عنوان انگلیسی مقاله:
DNA database matches: A p versus np problem
ترجمه فارسی عنوان مقاله:
پایگاه داده DNA مطابقت دارد: مسئله p در مقابل np
Sciencedirect - Elsevier - Forensic Science International: Genetics, 46 (2020) 102229. doi:10.1016/j.fsigen.2019.102229
R.W.J. Meestera, K. Slootena,b,*
The evidential value of a unique DNA database match has been extensively discussed. In principle the matter has
been mathematically resolved, since the posterior odds on the match being with the trace donor are unambiguously
defined. There are multiple ways to express these odds as a product of likelihood ratio and prior
odds, and so the mathematics do not immediately tell us what to do in concrete cases, in particular which
likelihood ratio to choose for reporting. With p the random match probability for the matching person, if innocent,
and n the database size, both 1/p, originating from a suspect-centered framework, and 1/(np), originating
from a database-centered framework, arise as likelihood ratio. Both have been defended and both have
been criticized in the literature.
We will clarify the situation by not introducing models and choices of prior probabilities until they are
needed. This allows to derive the posterior odds in their most general form, which applies whenever we know
that a single person among a list is not excluded as potential trace donor. We show that we need only three
probabilities, that pertain to the observed match, to the database, and to the matching person respectively.
How these required probabilities behave in a given context, then, differs from one situation to another. This is
understandable since database searches may be done under various circumstances. They may be carried out with
or without a suspect already in mind and, depending on the operational procedures, one may or may not be
informed about the personal details of the person who gives the match. We show how to evaluate the required
probabilities in all such cases.
We will motivate why we believe that for some database searches, the 1/p likelihood ratio is more natural,
whereas for others, 1/(np) seems the more sensible choice. This is not motivated by the mathematics: mathematically,
the approaches are equivalent. It is motivated by considering which model best reflects the actual
situation, taking into account what question was asked to begin with, and by the practical consideration of
judging which likelihood ratio comes closer to the posterior odds based on the information available in the case.
This article is intended to be both a research and a review article, and we end with an in-depth discussion of
various arguments that have been brought forward in favor or against either 1/p or 1/(np).
Keywords: DNA database | Likelihood ratio | Evidential value | Criminal casework | Database controversy