Overall mean estimation of trace evidence in a two-level normal–normal model

Overall mean estimation of trace evidence in a two-level normal–normal model

Kool, Fréderique Suzanne (Nederlands Forensisch Instituut (NFI))
van Dorp, I. (Nederlands Forensisch Instituut (NFI))
Bolck, Annabel (Nederlands Forensisch Instituut (NFI))
Leegwater, Anna Jeannette (Nederlands Forensisch Instituut (NFI))
Jongbloed, G. (TU Delft Delft Institute of Applied Mathematics)

2019

In the evaluation of measurements on characteristics of forensic trace evidence, Aitken and Lucy (2004) model the data as a two-level model using assumptions of normality where likelihood ratios are used as a measure for the strength of evidence. A two-level model assumes two sources of variation: the variation within measurements in a group (first level) and the variation between different groups (second level). Estimates of the variation within groups, the variation between groups and the overall mean are required in this approach. This paper discusses three estimators for the overall mean. In forensic science, two of these estimators are known as the weighted and unweighted mean. For an optimal choice between these estimators, the within- and between-group covariance matrices are required. In this paper a generalization to the latter two mean estimators is suggested, which is referred to as the generalized weighted mean. The weights of this estimator can be chosen such that they minimize the variance of the generalized weighted mean. These optimal weights lead to a “toy estimator” because they depend on the unknown within- and between-group covariance matrices. Using these optimal weights with estimates for the within- and between-group covariance matrices leads to the third estimator, the optimal “plug-in” generalized weighted mean estimator. The three estimators and the toy estimator are compared through a simulation study. Under conditions generally encountered in practice, we show that the unweighted mean can be preferred over the weighted mean. Moreover, in these situations the unweighted mean and the optimal generalized weighted mean behave similarly. An artificial choice of parameters is used to provide an example where the optimal generalized weighted mean outperforms both the weighted and unweighted mean. Finally, the three mean estimators are applied to real XTC data to illustrate the impact of the choice of overall mean estimator.

Evidence evaluation
Likelihood ratio
Multivariate distributions
Overall mean estimation
XTC

http://resolver.tudelft.nl/uuid:8604a08d-91c4-490b-9fdf-30e5c474cf9a

https://doi.org/10.1016/j.forsciint.2019.01.047

2020-03-20

0379-0738

Forensic Science International: an international journal dedicated to the applications of genetics in the administration of justice, 297, 342-349

Accepted author manuscript

Institutional Repository

review

© 2019 Fréderique Suzanne Kool, I. van Dorp, Annabel Bolck, Anna Jeannette Leegwater, G. Jongbloed