I found a really interesting "book" that not only helps understand Bayes, but understand Inverse Theory as well.
mesoscopic.mines.edu/~jscales/gp605/snapshot.pdf Ken > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of Giles Bowkett > Sent: Sunday, February 17, 2008 1:17 PM > To: [EMAIL PROTECTED]; The Friday Morning Applied > Complexity Coffee Group > Subject: Re: [FRIAM] Sour's Ear to Silk Purse > > On 2/17/08, Nicholas Thompson <[EMAIL PROTECTED]> wrote: > > Robert, > > > > Thanks for these comments. Are you actually a person who > could make > > me understand Bayes intuitively, a little bit? > > You could have free coffee from me anytime you wanted to try that. > > Here's a basic rundown of Bayes. I am not an expert; this is > more or less as much as I know. I can't collect the free > coffee as I'm in Los Angeles right now, but maybe it'll help. > > Bayes theorem goes like this: > > p(a ^ b) = (p(b ^ a) * p(a)) / p(b) > > where ^ means "given." > > So the probability of A, given B, is equal to (the > probability of A, given B, times the base probability of A > itself) divided by the base probability of B itself. > > > The question was, given a panzy, what is the probability of > > [panzy-blooming April 1 in Santa Fe]. So the data could be > faulted in two different ways. > > Tree-hugger Jones could know know what a panzy is, and > report the blooming > > of a "forget-me-not" on April first; or TJ could he could > have the date > > wrong. Or he could report his geographic coordinates > wrong. The hardest > > of these is the plant identification part, I would think. > > So I don't know if you could actually model this in a Bayesian way. > You are basically modelling cause and effect with Bayes. This > problem with the flower blooming at a particular time in a > particular place is just a combination of probabilities. A > nice canoncial Bayes example is, given that the grass is wet, > what is the probability that it rained last night? > > a = rained last night > b = grass wet > > p(a ^ b) = probability that it rained last night, given that > the grass is wet p(b ^ a) = probability that the grass is > wet, given that it rained last night (100%) > p(a) = base probability of it raining last night > p(b) = base probability of grass being wet > > p(b) will reflect both times when the grass was wet because > it rained and times when the grass was wet because the > automatic sprinklers turned on, or the kids were throwing > water balloons at each other. > p(a) can be high or low depending on the time of year. But > AFAIK you do need to initially collect some data on the > general probability of the grass being wet, given that it > rained last night, to solve the equation at all. That's why > this is a canonical example; it's easy to see that p(b ^ a) > will be about 100%, because lawns generally don't dry out > until the sun comes up. > > So to predict the probability of a particular flower blooming > in a particular place at a particular time, that's > calculating the probability of a coincidence, whereas Bayes > is really all about cause and effect and pattern recognition, > or inference - when X happens, Y often happens too, so since > I know Y obviously happened here, can I say that X must have > happened also? It's basically an equation that can do simple > kinds of detective work. > > For example, I'm working on something I can't necessarily > describe in too much detail, but it's a Web application which > creates probability matrices, such that it will know that if > User X is in Category Y, they probably want to look at item > Z. That's cool because we can say, "hello web site user, you > probably want to see item Z!" and make the text for item Z > bold or bright red so it's easy for them to find it. > But over time, we can not only get these probability matrices > fairly accurate - because you have to acquire a bunch of data > before they become genuinely useful - but we can also collect > the number of times > *anybody* clicked item Z or entered category Y. > > Since we can collect those numbers, we can calculate base > probabilities for category Y and item Z. And since we know > the probability that user X enters category Y looking for > item Z, when somebody enters category Y looking for item Z, > we'll be able to calculate the probability that they're user > X. And that becomes useful if we know other things about user > X - for instance, user X always chooses FedEx for their > shipping method, so if we calculate a high probability that > this user entering Y looking for Z is the user X we already > know about, then we go ahead and make FedEx the first option > in the list of shipping options, and put the link in bold > text and make it bright red just to make life easier for user X. > > Basically, you know if you get coffee at the same place every > time, you don't have to tell them what you want? They see you > come in the door and they start making the one-shot 12oz. soy > latte with cinammon and they ring it up for you without you > having to describe it in detail every time? Bayes' theorem > allows websites to do the same thing, in some cases. > > -- > Giles Bowkett > > Podcast: http://hollywoodgrit.blogspot.com > Blog: http://gilesbowkett.blogspot.com > Portfolio: http://www.gilesgoatboy.org > Tumblelog: http://giles.tumblr.com > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org > ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
