Sensitivity of inferences in forensic genetics to assumptions about founding genes

Bayesian networks, with inferences computed by probability propagation methods, offer an appealing practical modelling framework for structured systems involving discrete variables in numerous domains, including forensic genetics. However, when standard assumptions are violated -- for example when allele frequencies are unknown, there is identity by descent or the population is heterogeneous, dependence is generated among founding genes, that makes exact calculation of conditional probabilities by propagation methods less straightforward. Here we illustrate different methodologies for dealing with these problems by assessing sensitivity to assumptions about founders in forensic genetics problems. These methods include constrained steepest descent, linear fractional programming and representing dependence by structure. We illustrate these methodologies on several real casework forensic genetics examples comprising criminal identification, simple and complex disputed paternity and DNA mixtures.