5.13 Parallel evidence schemes
Another type of evidence scheme is shown in the graphical model of Figure 5.4 below (Koeijer et al. 2020).Figure 5.4: An example of a parallel evidence scheme in a graphical model. Item 1 and 2 from the chain of evidence only depend on each other through the activity and suspect.
The evidence scheme in Figure 5.4 represents a so-called parallel evidence scheme (Koeijer et al. 2020). This is due to the two (or more) chains of evidence running in parallel to each other.
In contrast to a serial evidence scheme, a parallel evidence scheme contains chains of evidence that do not depend upon each other. For example, in Figure 5.4 it is possible to remove the chain from either Item 1 or Item 2 and still maintain a link between the suspect and the activity through the item that was not removed. This means that the logical sequence between the suspect and the activity involving item 1 does not depend upon Item 2. This type of relationship can be modelled in probability terms as a conditional independence, where the conditioning information is the proposition involving the activity and other case circumstances. As we saw in Section 3.7, this simplifies joint probability calculations. This means that it also simplifies the LR calculations. In fact, LRs for conditionally independent parallel evidence chains can be combined by simple multiplication. In Figure 5.4, this means that the LR for the \(E_1\), \(E_2\) evidence chain can be multiplied by the LR for the \(E_3\), \(E_4\) evidence chain.
Statistical independence leads to convenient probability and LR calculations. However, when this assumption is incorrect then it leads to inaccurate probability and LR values and therefore to potentially misleading conclusions. For this reason, assumptions of statistical independence should be justified whenever they are made. Data sources, such as scientific experiments can be used to establish whether two events are (conditionally) statistically independent. Data sources that can help scientists to determine statistical independence between evidence types are limited in the scientific literature at this time.
Many case circumstances are more complicated than either of the simple diagrams in Figures 5.3 and 5.4 and they often require a mixture of the two approaches. This means that often in practice Bayesian Networks are required.