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In forensic casework it is common that multiple pieces of evidence are obtained in a single case. For the evaluation of such evidence, one cannot simply assume that they originated from the same source. If this can be disputed, one could decide to report the evidential value of the separate pieces by computing likelihood ratios (LRs) for them separately. However, by doing so, information regarding the conditional dependency structure is lost and the potentially difficult step of combining them is left to the trier of fact. Especially in situations where the pieces of evidence are of the same type, a combined evaluation could be substantially more informative. In such situations, it is not unrealistic that the separate evidential values are not optimally combined by the trier of fact. From a scientific point of view, the optimal way is that the forensic scientist combines the forensic evidence in a report using hypotheses at the 'activity level'. In practice, however, this is not always feasible for every case for reasons of efficiency. In this article, we explore what can be done in cases where the optimal solution is too costly. For a combined evaluation, the prior distribution for the number of distinct sources of the pieces of evidence becomes part of the LR. Generally, prior probabilities are beyond the scope of expertise of the forensic specialist and are left to the trier of fact to decide. We propose a lower bound LRapproach for such situations that is independent of the prior distribution. Using a set of examples, we present how this method can be applied in practice. [ABSTRACT FROM AUTHOR]

When a Y-chromosomal and a (partial) autosomal DNA profile are obtained from one crime sample, and both profiles match the suspect's profiles, we would like to know the combined evidential value. To calculate the likelihood ratio of observing the autosomal and Y-chromosomal DNA profiles combined, we need to know the conditional random match probability of the observed autosomal DNA profile, given the Y-chromosomal match. We examine this conditional probability in two ways: (1) with a database containing data of 2,085 men and (2) using a simulation model. We conclude that if the Y-chromosomal DNA profiles match, we can still regard the autosomal DNA profile as independent from the Y-chromosomal DNA profile if the matching person is not a descendant of the father of the donor of the (crime) sample. The evidential value can, in that case, be computed by multiplying the random match probabilities of the individual profiles. [ABSTRACT FROM AUTHOR]

Experts providing evidence in legal cases are universally recommended to be transparent, particularly in their reasoning, so that legal practitioners can critically check whether the conclusions are adequately supported by the results. However, when exploring the practical meaning of this recommendation it becomes clear that people have different things in mind. The UK appeal court case R v T painfully exposes the different views. In this article we argue that there can be a trade-off between clarity and transparency, and that in some cases it is impossible for the legal practitioner to be able to follow the expert’s reasoning in full detail because of the level of complexity. All that can be expected in these cases is that the legal practitioner is able to understand the reasoning up to a certain level. We propose that experts should only report the main arguments, but must make this clear and provide further details on request. Reporting guidelines should address the reasoning in more detail. Legal practitioners and scientists should not be telling each other what to do in the setting of a legal case, but in other settings more discussion will be beneficial to both. We see the likelihood ratio framework and Bayesian networks as tools to promote transparency and logic. Finally, we argue that transparency requires making clear whether a conclusion is a consensus and reporting diverging opinions on request. [ABSTRACT FROM AUTHOR]

In legal environmental control, solid wastes are sampled to determine whether the mean concentrations of contaminants meet the regulatory standard. Current sampling and statistical testing procedures for solid wastes often rely on assumptions about the heterogeneity of the contaminants and on the assumption that the frequency distribution of the data is (log)normal. To investigate the reliability of these assumptions, we analyzed the data of nineteen waste materials. Our results provide evidence that the variability of contaminant concentrations in solid wastes is large and difficult to predict. The concentrations followed different types of frequency distributions, and outliers occurred frequently. Large differences in concentration between the sub-lots were observed, and the concentration in a composite sample sometimes deviated considerably from the mean of the individual samples. The contaminant type did not seem to have a large effect on the coefficient of variation, the bias of the composite, or the frequency distribution type. Sampling standards and compliance criteria are often not adapted to the quality of the data encountered in practice. Regulatory standards should provide some prescribed level of statistical assurance that the standard is actually being met or violated. For compliance testing it seems better to measure uncertainty directly from sample results than to rely on assumptions. [ABSTRACT FROM AUTHOR]

The introduction of DNA evidence has transformed human individualization in criminal litigation, but it also introduced daunting statistical, philosophical and practical problems into the process. The current practice in many legal cases is that a forensic expert reports a match probability or a likelihood ratio. However, the value of the likelihood ratio depends on the particular hypotheses used by the expert. Often there are various choices possible for the hypotheses used, and the corresponding likelihood ratios for different hypotheses are typically different. We therefore argue that the findings of an expert should not be given with a single number, and that any report with a match probability or likelihood ratio should be accompanied by a discussion of the effect of these numbers. We suggest a way to do this, using the so‐called posterior odds, which are invariant under various sets of hypotheses. Our approach is applicable in legal systems where the judge or jury is not allowed to know that the suspect was in a database. However, juridical problems may arise when courts insist on, for example, only a frequency estimate to be reported. [ABSTRACT FROM PUBLISHER]

Does the evidential strength of a DNA match depend on whether the suspect was identified through database search or through other evidence ("probable cause")? In Balding and Donnelly (1995, Journal of the Royal Statistical Society, Series A 158, 21-53) and elsewhere, it has been argued that the evidential strength is slightly larger in a database search case than in a probable cause case, while Stockmarr (1999, Biometrics 55, 671-677) reached the opposite conclusion. Both these approaches use likelihood ratios. By making an excursion to a similar problem,the two-stain problem, we argue in this article that there are certain fundamental difficulties with the use of a likelihood ratio, which can be avoided by concentrating on the posterior odds. This approach helps resolving the above-mentioned conflict. [ABSTRACT FROM AUTHOR]