To evaluate evidence appropriately, you need to compare probabilities of the evidence under two different propositions. These propositions are usually those put forward by the prosecution and the defence. There are advanced statistical methods for doing this (for readers who are technically inclined, they are based on likelihood ratios or Bayes’ factors). Much theoretical work has been done in the development of these methods. Calculations based on them might sometimes be fairly straightforward, though it also often turns out that there are non-standard issues to consider.
One example of casework that a forensic statistician may be involved with is DNA profiling, which is a powerful method of identification using genetics. Often, the evidence to be evaluated involves human (or sometimes animal) biological material such as blood, semen or vaginal fluid. Considerable work has been done in statistical and population genetics in assessing the importance of such evidence. Applications, however, are often not restricted to simple cases with one sample of DNA left at the scene of a crime and one suspect. Complications very often arise, for example because relatives may be involved, or the suspect may have been identified by a search through a DNA profile database, or the sample found at the crime scene may be a mixture of body fluids from more than one person. More advanced statistical methods are required in such situations.
Another role of a forensic statistician relates to sampling problems and determination of sample size. In some cases, it is necessary to examine a consignment of similar-looking items, and it is often not practical to examine every item. This may be purely on financial grounds but may be on health grounds also. The question then arises as to how many items should be examined on a sampling basis. For example, the consignment to be examined may be a set of CDs, some of which are thought to contain pornographic material. Then it is desirable for the examining officers to examine as few CDs as is commensurate with a good description of the proportion of the CDs which are illicit. The sample size determination is really just a quality control problem; there are UN Guidelines where the problem concerns drugs.
Finally, an important part of being a forensic statistician, as indeed it is for any statistician, is the ability to communicate results effectively to non-statisticians. Forensic statisticians may be required to attend court cases as “expert witnesses”. This involves reporting calculated probabilities, or other statistical measures, to the jury, and explaining to them how the calculations were performed. This is a challenge in itself, as the jury will typically consist of people who have little knowledge of statistical methods, and is further complicated by the need to choose careful wording (so as not to “lead” the jury into a decision on guilt or innocence of a defendant).