# The Use of Bayesian Statistics in Court By: Nick Emerick 5/4/11.

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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 50 o F A part runs at 55 o F, 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

How this Relates to Court A determination of guilt Can determine, from a jurors prior probability of a persons 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: 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 persons 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 "Bayesian Inference." Wikipedia. Web. Bayesian statistics for dummies. (2005, February 1). Retrieved from Jordi. (2001, August 22). Bayesian statistics? [Online Forum Comment]. Retrieved from

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