Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science, 2nd Edition

5.1.8 Increasing the level of detail of selected propositions

The development of more elaborate Bayesian networks is of interest for two main reasons. A first reason is to enable the solution of an intrinsic complication related to entries of conditional probability tables, notably the so-called composite probabilities (e.g. or ). Second, one may wish to expand a particular node in order to take into account additional information related to the node of interest.

To deal with the particular issue of composite probabilities at the node Y, for example, an additional variable may be introduced in order to account for the fact that the scientist may observe y even if no transfer occurred, that is T₀ was true. One thus needs to inquire about circumstances under which this may be the case. One obvious possibility is that a group of fibres described as y was present on the receptor before the event of interest (proposition ) occurred. Call this event B, short for ‘background’. It can be introduced in a network in terms of a root node B with a direct influence on Y. The states of this variable are and B with (unconditional) probabilities b₀ and , representing, respectively, the probabilities ...