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Re: Will Armstrong confess??

Posted: Thu Jan 31, 2013 9:40 am
by basilic
ok, I do not see major disagreement, except details.

1. when the topic is not emotional, it's not a matter of shutting out evidence that does not agree with your beliefs; you can accept it and still maintain your belief. Look at the matter of negative tests by Armstrong. Based on circumstantial evidence (the pattern of riding, rumors in l'Equipe, the andreu testimony) you could have formed a 95% certainty that LA doped even in the early 2000s. Now you are told that LA has tested negative. Let's say the test is negative in 99% of clean riders, and positive in maybe 10% of (careful) riders who dope. Applying the Bayes theorem, you should still be 90% sure that LA dopes, even accounting for the negative. (and I'm not bringing in the manipulation of the testing system)

2. you seem to only trust a probability statement based on a statistical analysis (eg frequency of disease). So you are a frequentist. But others accept subjective probabilities (the bayesians). In the case of LA above, you do not have 1000 LA clones to base your beliefs on, you have to make a subjective assessment.

Re: Will Armstrong confess??

Posted: Thu Jan 31, 2013 5:24 pm
by swinter
but Bayesians don't know anything about cognition. belief is not a product of statistical probability.

Re: Will Armstrong confess??

Posted: Thu Jan 31, 2013 5:24 pm
by Weenie

Re: Will Armstrong confess??

Posted: Thu Jan 31, 2013 5:50 pm
by djconnel
basilic wrote:ok, I do not see major disagreement, except details.

1. when the topic is not emotional, it's not a matter of shutting out evidence that does not agree with your beliefs; you can accept it and still maintain your belief. Look at the matter of negative tests by Armstrong. Based on circumstantial evidence (the pattern of riding, rumors in l'Equipe, the andreu testimony) you could have formed a 95% certainty that LA doped even in the early 2000s. Now you are told that LA has tested negative. Let's say the test is negative in 99% of clean riders, and positive in maybe 10% of (careful) riders who dope. Applying the Bayes theorem, you should still be 90% sure that LA dopes, even accounting for the negative. (and I'm not bringing in the manipulation of the testing system)

2. you seem to only trust a probability statement based on a statistical analysis (eg frequency of disease). So you are a frequentist. But others accept subjective probabilities (the bayesians). In the case of LA above, you do not have 1000 LA clones to base your beliefs on, you have to make a subjective assessment.


Excellent analysis. But I suspect an error.

Simplifying down for my own benefit:

before test results:
95% chance: Armstrong doped
5% chance: Armstrong clean

Additional information: Armstrong tested negative

Chances of various results before knowing test results:

(95% Armstrong doped) (10% testing negative if doped) = 9.5%
(95% Armstrong doped) (90% testing positive if doped) = 85.5%
(5% Armstrong clean) (99% testing negative if clean) = 4.95%
(5% Armstrong clean) (1% testing positive if clean) = 0.05%

These sum to 100%. But I now know the test results. I thus care only about the negative probabilities:

(95% Armstrong doped) (10% testing negative if doped) = 9.5%
(5% Armstrong clean) (99% testing negative if clean) = 4.95%

I thus get a revised 65.7% chance that Armstrong doped.

Re: Will Armstrong confess??

Posted: Thu Jan 31, 2013 6:41 pm
by HammerTime2
If you are Bayesian, and believe basilic's data, and don''t make a calculation error, then the probability that Armstrong doped, given the negative doping test result, is 94.53% .

P(A|B) denotes probability of A given B.

The calculation is:
P(doped|negative test result)=
P(negative test result|doped)*P(prior belief he doped)/{P(negative test result|doped)*P(prior belief he doped)+P(negative test result|didn't dope)*P(prior belief not doped)}
= 0.9*0.95/{0.9*0.95+0.99*0.05}=0.9453=94.53% .


Optional Bonus Reading:
If you keep everything as is, but vary just P(negative test result|doped), then the resulting P(doped|negative test result) varies over the possible range of a low of 94.48% when P(negative test result|doped) = 100%, to a high of 100% when P(negative test result|doped) = 0% .

Re: Will Armstrong confess??

Posted: Thu Jan 31, 2013 8:24 pm
by HillRPete
That's all very cool and interesting, but he interviewed with cyclingnews now, I think we can close this book :mrgreen:

Re: Will Armstrong confess??

