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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Since the mid‐2000s, there has been a resurrection of interest in modern modifications of fiducial inference. To date, the main computational tool to extract a generalized fiducial distribution is Markov chain Monte Carlo (MCMC). We propose an alternative way of computing a generalized fiducial distribution that could be used in complex situations. In particular, to overcome the difficulty when the unnormalized fiducial density (needed for MCMC) is intractable, we design a fiducial autoencoder (FAE). The fitted FAE is used to generate generalized fiducial samples of the unknown parameters. To increase accuracy, we then apply an approximate fiducial computation (AFC) algorithm, by rejecting samples that when plugged into a decoder do not replicate the observed data well enough. Our numerical experiments show the effectiveness of our FAE‐based inverse solution and the excellent coverage performance of the AFC‐corrected FAE solution.
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