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Jury size and composition - a predictive approach
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In this article, the authors consider two basic aspects of juries that must decide on guilt verdicts and their composition in situations where society consists of sub-populations, using a lower probability of a guilty verdict naturally provides a "benefit of doubt to the defendant" robustness of the inference.Abstract:
We consider two basic aspects of juries that must decide on guilt verdicts, namely the size of juries and their composition in situations where society consists of sub-populations. We refer to the actual jury that needs to provide a verdict as the ‘first jury’, and as their judgement should reflect that of society, we consider an imaginary ‘second jury’ to represent society. The focus is mostly on a lower probability of a guilty verdict by the second jury, conditional on a guilty verdict by the first jury, under suitable exchangeability assumptions between this second jury and the first jury. Using a lower probability of a guilty verdict naturally provides a ‘benefit of doubt to the defendant’ robustness of the inference. By use of a predictive approach, no assumptions on the guilt of a defendant are required, which distinguishes this approach from those presented before. The statistical inferences used in this paper are relatively straightforward, as only cases are considered where the lower probabilities according to Coolen’s Nonparametric Predictive Inference for Bernoulli random quantities [5] and Walley’s Imprecise Beta Model [24, 25] coincide.read more
Citations
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An essay towards solving a problem in the doctrine of chances. [Facsimil]
TL;DR: The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon it’s 2 happening.
Journal ArticleDOI
Bayes theory: Hartigan, Springer-Verlag, New York 1983, p. 145, DM 46,-
TL;DR: The theory of Bayesian inference at a rather sophisticated mathematical level is discussed in this paper, which is based on lectures given to students who already have had a course in measure-theoretic probability and has the rather clipped style of notes.
Inferences from multinomial data: Learning about a bag of marbles - Discussion
Anthony O'Hagan,C.A.B. Smith,Christopher Jennison,George A. Barnard,A.N. Bisson,N. Wilson,C. Palmer,David Spiegelhalter,Nicky Best,A. P. Dawid,C.J. Geyer,M. Aitkin,Bartlett,Philip J. Brown,Chris Chatfield,Frank P. A. Coolen,David Cox,Seymour Geisser,M. Golstein,Irving John Good,Frank R. Hampel,Jane L. Hutton,H.E. Kyburg,I. Levi,Dennis V. Lindley,Luis R. Pericchi,R. Rotondi,Teddy Seidenfeld,Larry Wasserman,Stephen G. Walker +29 more
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Statistical Science in the Courtroom
TL;DR: Gastwirth et al. as mentioned in this paper present a survey of the state of the art in statistical science in the course of the COURTROOM, focusing on the following topics:
References
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Journal ArticleDOI
On Nonparametric Predictive Inference and Objective Bayesianism
TL;DR: An overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A(n) and uses interval probability to quantify uncertainty, and a discussion of NPI and objective Bayesianism.
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Low structure imprecise predictive inference for Bayes' problem
TL;DR: In this article, the authors present direct conditional imprecise probabilities for the number of successes in a finite number of future trials, given information about a limited number of past trials.
Journal ArticleDOI
Bayes theory: Hartigan, Springer-Verlag, New York 1983, p. 145, DM 46,-
TL;DR: The theory of Bayesian inference at a rather sophisticated mathematical level is discussed in this paper, which is based on lectures given to students who already have had a course in measure-theoretic probability and has the rather clipped style of notes.
Journal ArticleDOI
A Study of Poisson's Models for Jury Verdicts in Criminal and Civil Trials
Alan E. Gelfand,Herbert Solomon +1 more
TL;DR: In this article, an exposition of models provided by Poisson to account for actual jury decisions in criminal and civil trials in France in the first half of the 19th century is given.