The likelihood ratio as a random variable for linked markers in kinship analysis.

Abstract:

:The likelihood ratio is the fundamental quantity that summarizes the evidence in forensic cases. Therefore, it is important to understand the theoretical properties of this statistic. This paper is the last in a series of three, and the first to study linked markers. We show that for all non-inbred pairwise kinship comparisons, the expected likelihood ratio in favor of a type of relatedness depends on the allele frequencies only via the number of alleles, also for linked markers, and also if the true relationship is another one than is tested for by the likelihood ratio. Exact expressions for the expectation and variance are derived for all these cases. Furthermore, we show that the expected likelihood ratio is a non-increasing function if the recombination rate increases between 0 and 0.5 when the actual relationship is the one investigated by the LR. Besides being of theoretical interest, exact expressions such as obtained here can be used for software validation as they allow to verify the correctness up to arbitrary precision. The paper also presents results and advice of practical importance. For example, we argue that the logarithm of the likelihood ratio behaves in a fundamentally different way than the likelihood ratio itself in terms of expectation and variance, in agreement with its interpretation as weight of evidence. Equipped with the results presented and freely available software, one may check calculations and software and also do power calculations.

journal_name

Int J Legal Med

authors

Egeland T,Slooten K

doi

10.1007/s00414-016-1416-2

subject

Has Abstract

pub_date

2016-11-01 00:00:00

pages

1445-1456

issue

6

eissn

0937-9827

issn

1437-1596

pii

10.1007/s00414-016-1416-2

journal_volume

130

pub_type

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