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| peter zohrab... |
 Posted: Tue Nov 10, 2009 3:48 pm |
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The New Scientist magazine recently ran an article on statistics in
law cases, in which Bayes' Theorem was mentioned.
See http://en.wikipedia.org/wiki/Bayes'_theorem if you don't know what
that is.
I wrote the following letter to the New Scientist, which hasn't been
published so far, so I'm posting it here:
Bayes' Theorem is impressive. However, its application to criminal
cases is
crippled at both the input and output stages.
It requires a juror to have formulated a percentage which expresses
that
juror's preliminary belief as to the degree of certainty that the
accused is
innocent. However, in the absence of evidence to the contrary, there
is a
priori no reason to think that jurors do or can convert their feelings
about
the innocence of the accused accurately and meaningfully into a
percentage.
At the output stage, how do you convert a probability figure of 0.13
into a
juror's verdict? The juror has to be certain of guilt "beyond
reasonable
doubt." Unless a "reasonable doubt" can be given a precise
percentage
value, the output of Bayes' Theorem has no practical application to
the
criminal trial. Moreover, it is arguable that the word "reasonable"
refers
not to a particular percentage of doubt, but to the mental process
used to
arrive at the doubt. In other words, is the juror using reason to
arrive at
the doubt that acquits the accused -- not has the juror got the
required
percentage of doubt.
Peter Douglas Zohrab |
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| aruzinsky... |
| Posted: Wed Nov 11, 2009 7:08 am |
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On Nov 10, 7:48 pm, peter zohrab <pe... at (no spam) zohrab.name> wrote:
[quote]The New Scientist magazine recently ran an article on statistics in
law cases, in which Bayes' Theorem was mentioned.
Seehttp://en.wikipedia.org/wiki/Bayes'_theoremif you don't know what
that is.
I wrote the following letter to the New Scientist, which hasn't been
published so far, so I'm posting it here:
Bayes' Theorem is impressive. However, its application to criminal
cases is
crippled at both the input and output stages.
It requires a juror to have formulated a percentage which expresses
that
juror's preliminary belief as to the degree of certainty that the
accused is
innocent. However, in the absence of evidence to the contrary, there
is a
priori no reason to think that jurors do or can convert their feelings
about
the innocence of the accused accurately and meaningfully into a
percentage.
At the output stage, how do you convert a probability figure of 0.13
into a
juror's verdict? The juror has to be certain of guilt "beyond
reasonable
doubt." Unless a "reasonable doubt" can be given a precise
percentage
value, the output of Bayes' Theorem has no practical application to
the
criminal trial. Moreover, it is arguable that the word "reasonable"
refers
not to a particular percentage of doubt, but to the mental process
used to
arrive at the doubt. In other words, is the juror using reason to
arrive at
the doubt that acquits the accused -- not has the juror got the
required
percentage of doubt.
Peter Douglas Zohrab
[/quote]
See http://groups.google.com/group/sci.stat.math/browse_thread/thread/bbd7ef1ccdfa8109/b82c4933ba671767#b82c4933ba671767
As a judge or juror, I would use informal statistical decision theory
which is based on costs. For example, I would convict someone with
less evidence if they were accused of plotting to blow up the World
than I would if they were accused of jaywalking. |
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| Rich Ulrich... |
| Posted: Wed Nov 11, 2009 3:59 pm |
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On Tue, 10 Nov 2009 17:48:33 -0800 (PST), peter zohrab
<peter at (no spam) zohrab.name> wrote:
[quote]The New Scientist magazine recently ran an article on statistics in
law cases, in which Bayes' Theorem was mentioned.
See http://en.wikipedia.org/wiki/Bayes'_theorem if you don't know what
that is.
I wrote the following letter to the New Scientist, which hasn't been
published so far, so I'm posting it here:
Bayes' Theorem is impressive. However, its application to criminal
cases is
crippled at both the input and output stages.
[/quote]
I have not seen the New Scientist article, but I expect that
you have thoroughly missed the gist of the message.
I have seen several articles and arguments that invoke
Bayes' Theorem and courts.
Maybe there is a point, that juries are too often lousy
at judgements. More often, the main point is that "we the
readers" are assuredly guilty of bad judgements, at times,
if we never consider Prior probabilities. Actual court cases
serve as especially poignant examples. - Is there a particular
current case that serves as a "judicial atrocity"?
The (probable) purpose of the article is to teach us, the
readers, a "tactic" for acting more intelligently, if we
have not considered those problems before. And many people
have not.
We are a long way from replacing courts with computerized,
intelligent-agent systems, so I think that your concerns
about converting probabilities into court judgements of guilt
is premature.
[snip, details]
--
Rich Ulrich |
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