Assessment of Approximate Likelihood Ratios from Continuous Distributions: A Case Study of Digital Camera Identification*

Abstract

A reported likelihood ratio for the value of evidence is very often a point estimate based on various types of reference data. When presented in court, such frequentist likelihood ratio gets a higher scientific value if it is accompanied by an error bound. This becomes particularly important when the magnitude of the likelihood ratio is modest and thus is giving less support for the forwarded proposition. Here, we investigate methods for error bound estimation for the specific case of digital camera identification. The underlying probability distributions are continuous and previously proposed models for those are used, but the derived methodology is otherwise general. Both asymptotic and resampling distributions are applied in combination with different types of point estimators. The results show that resampling is preferable for assessment based on asymptotic distributions. Further, assessment of parametric estimators is superior to evaluation of kernel estimators when background data are limited.

Bayesian Networks for Evaluation of Evidence from Forensic Entomology

“…In reporting of evidence, V may be transformed into a qualitative statement using verbal scales. 5,17 According to the scale proposed by Evett (cited in reference 5), a value between 1 and 2 can be expressed as moderate evidence to support one hypothesis over another. For comparison, a log(V) of 5 or > 6 can be expressed as very strong evidence and extremely strong evidence, respectively.…”

Avoiding overstating the strength of forensic evidence: Shrunk likelihood ratios/Bayes factors

“…ELUB could also be applied to the output of other procedures. 7 In the present paper we do not explore the performance of procedures based on kernel density models or Gaussian mixture models because they do not induce shrinkage. When data are sparse, even if only locally sparse, this increases concern regarding imprecision and/or overestimating strength of evidence, and in such circumstances non-parametric, semi-parametric, and low-bias parametric procedures are prone to overfitting the training data and exacerbating the problem.…”

“…1 If the amount of sample data is large, the coverage interval will be small, hence there will be little adjustment to the reported value, but if the amount of sample data is small, the coverage interval will be large, hence the reported value will be substantially closer to 1. For discussion and examples of approaches of this sort, see [1][2][3][4][5][6][7][8][9]. From a subjectivist Bayesian perspective, there are no true but unknown population distributions, and the value of a Bayes factor (which is the Bayesian counterpart of the frequentist likelihood ratio) is a state of belief, not an estimate of a true but unknown value (in the context of evaluation of forensic evidence, this position is espoused in, for example [10,11]).…”

“…Also for comparison purposes, on some datasets we will also test non-regularized logistic regression. 7 In the remainder of the present paper:…”

Biometric score calibration for forensic face recognition

“…Crosscomparison of all the biometric specimens in the reference and the test data set results in a set of scores that can be used to model the distribution of scores under the prosecution hypothesis. Similarly, for modelling the distribution of scores under the defense hypothesis, biometric specimens in the test data set are compared with the reference biometric specimens of the potential population database [87]. The suspect-specific approach implies considering the following interpretations of the prosecution and defense hypotheses:…”