Posted: Thu Jan 31, 2013 9:12 pm
by basilic
HT2 wins - and guys, you are all too nice to indulge me in this probabilistic stuff.
To revise beliefs in light of evidence, the Bayes theorem says this (and the theorem is true regardless of beliefs, even non-bayesians agree):
posterior odds = likelihood ratio * prior odds
So prior odds of doping = 0.95/0.05 = 19
Likelihood ratio of a negative test = 0.90/0.99 = 0.91
posterior odds= 17.3
posterior probability = odds/(1+odds) = 0.9453
(so I was wrong doing it without a calculator previously)

Now this says what a rational person would/should think, not how people actually think. I think this was swinter's point, fair enough.

But I think the point is evidence alone is not the final answer. When evidence is weak (such as a negative test), not changing you belief is quite correct. When evidence is stronger (such as a positive test, which in my example would have a LR of 0.10/0.01, or 10), it really depends where you start from.

Re: Will Armstrong confess??

Posted: Thu Jan 31, 2013 10:42 pm
by HillRPete
basilic wrote:But I think the point is evidence alone is not the final answer. When evidence is weak (such as a negative test), not changing you belief is quite correct. When evidence is stronger (such as a positive test, which in my example would have a LR of 0.10/0.01, or 10), it really depends where you start from.

Evidence belongs to the real world. Belief to the internet. Better not mix them.

Re: Will Armstrong confess??

Posted: Fri Feb 01, 2013 2:37 pm
by HammerTime2
In "PRO" Cycling Discussion, ultyguy wrote:McQuaid calling in his IOC buddies for help against WADA.

http://www.cyclingnews.com/news/mcquaid-writes-to-ioc-members-for-support-after-spat-with-wada

I'm going to call on the rest of you corrupt bastards to help this corrupt bastard fend off WADA, ok?

Here is the UCI Press Release with referenced emails linked: Press release: UCI releases Fahey letters in response to WADA’s ‘blatant and aggressive’ untruths

Re: Will Armstrong confess??

Posted: Fri Feb 01, 2013 10:55 pm
by stella-azzurra
Right now Landis has a shot at riding pro

Re: Will Armstrong confess??

Posted: Fri Feb 01, 2013 11:45 pm
by prendrefeu
I think it is perfectly fine to have a difference of opinion, if not altogether welcome.
However, that being said, I believe it is helpful to all participating that should a person carry a difference of opinion or perspective, they will also do their part by not reiterating a prior point of discussion in the same topic/thread that has already been covered ad nausea. Even if that conversation was not completely concluded, that it has been discussed to a point of circularity or impass means that it should be avoided in the current topic/thread/discussion in the future. Should a considerable amount of time pass, or the thread be covering an entirely new subject, then it is fine to bring in past arguments from a prior subject/topic to the current one.
Bringing a new thought or new perspective to the conversation is welcome.

Let's not regurgitate what has already been passed through our bowels.

Re: Will Armstrong confess??

Posted: Sat Feb 02, 2013 9:40 am
by Tinea Pedis
What a piece.

Bill normally grates a little too much, but this is stunning.

http://www.grantland.com/story/_/id/890 ... d-question

Re: Will Armstrong confess??

Posted: Sat Feb 02, 2013 2:16 pm
by djconnel
Okay -- my math was correct, my reading was not. I thought you'd written a doped rider had a 10% chance of being negative. You'd actually written a 10% chance of being positive. Since it was many tests over which Armstrong was negative, 10% chance for accumulated positive may be realistic, but still seems a stretch. But then that's where UCI cooperation comes in.

Re: Will Armstrong confess??

Posted: Sun Feb 03, 2013 12:34 am
by swinter
In case people missed the Rasmussen press conference.

http://uk.eurosport.yahoo.com/blogs/blazin-saddles/rasmussen-blows-whistle-decade-dope-135249891.html

Guess what? He was never in Mexico.

Re: Will Armstrong confess??

Posted: Sun Feb 03, 2013 1:51 am
by stella-azzurra
Old news about Rasmussen. Davide Cassani had seen him in Italy (having an affair?) when he said he was in Mexico.

Re: Will Armstrong confess??

Posted: Sun Feb 03, 2013 1:51 am
by Weenie

Re: Will Armstrong confess??

Posted: Sun Feb 03, 2013 2:00 am
by swinter
of course it's old news. (apparently, sarcasm and irony don't read well on the web.)

the point was that he came clean and did so with the Danish cycling authorities and in a news conference and not on Oprah.

note the comment toward the end of the story about Contador and Saxo Bank.