A Bayesian approach for the analysis of error rate studies in forensic science

TL;DR

This paper introduces a Bayesian method using Approximate Bayesian Computation to analyze error rates in forensic science studies, effectively handling complex data issues and providing clearer uncertainty quantification.

Contribution

It applies a likelihood-free Bayesian approach to forensic error rate analysis, addressing unbalanced designs, dependencies, and missing data, which are often ignored in traditional methods.

Findings

Handles unbalanced and dependent data effectively

Provides probabilistic error estimates without confidence intervals

Reanalyzes a major forensic study demonstrating the method's utility

Abstract

Over the past decade, the field of forensic science has received recommendations from the National Research Council of the U.S. National Academy of Sciences, the U.S. National Institute of Standards and Technology, and the U.S. President's Council of Advisors on Science and Technology to study the validity and reliability of forensic analyses. More specifically, these committees recommend estimation of the rates of occurrence of erroneous conclusions drawn from forensic analyses. "Black box" studies for the various subjective feature-based comparison methods are intended for this purpose. In general, "black box" studies often have unbalanced designs, comparisons that are not independent, and missing data. These aspects pose difficulty in the analysis of the results and are often ignored. Instead, interpretation of the data relies on methods that assume independence between observations and a balanced experiment. Furthermore, all of these projects are interpreted within the frequentist framework and result in point estimates associated with confidence intervals that are confusing to communicate and understand. We propose to use an existing likelihood-free Bayesian inference method, called Approximate Bayesian Computation (ABC), that is capable of handling unbalanced designs, dependencies among the observations, and missing data. ABC allows for studying the parameters of interest without recourse to incoherent and misleading measures of uncertainty such as confidence intervals. By taking into account information from all decision categories for a given examiner and information from the population of examiners, our method also allows for quantifying the risk of error for the given examiner, even when no error has been recorded for that examiner. We illustrate our proposed method by reanalysing the results of the "Noblis Black Box" study by Ulery et al. in 2011.

Full text

In general, “black box” studies often have unbalanced designs, comparisons that are not independent, and missing data. These aspects pose difficulty in the analysis of the results and are often ignored. Instead, interpretation of the data relies on methods that assume independence between observations and a balanced experiment. Furthermore, all of these projects are interpreted within the frequentist framework and result in point estimates associated with confidence intervals that are confusing to communicate and understand.

We propose to use an existing likelihood-free Bayesian inference method, called Approximate Bayesian Computation (ABC), that is capable of handling unbalanced designs, dependencies among the observations, and missing data. ABC allows for studying the parameters of interest without recourse to incoherent and misleading measures of uncertainty such as confidence intervals. By taking into account information from all decision categories for a given examiner and information from the population of examiners, our method also allows for quantifying the risk of error for the given examiner, even when no error has been recorded for that examiner. This opens the door to the detection of behavioural patterns in the decision-making of examiners through their ABC rate estimates. These patterns could be used to detect error prone examiners, enabling additional training efforts to be more tailored to each examiner, limiting the risk of errors before they occur.

We illustrate our proposed method by reanalysing the results of the “Noblis Black Box” study by Ulery et al. in 2011. We did not choose this study because we disagree with their results, but because it is a good example of a study with dependent observations and missing data, and the data is publicly available. The ABC estimates for the population generally agreed Ulery et al.’s plug-in estimates. However, credible intervals obtained from ABC are much wider than the confidence intervals for the corresponding parameter estimates that did not account for the dependencies among observations.

Keywords: error rates, fingerprint, black-box study, Approximate Bayesian Computation

1 Introduction

Conclusions resulting from the examinations of forensic evidence are not exempt from errors. For example, following the ACE-V process, a fingerprint examiner may conclude that a fingermark does not originate from the same finger as a control impression, when it truly does.

Forensic analyses have received, and continue to receive, criticism (Cole:2005; Zabell:2005; SaksKoehler:2008) due in part to erroneous conclusions that occur at an unknown (but potentially low) rate. Building on this criticism, a committee appointed by the National Academy of Sciences (NAS:2009) recommended the study of the validity and reliability of forensic analyses, which includes the design and performance of scientific studies to estimate the rates of error present in the conclusions drawn from forensic analyses.

Additional reports have also focused on the study of the rate of occurrence of erroneous conclusions. The National Institute of Standards and Technology (NIST) emphasised the importance of quantifying the rate of erroneous conclusions resulting from forensic analyses (NIST2012). They assert that knowledge about error rates enables the assessment of the reliability and allows for appropriate confidence to be placed on a given evidence.

