Analysis of sampling issues using Bayesian networks
Alex Biedermann, Franco Taroni, Silvia Bozza, Colin G. G. Aitken · Law Probability and Risk · 2007
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).