mfb comments on The Bias You Didn't Expect - Less Wrong

92 Post author: Psychohistorian 14 April 2011 04:20PM

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Comment author: mfb 12 October 2012 07:09:26PM 2 points [-]

brazil84 stated that there are just two options, so let's stick to that example first.

"[rifle] no bullet will be find in or around the person's body 0.01% of the time" is contradictory evidence against the rifle (and for the handgun). But "[handgun] no bullet will be find in or around the person's body 0.001% of the time" is even stronger evidence against the handgun (and for the rifle). In total, we have some evidence for the rifle.

Now let's add a .001%-probability that it was not a gunshot wound - in this case, the probability to find no bullet is (close to) 100%. Rifle gets an initial probability of 60% and handgun gets 40% (+ rounding error).

So let's update: No gunshot: 0.001 -> 0.001 Rifle: 60 -> 0.006 Handgun: 40 -> 0.0004

Of course, the probability that one of those 3 happened has to be 1 (counting all guns as "handgun" or "rifle"), so let's convert that back to probabilities: 0.001+0.006+0.0004 = 0.0074 No gunshot: 0.001/0.0074=13.5% Rifle: 0.006/0.0074=81.1% Handgun: 0.0004/0.0074=5.4%

The rifle and handgun numbers increased the probability of a rifle shot, as the probability for "no gunshot" was very small. All numbers are our estimates, of course.