A probabilistic approach to evaluate salivary microbiome in forensic science when the Defense says: `It is my twin brother'.

Salivary microbiota profiles may represent a valid contribution to forensic investigation when standard DNA genotyping methods fail. Starting from questioned and control materials in the form of saliva, the evidence can be expressed by means of a distance between those materials taking into account specific aspects of the microbiota composition. The value of the evidence for forensic discrimination purposes is quantified by means of a Bayes' factor, that allows one to overcome the major limitations and pitfalls of intuition connected to the use of cut-off values as a mean of decision.

More on the question 'When does absence of evidence constitute evidence of absence?' How Bayesian confirmation theory can logically support the answer.

In forensic science it is not rare that common sayings are used to support particular inferences. A typical example is the adage 'The absence of evidence is not evidence of absence'. This paper analyzes the rationale hidden behind such statement and it offers a structural way to approach the analysis of this particular adage throughout a careful analysis of four different scenarios.

Critical analysis of forensic cut-offs and legal thresholds: A coherent approach to inference and decision.

In this paper we critically discuss the definition and use of cut-off values by forensic scientists, for example in forensic toxicology, and point out when and why such values - and ensuing categorical conclusions - are inappropriate concepts for helping recipients of expert information with their questions of interest. Broadly speaking, a cut-off is a particular value of results of analyses of a target substance (e.g., a toxic substance or one of its metabolites in biological sample from a person of interest), defined in a way such as to enable scientists to suggest conclusions regarding the condition of the person of interest. The extent to which cut-offs can be reliably defined and used is not unanimously agreed within the forensic science community, though many practitioners - especially in operational laboratories - rely on cut-offs for reasons such as ease of use and simplicity. In our analysis, we challenge this practice by arguing that choices made for convenience should not be to the detriment of balance and coherence. To illustrate our discussion, we will choose the example of alcohol markers in hair, used widely by forensic toxicologists to reach conclusions regarding the drinking behaviour of individuals. Using real data from one of the co-authors' own work and recommendations of cut-offs published by relevant professional organisations, we will point out in what sense cut-offs are incompatible with current evaluative guidelines (e.g., [31]) and show how to proceed logically without cut-offs by using a standard measure for evidential value. Our conclusions run counter to much current practice, but are inevitable given the inherent definitional and conceptual shortcomings of scientific cut-offs. We will also point out the difference between scientific cut-offs and legal thresholds and argue that the latter - but not the former - are justifiable and can be dealt with in logical evaluative procedures.

Analysing and exemplifying forensic conclusion criteria in terms of Bayesian decision theory.

There is ongoing discussion in forensic science and the law about the nature of the conclusions reached based on scientific evidence, and on how such conclusions - and conclusion criteria - may be justified by rational argument. Examples, among others, are encountered in fields such as fingermarks (e.g., 'this fingermark comes from Mr. A's left thumb'), handwriting examinations (e.g., 'the questioned signature is that of Mr. A'), kinship analyses (e.g., 'Mr. A is the father of child C') or anthropology (e.g., 'these are human remains'). Considerable developments using formal methods of reasoning based on, for example (Bayesian) decision theory, are available in literature, but currently such reference principles are not explicitly used in operational forensic reporting and ensuing decision-making. Moreover, applied examples, illustrating the principles, are scarce. A potential consequence of this in practical proceedings, and hence a cause of concern, is that underlying ingredients of decision criteria (such as losses quantifying the undesirability of adverse decision consequences), are not properly dealt with. There is merit, thus, in pursuing the study and discussion of practical examples, demonstrating that formal decision-theoretic principles are not merely conceptual considerations. Actually, these principles can be shown to underpin practical decision-making procedures and existing legal decision criteria, though often not explicitly apparent as such. In this paper, we will present such examples and discuss their properties from a Bayesian decision-theoretic perspective. We will argue that these are essential concepts for an informed discourse on decision-making across forensic disciplines and the development of a coherent view on this topic. We will also emphasize that these principles are of normative nature in the sense that they provide standards against which actual judgment and decision-making may be compared. Most importantly, these standards are justified independently of peoples' observable decision behaviour, and of whether or not one endorses these formal methods of reasoning.

The meaning of justified subjectivism and its role in the reconciliation of recent disagreements over forensic probabilism.