In 2016, the President’s Council of Advisors on Science and Technology (PCAST) (PCAST2016) emphasised that the validity of subjective feature-based comparison methods (such as fingerprint examination, firearms analysis, or footwear analysis) must be assessed through “black box” studies that analyse the rates of occurrence of erroneous conclusions. They found that only several “black box” studies have been performed for the evidence types they reviewed: the Noblis study by Ulery2011 and the Miami-Dade study by Pacheco2014, both for fingerprint examination, and a study by Baldwin2014 for firearms analysis. PCAST recommended that additional “black box” studies be conducted for the various subjective feature-based comparison methods to further study their validity and reliability.

Whether we agree with the appropriateness for forensic scientists to report categorical conclusions, we can expect that additional error rate studies will be performed in the future to answer the recommendations from the NRC, NIST and PCAST. In any case, it is critical that the results of these studies are correctly analysed. However, complex experimental designs can make this difficult. For example, PCAST correctly points out that what they name “set-based analyses” result in dependent observations (PCAST2016). Estimating error rates based on such dependent observations cannot rely on straightforward plug-in estimates. However, PCAST incorrectly claims that the observations resulting from “black box” studies are independent. Firstly, from the design of “black box” studies, it is not clear whether the forensic scientists or the test cases are the experimental units. Secondly, forensic scientists and test cases are re-used throughout a given experiment, usually not in a balanced manner. This creates dependencies in the resulting observations that cannot be studied using the traditional tools developed in the context of the statistical design of experiments (Casella2008).

In this paper, we propose a method to analyse the results of “black box” experiments that can handle the most complex designs in a rigorous manner. Our method is based on a class of computational methods called Approximate Bayesian Computation (ABC), which relies on strong statistical foundations with well-understood asymptotic properties. Our method can deal with unbalanced designs, dependent observations and missing data. Our method allows for studying the parameters of interest without recourse to incoherent and misleading measures of uncertainty such as confidence intervals. Finally, our method allows us to go beyond simply reporting point estimates for error rates: our method can result in predictive models that quantify the risk of errors of any given examiner, even when no error has been recorded for that examiner.

In this paper, we provide an example of the application of our method by reanalysing the results of the well-known “Noblis Black Box” study (Ulery2011). We have not chosen this study because we disagree with their results, but because it is a good example of a design that involves numerous uncontrollable factors, dependent observations, and missing data. Additionally, the original data collected during the study is publicly available (BBResults).

Section 2 summarises the study by Ulery2011 and provides a motivation for our approach. In section LABEL:ABC, we briefly discuss frequentist approaches for analysis of error rate studies, and then introduce a likelihood-free Bayesian approach (ABC) that can account for the dependencies among observations and missing data. In section LABEL:Application, we present the application of ABC to the data from the Ulery et al.’s study. In section LABEL:Results, we use our results to infer population and individual examiners’ rates of erroneous conclusions resulting from the fingerprint examination process, and examine behavioural patterns in the decision making of fingerprint examiners. Finally, in section LABEL:Conclusion, we present our conclusions, and recommendations for the analysis of future error rate studies and implementation of predictive models that may detect high-risk examiners.

2 “Noblis Black Box” study (Ulery2011)

Following the erroneous identification made by the FBI in connection with the 2004 terrorist attacks in Madrid, Spain, the review of the FBI’s handling of the error (OIG2006) and the research recommendations made by an FBI committee (Budowle2006), a “black box” study was performed by scientists at Noblis and reported in Ulery2011. The purpose of this research project was to study the accuracy and reliability of decisions in forensic examination of fingerprints, and more specifically the rates at which fingerprint examiners make erroneous identifications or exclusions.

During the first phase of the study, 169 participating examiners were each presented with a total of 100 pairs of fingermark and control impression out of 744 unique test cases prepared for the experiment. Out of the 16,900 possible conclusions, 16,873 were considered for the estimation of the error rates (27 were removed due to data entry error or inadvertent submission of multiple instances of the same test case to an examiner). During the second phase, 42 examiners from phase one were presented with several additional image pairs, resulting in an additional 248 responses considered for the data analysis. A total of 17,121 responses were considered to estimate the error rates reported by (Ulery2011).

For each pair of images, examiners were first asked to determine if the fingermark was of value for individualisation 111We do not necessarily support the use of the term “individualisation”; however, this was the term used in the original study. (VID), value for exclusion (VEO), or no value (NV). If the image was deemed NV, the fingermark was not compared to the assigned control print. If the image was deemed either VID or VEO, the fingermark was compared with the control print. After the comparison stage, examiners were asked to provide a final decision of individualisation or exclusion, or to deem the comparison inconclusive. Therefore, a total of seven decision categories were possible: