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Law, Probability and Risk Advance Access originally published online on December 14, 2007
Law, Probability and Risk 2008 7(1):35-60; doi:10.1093/lpr/mgm041
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© The Author [2007]. Published by Oxford University Press. All rights reserved.

Analysis of sampling issues using Bayesian networks

A. Biedermann{dagger} and F. Taroni{ddagger}

Ecole des Sciences Criminelles, Institut de Police Scientifique, The University of Lausanne, le Batochime, 1015 Lausanne-Dorigny, Switzerland

S. Bozza§

Department of Statistics, University Ca' Foscari, 30121 Venice, Italy

C. G. G. Aitken

School of Mathematics, The University of Edinburgh, The King's Buildings, Edinburgh EH9 3JZ, UK

{dagger} Corresponding author. Email: alex.biedermann{at}unil.ch

{ddagger} Email: franco.taroni{at}unil.ch

§ Email: silvia.bozza{at}unive.it

Email: c.g.g.aitken{at}ed.ac.uk

Received on 19 January 2007. Revised on 19 September 2007. Accepted on 20 September 2007.


  Abstract

This paper addresses the implementation of Bayesian sampling methodology in a graphical probability environment, i.e. Bayesian networks (BNs). An architecture of BNs which is able to be used for sampling from small and large consignments is outlined in detail. Through direct interaction with their users, the proposed models provide a framework that is capable of dealing with several distinct sampling issues, such as (i) the calculation of posterior probability distributions for the proportion of ‘positives’ (i.e. discrete units with a characteristic of interest) in a consignment as well as for the number of positives among a consignment's uninspected items, (ii) case preassessment and (iii) likelihood-ratio evaluation. A discussion is included on features of the proposed models that allow one to account for further complications such as competing prior beliefs about the proportion of positives in a consignment and potentially misclassified data (e.g. positive testing results obtained from units that are actually negative).

Keywords: sampling; forensic science; Bayesian networks; likelihood ratio; Bayes'; theorem; preassessment; evidence evaluation


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