In this paper we reply to recent comments in this Special Issue according to which subjective probability is not considered to be a concept fit for use in forensic evaluation and expert reporting. We identify the source of these criticisms to lie in a misunderstanding of subjective probability as unconstrained subjective probability; a lack of constraint that neither corresponds to the way in which we referred to subjective probability in our previous contributions, nor to the way in which probability assignment is understood by current evaluative guidelines (e.g., of ENFSI). Specifically, we explain that we understand subjective probability as a justified assertion, i.e. a conditional assessment based on task-relevant data and information, that may be thought of as a constrained subjective probability. This leads us to emphasise again the general conclusion that there is no gap between justified (or, reasonable) subjective probability and other concepts of probability in terms of its ability to provide assessments that are soundly based on whatever relevant information available. We also note that the challenges an expert faces in reporting probabilities apply equally to all interpretations of probability, not only to subjective probability.

The consequences of understanding expert probability reporting as a decision.

In this paper we reiterate that the personalist interpretation of probability is inevitable and as least as informed as any other allegedly more 'objective' definition of probability. We also argue that the problem faced by forensic scientists, the reporting on imperfect personal knowledge, in terms of probabilities, can be reconstructed as a decision problem. Tackling this problem through a rigorous decision theoretic analysis provides further argument in support of the view that optimal probability reporting is in terms of single numbers, not intervals.

Reframing the debate: A question of probability, not of likelihood ratio.

Evidential value is measured by a likelihood ratio. This ratio has two components, the probability, or probability density, of the evidence if the prosecution proposition is true and the probability (density) of the evidence if the defence proposition is true. It takes the form of a single value, even if these probabilities are subjective measures of belief of the reporting forensic scientist.

Analysis and evaluation of magnetism of black toners on documents printed by electrophotographic systems.

This paper reports on a study to assess the potential of measurements of magnetism, using a proprietary magnetic analysis system, for the routine analysis of toners on documents printed by black and white electrophotographic systems. Magnetic properties of black toners on documents printed by a number of different devices were measured and compared. Our results indicate that the analysis of magnetism is complementary to traditional methods for analysing black toners, such as FTIR. Further, we find that the analysis of magnetism is realistically applicable in closed set cases, that is when the number of potential printing devices can be clearly defined.

The decisionalization of individualization.

Throughout forensic science and adjacent branches, academic researchers and practitioners continue to diverge in their perception and understanding of the notion of 'individualization', that is the claim to reduce a pool of potential donors of a forensic trace to a single source. In particular, recent shifts to refer to the practice of individualization as a decision have been revealed as being a mere change of label [1], leaving fundamental changes in thought and understanding still pending. What is more, professional associations and practitioners shy away from embracing the notion of decision in terms of the formal theory of decision in which individualization may be framed, mainly because of difficulties to deal with the measurement of desirability or undesirability of the consequences of decisions (e.g., using utility functions). Building on existing research in the area, this paper presents and discusses fundamental concepts of utilities and losses with particular reference to their application to forensic individualization. The paper emphasizes that a proper appreciation of decision tools not only reduces the number of individual assignments that the application of decision theory requires, but also shows how such assignments can be meaningfully related to constituting features of the real-world decision problem to which the theory is applied. It is argued that the decisonalization of individualization requires such fundamental insight to initiate changes in the fields' underlying understandings, not merely in their label.

Statistical hypothesis testing and common misinterpretations: Should we abandon p-value in forensic science applications?

Many people regard the concept of hypothesis testing as fundamental to inferential statistics. Various schools of thought, in particular frequentist and Bayesian, have promoted radically different solutions for taking a decision about the plausibility of competing hypotheses. Comprehensive philosophical comparisons about their advantages and drawbacks are widely available and continue to span over large debates in the literature. More recently, controversial discussion was initiated by an editorial decision of a scientific journal [1] to refuse any paper submitted for publication containing null hypothesis testing procedures. Since the large majority of papers published in forensic journals propose the evaluation of statistical evidence based on the so called p-values, it is of interest to expose the discussion of this journal's decision within the forensic science community. This paper aims to provide forensic science researchers with a primer on the main concepts and their implications for making informed methodological choices.

Bayesian classification criterion for forensic multivariate data.

This study presents a classification criteria for two-class Cannabis seedlings. As the cultivation of drug type cannabis is forbidden in Switzerland, law enforcement authorities regularly ask laboratories to determine cannabis plant's chemotype from seized material in order to ascertain that the plantation is legal or not. In this study, the classification analysis is based on data obtained from the relative proportion of three major leaf compounds measured by gas-chromatography interfaced with mass spectrometry (GC-MS). The aim is to discriminate between drug type (illegal) and fiber type (legal) cannabis at an early stage of the growth. A Bayesian procedure is proposed: a Bayes factor is computed and classification is performed on the basis of the decision maker specifications (i.e. prior probability distributions on cannabis type and consequences of classification measured by losses). Classification rates are computed with two statistical models and results are compared. Sensitivity analysis is then performed to analyze the robustness of classification criteria.

Bayes factor for investigative assessment of selected handwriting features.

This paper extends previous research on the use of multivariate continuous data in comparative handwriting examinations, notably for gender classification. A database has been constructed by analyzing the contour shape of loop characters of type a and d by means of Fourier analysis, which allows characters to be described in a global way by a set of variables (e.g., Fourier descriptors). Sample handwritings were collected from right- and left-handed female and male writers. The results reported in this paper provide further arguments in support of the view that investigative settings in forensic science represent an area of application for which the Bayesian approach offers a logical framework. In particular, the Bayes factor is computed for settings that focus on inference of gender and handedness of the author of an incriminated handwritten text. An emphasis is placed on comparing the efficiency for investigative purposes of characters a and d.

Decision analysis for the genotype designation in low-template-DNA profiles.

What genotype should the scientist specify for conducting a database search to try to find the source of a low-template-DNA (lt-DNA) trace? When the scientist answers this question, he or she makes a decision. Here, we approach this decision problem from a normative point of view by defining a decision-theoretic framework for answering this question for one locus. This framework combines the probability distribution describing the uncertainty over the trace's donor's possible genotypes with a loss function describing the scientist's preferences concerning false exclusions and false inclusions that may result from the database search. According to this approach, the scientist should choose the genotype designation that minimizes the expected loss. To illustrate the results produced by this approach, we apply it to two hypothetical cases: (1) the case of observing one peak for allele xi on a single electropherogram, and (2) the case of observing one peak for allele xi on one replicate, and a pair of peaks for alleles xi and xj, i ≠ j, on a second replicate. Given that the probabilities of allele drop-out are defined as functions of the observed peak heights, the threshold values marking the turning points when the scientist should switch from one designation to another are derived in terms of the observed peak heights. For each case, sensitivity analyses show the impact of the model's parameters on these threshold values. The results support the conclusion that the procedure should not focus on a single threshold value for making this decision for all alleles, all loci and in all laboratories.

Decision-theoretic reflections on processing a fingermark.

A recent publication in this journal [1] presented the results of a field study that revealed the data provided by the fingermarks not processed in a forensic science laboratory. In their study, the authors were interested in the usefulness of this additional data in order to determine whether such fingermarks would have been worth submitting to the fingermark processing workflow. Taking these ideas as a starting point, this communication here places the fingermark in its context of a case brought before a court, and examines the question of processing or not processing a fingermark from a decision-theoretic point of view. The decision-theoretic framework presented provides an answer to this question in the form of a quantified expression of the expected value of information (EVOI) associated with the processed fingermark, which can then be compared with the cost of processing the mark.

Decision-theoretic analysis of forensic sampling criteria using bayesian decision networks.

Sampling issues represent a topic of ongoing interest to the forensic science community essentially because of their crucial role in laboratory planning and working protocols. For this purpose, forensic literature described thorough (bayesian) probabilistic sampling approaches. These are now widely implemented in practice. They allow, for instance, to obtain probability statements that parameters of interest (e.g., the proportion of a seizure of items that present particular features, such as an illegal substance) satisfy particular criteria (e.g., a threshold or an otherwise limiting value). Currently, there are many approaches that allow one to derive probability statements relating to a population proportion, but questions on how a forensic decision maker--typically a client of a forensic examination or a scientist acting on behalf of a client--ought actually to decide about a proportion or a sample size, remained largely unexplored to date. The research presented here intends to address methodology from decision theory that may help to cope usefully with the wide range of sampling issues typically encountered in forensic science applications. The procedures explored in this paper enable scientists to address a variety of concepts such as the (net) value of sample information, the (expected) value of sample information or the (expected) decision loss. All of these aspects directly relate to questions that are regularly encountered in casework. Besides probability theory and bayesian inference, the proposed approach requires some additional elements from decision theory that may increase the efforts needed for practical implementation. In view of this challenge, the present paper will emphasise the merits of graphical modelling concepts, such as decision trees and bayesian decision networks. These can support forensic scientists in applying the methodology in practice. How this may be achieved is illustrated with several examples. The graphical devices invoked here also serve the purpose of supporting the discussion of the similarities, differences and complementary aspects of existing bayesian probabilistic sampling criteria and the decision-theoretic approach proposed throughout this paper.

The database search problem: a question of rational decision making.

