The use of likelihood ratios for quantifying the strength of forensic evidence in criminal cases is gaining widespread acceptance in many forensic disciplines. Although some forensic scientists feel that subjective likelihood ratios are a reasonable way of expressing expert opinion regarding strength of evidence in criminal trials, legal requirements of reliability of expert evidence in the United Kingdom, United States and some other countries have encouraged researchers to develop likelihood ratio systems based on statistical modelling using relevant empirical data. Many such systems exhibit exceptional power to discriminate between the scenario presented by the prosecution and an alternate scenario implying the innocence of the defendant. However, such systems are not necessarily well calibrated. Consequently, verbal explanations to triers of fact, by forensic experts, of the meaning of the offered likelihood ratio may be misleading. In this article, we put forth a statistical approach for testing the calibration discrepancy of likelihood ratio systems using ground truth known empirical data. We provide point estimates as well as confidence intervals for the calibration discrepancy. Several examples, previously discussed in the literature, are used to illustrate our method. Results from a limited simulation study concerning the performance of the proposed approach are also provided.
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Abstract Objectives We apply new statistical models to daily diary data to advance both methodological and conceptual goals. We examine age effects in within-person slopes in daily diary data and introduce Generalized Fiducial Inference (GFI), which provides a compromise between frequentist and Bayesian inference. We use daily stressor exposure data across six domains to generate within-person emotional reactivity slopes with daily negative affect. We test for systematic age differences and similarities in these reactivity slopes, which are inconsistent in previous research.
Method One hundred and eleven older (aged 60–90) and 108 younger (aged 18–36) adults responded to daily stressor and negative affect questions each day for eight consecutive days, resulting in 1,438 total days. Daily stressor domains included arguments, avoided arguments, work/volunteer stressors, home stressors, network stressors, and health-related stressors.
Results Using Bayesian, GFI, and frequentist paradigms, we compared results for the six stressor domains with a focus on interpreting age effects in within-person reactivity. Multilevel models suggested null age effects in emotional reactivity across each of the paradigms within the domains of avoided arguments, work/volunteer stressors, home stressors, and health-related stressors. However, the models diverged with respect to null age effects in emotional reactivity to arguments and network stressors.
Discussion The three paradigms converged on null age effects in reactivity for four of the six stressor domains. GFI is a useful tool that provides additional information when making determinations regarding null age effects in within-person slopes. We provide the code for readers to apply these models to their own data.
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Steed et al . ( 1 ) illustrates the crucial impact that the quality of official statistical data products may exert on the accuracy, stability, and equity of policy decisions on which they are based. The authors remind us that data, however responsibly curated, can be fallible. With this comment, we underscore the importance of conducting principled quality assessment of official statistical data products. We observe that the quality assessment procedure employed by Steed et al . needs improvement, due to (i) the inadmissibility of the estimator used, and (ii) the inconsistent probability model it induces on the joint space of the estimator and the observed data. We discuss the design of alternative statistical methods to conduct principled quality assessments for official statistical data products, showcasing two simulation-based methods for admissible minimax shrinkage estimation via multilevel empirical Bayesian modeling. For policymakers and stakeholders to accurately gauge the context-specific usability of data, the assessment should take into account both uncertainty sources inherent to the data and the downstream use cases, such as policy decisions based on those data products.more » « lessFree, publicly-accessible full text available June 2, 2024
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Free, publicly-accessible full text available June 1, 2024
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Data matrix centering is an ever-present yet under-examined aspect of data analysis. Functional data analysis (FDA) often operates with a default of centering such that the vectors in one dimension have mean zero. We find that centering along the other dimension identifies a novel useful mode of variation beyond those familiar in FDA. We explore ambiguities in both matrix orientation and nomenclature. Differences between centerings and their potential interaction can be easily misunderstood. We propose a unified framework and new terminology for centering operations. We clearly demonstrate the intuition behind and consequences of each centering choice with informative graphics. We also propose a new direction energy hypothesis test as part of a series of diagnostics for determining which choice of centering is best for a data set. We explore the application of these diagnostics in several FDA settings.more » « lessFree, publicly-accessible full text available April 26, 2024
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String edit distances have been used for decades in applications ranging from spelling correction and web search suggestions to DNA analysis. Most string edit distances are variations of the Levenshtein distance and consider only single-character edits. In forensic applications polymorphic genetic markers such as short tandem repeats (STRs) are used. At these repetitive motifs the DNA copying errors consist of more than just single base differences. More often the phenomenon of “stutter” is observed, where the number of repeated units differs (by whole units) from the template. To adapt the Levenshtein distance to be suitable for forensic applications where DNA sequence similarity is of interest, a generalized string edit distance is defined that accommodates the addition or deletion of whole motifs in addition to single-nucleotide edits. A dynamic programming implementation is developed for computing this distance between sequences. The novelty of this algorithm is in handling the complex interactions that arise between multiple- and single-character edits. Forensic examples illustrate the purpose and use of the Restricted Forensic Levenshtein (RFL) distance measure, but applications extend to sequence alignment and string similarity in other biological areas, as well as dynamic programming algorithms more broadly.more » « less
