Forensic inference and statistics for the evaluation and interpretation of evidence

Evidence in a criminal investigation and trial should be evaluated and interpreted in the best manner possible. An excellent, and widely supported, approach to evaluation is one - by nature probabilistic - based on the likelihood ratio, the ratio of the probability of the evidence if a certain (set of) proposition(s) (e.g., prosecution) is assumed true to the probability of the evidence if a contrasting (set of) proposition(s) (e.g., defence) is assumed true. The justification for this approach is given together with a note of the benefits arising from the use of this ratio. There is a discussion about the meaning of probability as a measure of belief, the use of numerical assignments and verbal expressions and the use of the likelihood ratio for interpretation. It is explained how beliefs can be updated in the light of new evidence, how multiple pieces of evidence may be evaluated with the use of graphical structures and how uncertainty associated with the numerical evaluation, which is probabilistic, may be handled. A procedure for judgement of the quality of the mathematical formulae used in the calculation of the likelihood ratio is outlined. A conclusion gives three important principles that an expert, and a forensic scientist in particular, should follow when trying to understand the importance of evidence.