Conditional Dependence in Microbial Forensic Assays - A Primer
This report provides an introduction to the topic of conditional dependence in the context of microbial forensic assays. Conditional dependence between two items of evidence E1 and E2 occurs when they are both used to support a hypothesis, but E1 affects the probability of E2 and vice versa. Ignoring this dependence can lead to very large errors in estimating the diagnosticity of the combined evidence. To introduce readers to this concept, a number of definitions of conditional dependence that have been used by authors in the past have been collected together and compared. Formal mathematical relationships that constrain conditional dependence are summarized. There are several specific scenarios in which unrecognized conditional dependence can arise in microbial forensic contexts. This report provides some notional examples that illustrate dramatic effects of conditional dependence on the weight of microbial forensic evidence, and discusses the relevance of these observations for the validation of microbial forensic assays. A two-parameter model that describes the transition between various limiting forms of conditional dependence relations is provided in an appendix.