(AB) by P(B) to get P(A|B).

It's just the same as memorizing P(A|B) = P(B|A)P(A)/P(B), but it makes more sense to me because the only things you have to remember is that the endpoint value is the product of the branches leading to it, and that pairs of branches sum to 1, both of which are facts that are obvious (to me) in this context.

I think when Prof. Rota taught it, he used a similar analogy involving spatial areas, and it mostly made sense the first time I learned it, but the part that really clicked with this formulation was realizing that the endpoint probabilities are are always the same, and we can reorder the tree leading up to them however we want. It's just rearranging subsets of outcomes to get the grouping we want, and then it's all algebra.

[melted-snowball.livejournal.com]

OK. I guess I find the Venn diagram way of doing it more natural, since to me it points out that the only difference between P[A|B] and P [B|A] is what the denominator in the conditional formula is, and pretty quickly makes me remember that if A is big and B is small that P [A|B] will be a lot smaller than P [B|A], which is the part in Bayes Rule I always get wrong...

[bikerbearmark.livejournal.com]

Yeah, tell us about your new mental visualization tool! I used to work extensively with Bayesian techniques, and today I work with an entire team of data visualization experts, so your teaser above sounds like it's smack dab in the intersection of two of my professional interests.

[melted-snowball.livejournal.com]

Do you work for the Census, or someone like that?

[bikerbearmark.livejournal.com]

Until Sep last year, I worked in Microsoft's Speech and Natural Language Group, developing human language understanding systems. Since September, I've worked on the IT segment of Gallup's new World Poll project, an economic development and well-being instrument to help leaders of businesses, governments and NGOs understand the living situations, beliefs and opinions of communities world-wide.

And yourself? What fires up your intellectual faculties these days?

[melted-snowball.livejournal.com]

Wow. Both of those sound like terrific projects. (I guess I wasn't too far off with the census...) How much of the resultant data from the Gallup project will I be able to see without paying lots of $$?

I'm a theoretical bioinformaticist; I apply probabilistic techniques to understand biological sequence data, and (more theoretically) to understand why certain analysis techniques work surprisingly well. It's fun work. I'm also on sabbatical right now, missing a Canadian winter, and instead living in northern California.

[dr-tectonic.livejournal.com]

See my reply to melted_snowball!