Impact of model choice on LR assessment in case of rare haplotype match (frequentist approach)

Bayesian approach to LR assessment in case of rare type match

“…Alternatively, Good (1953), based on an intuition on A.M. Turing, proposed the nonparametric Good Turing estimator for the total unobserved probability mass, based on the proportion of singleton observations in the sample. An extension of this estimator is applied to the LR assessment in the rare type match in Cereda (2015b). For a comparison between add one and Good-Turing estimator, see Orlitsky et al (2003).…”

“…Papers that address the rare Y-STR haplotype problem in forensic context are for instance Egeland and Salas (2008), Brenner (2010), andCereda (2015a,c). Moreover, the Discrete Laplace method presented in Andersen et al (2013), even though not specifically designed for the rare type match can be successfully applied to that extent (Cereda, 2015b). Bayesian nonparametric estimators for the probability of observing a new type have been proposed by Tiwari and Tripathi (e.g.…”

“…This leads to the so-called plug-in estimation LR = LR ( θ) of the LR . However, that's not the only option (Cereda, 2015b).…”

“…Once a choice has been made, it is important to be consistent with it, while literature often mixes up the two. To our knowledge, this paper and (Cereda, 2015b) constitute the only forensic literature that discuss the differences between the two approaches. (Cereda, 2015b) is concerned with the theoretical foundations of frequentist solutions, while this paper provides a simple and careful derivation of the proper Bayesian LR, for the rare type match problem (described in Section 2): the situation in which the DNA profile of the crime stain and that of the suspect match but they are not among the DNA profiles observed in the reference database.…”

“…To our knowledge, this paper and (Cereda, 2015b) constitute the only forensic literature that discuss the differences between the two approaches. (Cereda, 2015b) is concerned with the theoretical foundations of frequentist solutions, while this paper provides a simple and careful derivation of the proper Bayesian LR, for the rare type match problem (described in Section 2): the situation in which the DNA profile of the crime stain and that of the suspect match but they are not among the DNA profiles observed in the reference database. In Section 3 we will discuss the fact that influential Bayesian forensic literature (Weir, 1996;Aitken and Taroni, 2004;Taroni et al, 2010Taroni et al, , 2014Sjerps et al, 2015) seems to suggest the use of frequentist defined likelihood ratio (LR ) and use Bayesian methodologies only inasmuch they provide a Bayesian estimate of θ to be plugged into LR .…”