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Forensic mathematics means the mathematics of evidence. In practice the subject is identification through DNA evidence because that’s what I enjoy and do. More than any other forensic area DNA identification offers scope for explicit mathematical treatment.
Emphasis is on the practical but with necessary forays into theory. Examples will come from particular cases or situations typical in casework, anecdotes from fieldwork and the courtroom.
The likelihood principle is the central concept of forensic mathematics. For example, if dogs are more reliably stimulated to bark by strangers than by loneliness, then a barking dog is evidence of a stranger (as opposed to loneliness). Evidence is quantified by the likelihood ratio. Any other way to quantify evidence is either equivalent to the likelihood ratio or nonsense. For example fingerprint identification traditionally assumes that “match” is proof positive of identity, which is nonsense. (Fingerprint impressions are neither in theory nor in practice uniquely individualistic.)
DNA identification relies on a convenient biochemical assay that assigns, for any person, a simple profile consisting in essence of a few dozen small integers. The variety and distribution in the population of those integers is reasonably well explained by simple principles of genetics and population genetics. Therefore forensic DNA mathematics rests on basic combinatorial and probability principles — discrete mathematics.
Mathematical models are the bridge from mathematics to the real world of DNA evidence. The rules of genetics are simple but the consequences can be far from obvious.