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Grant




Why I think AE may be an application of Bayes' Theorem to epistemology is that the fundamental Bayes insight is that when assessing evidence you must take into account the chance of seeing that evidence even if your theory is wrong .
Applied to Mick's THBR, we could say that there is indeed evidence that English developed after 1066, but this evidence might exist even if English was much older. The supporters of orthodoxy say "here's some evidence; it's proved; let's move on"
I'm struggling to make this more rigorous. Why don't we all study the best Bayes' introduction on the web and see what we can come up with?
http://yudkowsky.net/rational/bayes






Wile E. Coyote
In: Arizona




I am pretty sure that Bayes won't help yet, with this type of linguistic problem. It's not just a problem of drilling further down. It's not having the stats to start off with.
I could be wrong. I only really got interested in Bayes when considering "evidence" in court cases.
It is now widely used in American political science, for example the better understanding of polls.
http://lesswrong.com/lw/774/a_history_of_bayes_theorem/
The Bayes revolution is underway.






Mick Harper
Site Admin
In: London




I find reading from the screen plus math too taxing for my lickle noggin. Isn't there some nonmathematician waxing lyrical on the screen somewhere?
PS Coyote, were you able to access the Scottish case I gave you? I accept half an hour of your time might be too much. Especially with the Dbacks still in it.






Mick Harper
Site Admin
In: London




The point that arises from the Norris case (and others) is that because the police are not trained in statistics, and certainly not in Bayesian statistics, it follows that they make Bayesian errors. In this case not realising that certain kinds of insulin deaths might be very rare but given the overall numbers of insulin deaths, they must happen reasonably frequently.
Now the muggins who is nursing the patient when it does happen is certain to be suspected of insulin poisoning since the two types of insulininduced death cannot easily be distinguished. At this point no great harm is done because one death can be argued away however much distress is caused to the unfortunate nurse.
What makes Bayesian Police Training urgent is that the police have the powers (and the propensity) to create crimes where none have occurred once they are on the trail of 'a serial killer'. Since Norris, like all nurses, comes into contact with thousands of patients over his career it is simplicity itself to trawl through these 'patientcontacts' and come up with enough suspicious cases to impress Bayesianinnocent judges and juries.
I hope I have got Bayes right and (of course) I am not claiming Norris is innocent.






Grant




The other problem with the police is that they fail to distinguish between reallife probabilities and telly probabilities as in the recent Amanda Knox case.
The scanario was: idiot Italian police find a dead girl in a flat who has been stabbed. Later they arrest a young black man who has a record of breaking and entering armed with a knife. His DNA is inside her and under her body. Now, the dead girl had a flaky but very beautiful middleclass flatmate.
In Real Life
Probability that black man did it alone  99%
Probability that flaky girl was involved  0.001%
On telly
Probability that black man did it alone  1%
Probability that flaky girl was involved  99%






Mick Harper
Site Admin
In: London




Even the 'flakiness' of Ms Knox is at issue. If you assume she is an absolutely normal American teenageratuniversity, all her actions seem normal including for instance being gently hugged by her boyfriend after the crime etc. Italian police seem to have a 'television' view of normal American teenagers.






Grant




The point that arises from the Norris case (and others) is that because the police are not trained in statistics, and certainly not in Bayesian statistics, it follows that they make Bayesian errors. In this case not realising that certain kinds of insulin deaths might be very rare but given the overall numbers of insulin deaths, they must happen reasonably frequently. 
Ever since the Harold Shipman case (for nonBritish readers, he was a doctor who killed 200 of his elderly patients with a quick overdose) doctor's death rates are supposed to be monitored for any excess over the national average.
If this analysis is truly taking place it won't be long before some poor doctor or nurse is pulled up for what is actually a random deviation from the norm. In fact that may have already happened






Wile E. Coyote
In: Arizona




I couldnt watch it last night due to power cut.
Yep I am afraid this an innocent locked up.
Bayes theorum. Another example.






Wile E. Coyote
In: Arizona




Yeah you nailed it Mick.
The programme makers knew their Bayes.
Nasty old business.
You can see exactly why the police thought they had a killer.
It then becomes fairly obvious why he is innocent.
Worrying.
Seems to me that Bayes, if sensibly applied, on a certain type of statistical problem does have some utility.
I keep it at the back of my toolkit...






Mick Harper
Site Admin
In: London




Bayes might be striking again. In the Stockport case of multiple murder by insulin injection, the (female) nurse in the summer was arrested and then freed, and now another (male) one has been arrested and "freed on police bail" ie they know he can't possibly be a multiple murderer.
It looks like no crime was committed in the first place. But it will take forever for the authorities to admit this since they have the whole country in an uproar.






Wile E. Coyote
In: Arizona




This is a bi product of NHS efficiency drives.
Hospital administrators use stats to improve efficiency, eg measure death rates of patients undergoing certain procedures.
So we can expect a few more of these.






Mick Harper
Site Admin
In: London




This is most interesting. The whole use of league tables in public administration is a very new and a very radical departure which must set in train a whole manner of unintended consequences. My first thought is that, re Bayes (even though I do not claim to really understand this), a new statistical layer of 'proof' will be added.
Though I agree that the main danger comes from there being now a mechanism that will, as it were, lead people by the nose to an 'injustice'. Presently I presume that it takes a really freakish cluster to lead to the identification of a 'crime' but if we have amateur statisticians coming up with (as they do presently to monitor surgeons' skills) merely normal fluctuations or even 'hard cases' as a reason for suspicion, we are as you say in for some exciting times.






Brian Ambrose




re. Bayes
Here's a story problem about a situation that doctors often encounter:
1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
What do you think the answer is? If you haven't encountered this kind of problem before, please take a moment to come up with your own answer before continuing. 
See http://yudkowsky.net/rational/bayes for the answer and a reasonably comprehensible explanation of Bayes theorem






Wile E. Coyote
In: Arizona






N R Scott
In: Middlesbrough




I recently tried to use Bayes to win some money during the World Cup. At the start of the second round there was a competition where you had to guess which of the remaining 16 teams would win the tournament. The people that guessed the correct team would then be put into a prize draw to win a cash prize.
I surmised I'd have a better chance of winning if I picked one of the less likely teams.
For example, say 10,000 people entered the competition and 40% of those guessed that Brazil would win (at that point they were favourites!). If I guessed Brazil, I'd have a good chance of being correct, but I'd end up in a prize draw with 40% of the 10,000 entrants  a 1 in 4000 chance of winning.
So I picked Mexico, thinking "Okay, I'll have little chance of being right, but if I am I'll be in a draw with the 2% that guessed Mexico"  a 1 in 200 chance.
In hindsight though I shoulda just gone with the Germans.






