FOM: Re: A problem in Foundations of Statistics

Dean Buckner Dean.Buckner at
Sat Apr 20 08:03:46 EDT 2002

Re Shipman's problem.

I'm not sure I understand it.  If I know for a fact that there is a bag
containing two red balls and one white, then I can calculate for a certainty
the probability of drawing 2 reds and then a white (assuming I replace ball
after each trial & don't look).

But is the problem that we don't know the number of balls in the bag?

If so, it's an interesting problem in the area I work (risk management).  In
real life we aren't given the probability of anything, we have to work it
out or estimate it somehow from a finite (usually quite small) number of
samples.  You just can't tell from a small sample whether you got a bunch of
outliers, or not.

In my work I look at models that try and estimate the probability of events,
when that probability is constantly changing.  One thing I found is that
when the model is particularly bad at estimating probability, then the
probability of an accident is itself increased.  For example, if you know
the probability of rain is high, you stay indoors.  If you don't, you go out
and (probably) get wet.

This has an application in public policy.  Risk managers used to try and
remove risks.  For example, they would try and straighten roads to stop
people going too fast round the bends.  But then people would just drive
faster and still have as many accidents.  What policy makers should be doing
is giving people better information so they can calculate risks better, so
they know how many balls in the bag.  This hasn't always filtered through.
For example in my area they have increased the time of the "don't walk"
phase at pedestrian crossings, to stop people crossing at "dangerous" times.
Unfortunately people know this, they know the information is unreliable, and
just cross at any time, thus increasing the risk of accidents.

There was a very good book written about this (about 1996) called "Risk".  I
can't remember the author, can find out if anyone interested.

In Naples, they don't have have traffic light phasing at all, they just go
straight from red to green and back.  Of course they have a huge number of
accidents there, but that's because they drive through whether it's red or
green, they ignore the information altogether.

But maybe I have misunderstood the problem?  If not, would be interested in
how to solve it.  There are many heuristic approaches, but I have never seen
fully worked out account.

Dean Buckner
4 Spencer Walk
London, SW15 1PL

Work 020 7676 1750 (Risk Review Department, FSA)
Home 020 8788 4273

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