Estimating a probability mass function with unknown labels

2017

Statistica Neerlandica

The likelihood ratio (LR) is largely used to evaluate the relative weight of forensic data regarding two hypotheses, and for its assessment, Bayesian methods are widespread in the forensic field. However, the Bayesian ‘recipe’ for the LR presented in most of the literature consists of plugging‐in Bayesian estimates of the involved nuisance parameters into a frequentist‐defined LR: frequentist and Bayesian methods are thus mixed, giving rise to solutions obtained by hybrid reasoning. This paper provides the derivation of a proper Bayesian approach to assess LRs for the ‘rare type match problem’, the situation in which the expert wants to evaluate a match between the DNA profile of a suspect and that of a trace from the crime scene, and this profile has never been observed before in the database of reference. LR assessment using the two most popular Bayesian models (beta‐binomial and Dirichlet‐multinomial) is discussed and compared with corresponding plug‐in versions.

Section: The Rare Type Match Problemmentioning

confidence: 99%

Bayesian approach to LR assessment in case of rare type match

2017

Statistica Neerlandica

“…The limitation of this method is that it cannot be used if N 2 = 0(this corresponds to an infinite likelihood ratio), and it does not perform well also in case the number of singletons is very small or zero. We believe it can be improved and extended by smoothing techniques (Good, ; Anevski et al, ), but we are going to ignore this problem.…”

Section: The Generalized‐good Methodsmentioning

confidence: 99%

Impact of Model Choice on LR Assessment in Case of Rare Haplotype Match (Frequentist Approach)

Scandinavian J Statistics

2016

The likelihood ratio (LR) measures the relative weight of forensic data regarding two hypotheses. Several levels of uncertainty arise if frequentist methods are chosen for its assessment: the assumed population model only approximates the true one, and its parameters are estimated through a limited database. Moreover, it may be wise to discard part of data, especially that only indirectly related to the hypotheses. Different reductions define different LRs. Therefore, it is more sensible to talk about 'a' LR instead of 'the' LR, and the error involved in the estimation should be quantified. Two frequentist methods are proposed in the light of these points for the 'rare type match problem', that is, when a match between the perpetrator's and the suspect's DNA profile, never observed before in the database of reference, is to be evaluated.

“…More recently, Orlitsky et al [ 14 ] have introduced the high-profile estimator , which extends the tail of the naive estimator to the region of unobserved types. Anevski et al [ 15 ] improved this estimator and provided a consistency proof for their modified estimator (original authors only provided heuristic reasoning that turned out to be rather difficult to make rigorous).…”

Section: State Of the Artmentioning

confidence: 99%

“…Since it holds that

for every accepted

, we calculate the sum of all

s such that

and we use the average to approximate the denominator of ( 14 ). The algorithm is based on a similar one proposed in Anevski et al [ 15 ].…”

Section: Analysis On the Yhrd Databasementioning

confidence: 99%

A Nonparametric Bayesian Approach to the Rare Type Match Problem

Gill

2020

Entropy

Self Cite

The "rare type match problem" is the situation in which the suspect's DNA profile, matching the DNA profile of the crime stain, is not in the database of reference. The evaluation of this match in the light of the two competing hypotheses (the crime stain has been left by the suspect or by another person) is based on the calculation of the likelihood ratio and depends on the population proportions of the DNA profiles, that are unknown. We propose a Bayesian nonparametric method that uses a two-parameter Poisson Dirichlet distribution as a prior over the ranked population proportions, and discards the information about the names of the different DNA profiles. This fits very well the data coming from European Y-STR DNA profiles, and the calculation of the likelihood ratio becomes quite simple thanks to a justified Empirical Bayes approach.