Transcript The Use of Bayesian Statistics in Court

The Use of Bayesian
Statistics in Court
By: Nick Emerick
5/4/11
Bayesian vs. Frequentist
 Where the frequentist estimates what an answer could be
bayesian states the answer is unknown without further
information.
 Bayesians consider probability statements to be a degree of
“personal belief” (prior probability) when not all of the factors
are known.
 Example: 99.5% of faulty computer parts run over 50oF
 A part runs at 55oF, how like is that part to be faulty?
 Frequentist- not enough information
 Bayesian- more accurate prediction with the prior probability
The Formulation of Bayesian
Statistics
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How this Relates to Court
 A determination of guilt
 Can determine, from a juror’s prior probability of a person’s
guilt and evidence probabilities, how guilty a person could be
 Turns preponderance of evidence and beyond a reasonable
doubt to a mathematical problem instead of a personal guess
 R v Adams 1996:
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Victim did not identify Adams,
20 year age gap
Had an alibi that was uncontested
DNA match was 1 in 20 million
Was convicted then appealed
Bayesian Method in R v Adams
 Production of Bayes factors
 It was him, but she could not identify him
 It was not him, but she could not identify him
 Remains convicted
 Problem
 Still relies on person probability statements
 No way of determining evidential Bayes factors… yet
The Research Idea
 To produce a program capable to accurately calculate a
person’s probability of guilt based on evidential Bayes factors
 To graph the progression of the probability of guilt for a visual
reference
 To make a practical program that could be tested in real trials
First Run
Evidence Order:
1) 1.0
2) 0.8
3) 0.6
4) 0.4
5) 0.2
Second Run
Evidence Order:
1) 0.2
2) 0.4
3) 0.6
4) 0.8
5) 1.0
Third Run
Evidence Order:
1) 0.6
2) 0.4
3) 1.0
4) 0.2
5) 0.8
Zero Prior
Evidence Order:
1) 0.99
2) 0.8
3) 0.6
4) 0.4
5) 0.2
Interesting Outcomes
 Order of evidence input can alter the guilt probability
 A prior probability of 0% will remain 0% no matter what the
evidence shows
 Prevents admissibility in court
Conclusion
 The basic algorithm seems to have some challenges
regarding evidence order and zero prior probability. It may
need new parameters or the equation needs to be reworked.
 Legal research needs to be conducted to give better
percentage values to different pieces of evidence. As it
stands now all values are based on personal opinion.
References
 [1998] 1 Cr App R 377, [1997] EWCA Crim 2474
<http://www.bailii.org/ew/cases/EWCA/Crim/1997/2474.html>
 "Bayesian Inference." Wikipedia. Web.
<http://en.wikipedia.org/wiki/Bayesian_inference#In_the_courtro
om>
 Bayesian statistics for dummies. (2005, February 1). Retrieved from
<http://web.vu.union.edu/~coulombj/Articles/SCIENCETECHNOLOGY/Bayesian%20statistics%20for%20dummies/inde
x.html>
 Jordi. (2001, August 22). Bayesian statistics? [Online Forum Comment].
Retrieved from
<http://mathforum.org/library/drmath/view/52221.html>