Bayesian adaptive approach to estimating sample sizes for seizures of illicit drugs

A considerable amount of discussion can be found in the forensics literature about the issue of using statistical sampling to obtain for chemical analyses an appropriate subset of units from a police seizure suspected to contain illicit material. Use of the Bayesian paradigm has been suggested as the most suitable statistical approach to solving the question of how large a sample needs to be to ensure legally and practically acceptable purposes. Here, we introduce a hypergeometric sampling model combined with a specific prior distribution for the homogeneity of the seizure, where a parameter for the analyst's expectation of homogeneity (α) is included. Our results show how an adaptive approach to sampling can minimize the practical efforts needed in the laboratory analyses, as the model allows the scientist to decide sequentially how to proceed, while maintaining a sufficiently high confidence in the conclusions.