Forensic mathematics glossary

Not really a glossary; just a collection of miscellaneous words, not even including the most important ones (just use a search for those). In fact the intent isn’t even definitions, often just comments or links.
avuncular index (AI)
is a name I coined for the likelihood ratio that supports a tested man to be the uncle of a tested child rather than unrelated to the child.

The AI is useful to help settle the question of paternity when the DNA profiles are consistent with paternity at nearly all loci but “inconsistent” at a few loci. In that situation it may be either that

  1. The man is the father (the “inconsistencies” being mutations), or
  2. The man is the uncle (or other close relative of the father).
Conflicting explanations — in one case the man is the father, in the other case he is not. Comparing the PI and AI can help in choosing between the possibilities.
 
inconsistent, inconsistency
The term “inconsistency” is often used to mean genotypes for alleged father (AF), child, and perhaps mother, at a particular locus that is inconsistent with paternity barring mutation (and perhaps barring null alleles — usage varies). For example the pattern child=(14,17), AF=(15) is “inconsistent”.
baseline prior probability

consanguinous mating — see incest

disaster identification

exclude, exclusion
frequently misused word. Consider “We excluded the man of paternity because of three exclusions.” See What’s wrong with the “exclusion probability” for a start.
The concept, while appealing, is dubious as well. Don’t get me started.

contributor
The meaning of “contributor” to a mixture depends on the meaning of mixture.
  1. Contributor to a mixture consisting of DNA molecules (mixture substance) is best defined in vague terms such as “someone who contributed a ‘significant’(?) amount of DNA”.
  2. Contributor in the sense of mixture data is also hard to define in simple terms, but it must relate to how including a (known or unknown) DNA profile affects the computed likelihood of the mixture data.
frequency spectrum
The probability distribution of (allele or haplotype) frequencies that occur. For example, for YFiler haplotypes the spectrum shows a very high probability of haplotype frequencies between 0.0001 and 0.0002 (many haplotypes have population frequencies in this range), a much lower probability of haplotype frequencies between 0.0005 and 0.0006.

Theory or data may suggest an expected frequency spectrum, which can then be regarded as prior probabilities for the frequencies of allelic or haplo-types. Such a prior can be used along with Bayes’ theorem and a sample reference database of allelic types, to infer allele probabilities.

Brenner’s Law is a statement about the frequency spectrum for forensic STR loci.

fallacy
The terms prosecutor’s fallacy and defense fallacy were, I think, invented by UC Irvine law Prof. William Thompson.

incest
Ebenezer, the father of Judy, is alleged to be the father of Judy’s child. What modification to the normal paternity calculation is appropriate?
Answer — None, normally. So long as the testing uses unlinked co-dominant markers (like standard forensic STRs) and both the mother and the alleged father are tested (normal trio paternity), the fact of the adults’ relationship is irrelevant.

mass identification; mass disaster identification
a DNA•VIEW speciality.

likelihood ratio (LR)
The central concept of Forensic Mathematics. The way to quantify forensic — or any — evidence. Any other method is either equivalent to a likelihood ratio or is nonsense.

The framework we consider is trying to judge between two possible hypotheses. A typical pair of hypotheses would be:

  1. The suspect is the donor of the rape kit semen, versus the suspect is a random man;
  2. The tested body B is the missing relative of family F, versus B and F are unrelated.

Evidence, i.e. information or data such as DNA profiles, may be better explained by one of the hypotheses than by the other.

mixture
The word mixture is used carelessly and ambiguously in forensic DNA. Software analyzes mixture data.

Implication: Since the term “ground truth” of a mixture is a description of mixture substance, it has limited relevance to mixture data. In particular, analysis by Mixture Solution or other software that (for example) estimates number of contributors, is not right or wrong according to whether it agrees with ground truth. It’s a tortuous route from the moment DNA is deposited as mixture substance to the final version of mixture data. It’s not a paradox that the best possible analysis of mixture data, the most correct analysis, sometimes differs from the ground truth about something else.
 

paternity index
a quaint synonym for likelihood ratio used in the context of disputed paternity

 
probability
unrelated
Everyone is related, so why do we say for example “The suspect is either the father, or is unrelated to the child” to describe the alternative hypotheses in a paternity question? Two answers:
  1. It’s hard to find an accurate wording that is simple;
  2. The fiction of literally being unrelated is sometimes a premise of our computational model. (The paternity formula 1/2q rests on a premise of unrelatedness.)
All that said, when I or anyone says “unrelated” there is a good chance that what we really mean is “randomly selected, with no more and no less than a random chance to have any particular close or distant relationship”.

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