# Can you do probabilities backwards?

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• #2841
Katie Metzler
Participant

http://www.buzzfeed.com/cityofglass/what-are-the-odds-that-exist-as-you-today-4eor

Lots of people like this sort of thing, but is it ‘Bad Science’, or at least bad maths?

#2847
Jeremy Miles
Participant

Bad science, not bad maths, but bad application of maths. Before the event, the chances of anything happening are pretty close to zero.  How often would you have to play a game of snakes and ladders, before you repeated the same game? On the other hand, the probability that you do exist is 1.00. Because you exist.

#2846
Ron Melchers
Member

Silly fun!  But there are lots of practical applications of what is called “conditional probabilities”. Not the least of these is in the area of intelligence analysis. The applications flowing from the Bayesian theorem is also one of the most complex least understood areas of math.  It’s not that the actual operations are that difficult. You can see how these calculations are performed at http://mathworld.wolfram.com/ConditionalProbability.html  But where everything always starts to fall down is in the inevitably imperfect knowledge available on both rates of occurrence of events in a sequence and the full range of possible sequences following any event.  One often winds up with a perilous string of what are basically just assumptions.

#2845
Katie Metzler
Participant

Thanks Ron, I hadn’t seen that site before, it’s good to link to!

#2844
Ron Melchers
Member

Thank you!  The shoe-print case is very interesting.  I am impressed by the judge’s sound judgment.  It does all come down to how good the assumptions of paths of conditions and base rate information are.  The other problem the judge seemed to grasp well is that error rates multiply in conditional probabilities, so that even a seemingly small error rate of 10% at each step (0.9 * 0.9 * 0.9 …) will quickly lead to sky-high) likelihoods of false positive predictions.  Worse yet, in most such evidence error rates are unknown. On your initial question about “postdiction” vs prediction have a look at:

Deborah Davis and William C. Follette, “Rethinking the Probative Value of Evidence: Base Rates, Intuitive Profiling, and the “Postdiction” of Behavior” Law and Human Behavior, Vol. 26, No. 2, April 2002 (2002)

The following book, with a chpter on conditional probabilities, is written in simple layman’s language.  It was written for lawyers 😉  Philip Good, “Applying Statistics in the Courtroom: A New Approach for Attorneys and Expert Witnesses”, Chapman and Hall/CRC 2001

#2843
Katie Metzler
Participant

Nothing like a stats joke to get you through a Thursday afternoon!

#2842