This paper applies probability and decision theory in the graphical interface of an influence diagram to study the formal requirements of rationality which justify the individualization of a person found through a database search. The decision-theoretic part of the analysis studies the parameters that a rational decision maker would use to individualize the selected person. The modeling part (in the form of an influence diagram) clarifies the relationships between this decision and the ingredients that make up the database search problem, i.e., the results of the database search and the different pairs of propositions describing whether an individual is at the source of the crime stain. These analyses evaluate the desirability associated with the decision of 'individualizing' (and 'not individualizing'). They point out that this decision is a function of (i) the probability that the individual in question is, in fact, at the source of the crime stain (i.e., the state of nature), and (ii) the decision maker's preferences among the possible consequences of the decision (i.e., the decision maker's loss function). We discuss the relevance and argumentative implications of these insights with respect to recent comments in specialized literature, which suggest points of view that are opposed to the results of our study.

Inference about the number of contributors to a DNA mixture: Comparative analyses of a Bayesian network approach and the maximum allele count method.

In the forensic examination of DNA mixtures, the question of how to set the total number of contributors (N) presents a topic of ongoing interest. Part of the discussion gravitates around issues of bias, in particular when assessments of the number of contributors are not made prior to considering the genotypic configuration of potential donors. Further complication may stem from the observation that, in some cases, there may be numbers of contributors that are incompatible with the set of alleles seen in the profile of a mixed crime stain, given the genotype of a potential contributor. In such situations, procedures that take a single and fixed number contributors as their output can lead to inferential impasses. Assessing the number of contributors within a probabilistic framework can help avoiding such complication. Using elements of decision theory, this paper analyses two strategies for inference on the number of contributors. One procedure is deterministic and focuses on the minimum number of contributors required to 'explain' an observed set of alleles. The other procedure is probabilistic using Bayes' theorem and provides a probability distribution for a set of numbers of contributors, based on the set of observed alleles as well as their respective rates of occurrence. The discussion concentrates on mixed stains of varying quality (i.e., different numbers of loci for which genotyping information is available). A so-called qualitative interpretation is pursued since quantitative information such as peak area and height data are not taken into account. The competing procedures are compared using a standard scoring rule that penalizes the degree of divergence between a given agreed value for N, that is the number of contributors, and the actual value taken by N. Using only modest assumptions and a discussion with reference to a casework example, this paper reports on analyses using simulation techniques and graphical models (i.e., Bayesian networks) to point out that setting the number of contributors to a mixed crime stain in probabilistic terms is, for the conditions assumed in this study, preferable to a decision policy that uses categoric assumptions about N.

The use of the likelihood ratio for evaluative and investigative purposes in comparative forensic handwriting examination.

This paper extends previous research and discussion on the use of multivariate continuous data, which are about to become more prevalent in forensic science. As an illustrative example, attention is drawn here on the area of comparative handwriting examinations. Multivariate continuous data can be obtained in this field by analysing the contour shape of loop characters through Fourier analysis. This methodology, based on existing research in this area, allows one describe in detail the morphology of character contours throughout a set of variables. This paper uses data collected from female and male writers to conduct a comparative analysis of likelihood ratio based evidence assessment procedures in both, evaluative and investigative proceedings. While the use of likelihood ratios in the former situation is now rather well established (typically, in order to discriminate between propositions of authorship of a given individual versus another, unknown individual), focus on the investigative setting still remains rather beyond considerations in practice. This paper seeks to highlight that investigative settings, too, can represent an area of application for which the likelihood ratio can offer a logical support. As an example, the inference of gender of the writer of an incriminated handwritten text is forwarded, analysed and discussed in this paper. The more general viewpoint according to which likelihood ratio analyses can be helpful for investigative proceedings is supported here through various simulations. These offer a characterisation of the robustness of the proposed likelihood ratio methodology.

Implementing statistical learning methods through Bayesian networks (Part 2): Bayesian evaluations for results of black toner analyses in forensic document examination.

This paper presents and discusses the use of Bayesian procedures - introduced through the use of Bayesian networks in Part I of this series of papers - for 'learning' probabilities from data. The discussion will relate to a set of real data on characteristics of black toners commonly used in printing and copying devices. Particular attention is drawn to the incorporation of the proposed procedures as an integral part in probabilistic inference schemes (notably in the form of Bayesian networks) that are intended to address uncertainties related to particular propositions of interest (e.g., whether or not a sample originates from a particular source). The conceptual tenets of the proposed methodologies are presented along with aspects of their practical implementation using currently available Bayesian network software.