[FRIAM] Sour's Ear to Silk Purse

[Ken Lloyd]

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: friam-bounces at redfish.com 
> [mailto:friam-bounces at redfish.com] On Behalf Of Giles Bowkett
> Sent: Sunday, February 17, 2008 1:17 PM
> To: nickthompson at earthlink.net; The Friday Morning Applied 
> Complexity Coffee Group
> Subject: Re: [FRIAM] Sour's Ear to Silk Purse
> 
> On 2/17/08, Nicholas Thompson <nickthompson at earthlink.net> 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
> 
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