Re: "Statistically demonstrable"

strgh_at_primrose.csv.warwick.ac.uk
Date: 07/07/04 

Date: Wed, 7 Jul 2004 08:17:06 +0000 (UTC)

Every proposed measure of statistical evidence has dangers,
especially when interpreted by lawyers or laymen. The very word
'demonstrable' has resonances of 'QED' following a formal proof.
Similarly the word 'likelihood' suggests probability, rather than
a measure of compatibility between a point in the sample space
and a point in the parameter space; i.e. in practice between
inevitably messy+biased data and an inevitably simplistic model.

I'd be grateful for comments on the following stark example,
which I throw out to 2nd year students in the hope that
they will discuss (over late-night coffee or whatever)
the need for common sense and/or priors when using likelihood.
Sorry for the \TeX-speak.

%------------------------- begin{example} -------------------------
\emph{Light relief}:
Discuss the following possible defence submission at a murder trial:

`The supposed DNA match placing the defendant
at the scene of the crime would have arisen
with even higher probability if the defendant
had a secret identical twin \\
{}[the more people with that DNA,
the more chances of getting a match at the crime scene].

`Now assume that my client has been cloned $\theta$ times,
$\theta\in\{0,1,\dots,n\}$ for some $n>0$.
Clearly the larger the value of $\theta$,
the higher the probability of obtaining the observed DNA results \\
{}[every increase in $\theta$ means another clone who might have
been at the scene of the crime].

`Therefore the m.l.e.\ of $\theta$ is $n$.

`But then, even assuming somebody with my client's DNA committed
this terrible crime, the probability that it was my client is only
$1/(n+1)$ (under reasonable assumptions).

`Therefore you cannot say that my client is,
beyond a reasonable doubt, guilty.

`The defence rests.'
%-------------------------- end{example} -------------------------- 

-- 
J.E.H.Shaw   [Ewart Shaw]      strgh@uk.ac.warwick    TEL: +44 2476 523069
  Department of Statistics,  University of Warwick,  Coventry CV4 7AL,  UK
  http://www.warwick.ac.uk/statsdept            http://www.ewartshaw.co.uk
3  ((4&({*.(=+/))++/=3:)@([:,/0&,^:(i.3)@|:"2^:2))&.>@]^:(i.@[)  <#:3 6 2

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