Alex Biedermann

Bayesian Networks and Probabilistic Inference in Forensic Science: Taroni/Bayesian Networks and Probabilistic Inference in Forensic Science

Preface. Foreword. 1. The logic of uncertainty. 1.1 Uncertainty and probability. 1.2 Reasoning under uncertainty. 1.3 Frequencies and probabilities. 1.4 Induction and probability. 1.5 Further readings. 2. The logic of Bayesian networks. 2.1 Reasoning with graphical models. 2.2 Reasoning with Bayesian networks. 2.3 Further readings. 3. Evaluation of scientific evidence. 3.1 Introduction. 3.2 The value of evidence. 3.3 Relevant propositions. 3.4 Pre-assessment of the case. 3.5 Evaluation using graphical models. 4. Bayesian networks for evaluating scientific evidence. 4.1 Issues in one-trace transfer cases. 4.2 When evidence has more than one component: footwear marks evidence. 4.3 Scenarios with more than one stain. 5. DNA evidence. 5.1 DNA likelihood ratio. 5.2 Network approaches to the DNA likelihood ratio. 5.3 Missing suspect. 5.4 Analysis when the alternative proposition is that a sibling of the suspect left the stain. 5.5 Interpretation with more than two propositions. 5.6 Evaluation of evidence with more than two propositions. 5.7 Partial matches. 5.8 Mixtures. 5.9 Relatedness testing. 5.10 Database search. 5.11 Error rates. 5.12 Sub-population and co-ancestry coefficient. 5.13 Further reading. 6. Transfer evidence. 6.1 Assessment of transfer evidence under crime level propositions. 6.2 Assessment of transfer evidence under activity level propositions. 6.3 Cross- or two-way transfer of evidential material. 6.4 Increasing the level of detail of selected nodes. 6.5 Missing evidence. 7. Aspects of the combination of evidence. 7.1 Introduction. 7.2 A difficulty in combining evidence. 7.3 The likelihood ratio and the combination of evidence. 7.4 Combination of distinct items of evidence. 8. Pre-assessment. 8.1 Introduction. 8.2 Pre-assessment. 8.3 Pre-assessment for a fibres scenario. 8.4 Pre-assessment in a cross-transfer scenario. 8.5 Pre-assessment with multiple propositions. 8.6 Remarks. 9. Qualitative and sensitivity analyses. 9.1 Qualitative probability models. 9.2 Sensitivity analyses. 10. Continuous networks. 10.1 Introduction. 10.2 Samples and estimates. 10.3 Measurements. 10.4 Use of a continuous distribution which is not normal. 10.5 Appendix. 11. Further applications. 11.1 Offender profiling. 11.2 Decision making. Bibliography. Author Index. Subject Index.

Data analysis in forensic science: a Bayesian decision perspective

Foreword. Preface. I The Foundations of Inference and Decision in Forensic Science. 1 Introduction. 1.1 The Inevitability of Uncertainty. 1.2 Desiderata in Evidential Assessment. 1.3 The Importance of the Propositional Framework and the Nature of Evidential Assessment. 1.4 From Desiderata to Applications. 1.5 The Bayesian Core of Forensic Science. 1.6 Structure of the Book. 2 Scientific Reasoning and Decision Making. 2.1 Coherent Reasoning Under Uncertainty. 2.2 Coherent Decision Making Under Uncertainty of Reasoning. 2.3 Scientific Reasoning as Coherent Decision Making. 2.4 Forensic Reasoning as Coherent Decision Making. 3 Concepts of Statistical Science and Decision Theory. 3.1 Random Variables and Distribution Functions. 3.2 Statistical Inference and Decision Theory. 3.3 The Bayesian Paradigm. 3.4 Bayesian Decision Theory. 3.5 R Code. II Forensic Data Analysis. 4 Point Estimation. 4.1 Introduction. 4.2 Bayesian Decision for a Proportion. 4.3 Bayesian Decision for a Poisson Mean. 4.4 Bayesian Decision for Normal Mean. 4.5 R Code. 5 Credible Intervals. 5.1 Introduction. 5.2 Credible Intervals. 5.3 Decision-Theoretic Evaluation of Credible Intervals. 5.4 R Code. 6 Hypothesis Testing. 6.1 Introduction. 6.2 Bayesian Hypothesis Testing. 6.3 One-sided testing. 6.4 Two-Sided Testing. 6.5 R Code. 7 Sampling. 7.1 Introduction. 7.2 Sampling Inspection. 7.3 Graphical Models for Sampling Inspection. 7.4 Sampling Inspection under a Decision-Theoretic Approach. 7.5 R Code. 8 Classification of Observations. 8.1 Introduction. 8.2 Standards of Coherent Classification. 8.3 Comparing Models using Discrete Data. 8.4 Comparison of Models using Continuous Data. 8.5 Non-Normal Distributions and Cocaine on Bank Notes. 8.6 A note on Multivariate Continuous Data. 8.7 R Code. 9 Bayesian Forensic Data Analysis: Conclusions and Implications. 9.1 Introduction. 9.2 What is the Past and Current Position of Statistics in Forensic Science? 9.3 Why Should Forensic Scientists Conform to a Bayesian Framework for Inference and Decision Making? 9.4 Why Regard Probability as a Personal Degree of Belief? 9.5 Why Should Scientists be Aware of Decision Analysis? 9.6 How to Implement Bayesian Inference and Decision Analysis? A Discrete Distributions. B Continuous Distributions. Bibliography. Author Index. Subject Index.

Probabilistic evidential assessment of gunshot residue particle evidence (Part I): Likelihood ratio calculation and case pre-assessment using Bayesian networks

Well developed experimental procedures currently exist for retrieving and analyzing particle evidence from hands of individuals suspected of being associated with the discharge of a firearm. Although analytical approaches (e.g. automated Scanning Electron Microscopy with Energy Dispersive X-ray (SEM-EDS) microanalysis) allow the determination of the presence of elements typically found in gunshot residue (GSR) particles, such analyses provide no information about a given particles actual source. Possible origins for which scientists may need to account for are a primary exposure to the discharge of a firearm or a secondary transfer due to a contaminated environment. In order to approach such sources of uncertainty in the context of evidential assessment, this paper studies the construction and practical implementation of graphical probability models (i.e. Bayesian networks). These can assist forensic scientists in making the issue tractable within a probabilistic perspective. The proposed models focus on likelihood ratio calculations at various levels of detail as well as case pre-assessment.

Probabilistic evidential assessment of gunshot residue particle evidence (Part II): Bayesian parameter estimation for experimental count data

Part I of this series of articles focused on the construction of graphical probabilistic inference procedures, at various levels of detail, for assessing the evidential value of gunshot residue (GSR) particle evidence. The proposed models--in the form of Bayesian networks--address the issues of background presence of GSR particles, analytical performance (i.e., the efficiency of evidence searching and analysis procedures) and contamination. The use and practical implementation of Bayesian networks for case pre-assessment is also discussed. This paper, Part II, concentrates on Bayesian parameter estimation. This topic complements Part I in that it offers means for producing estimates usable for the numerical specification of the proposed probabilistic graphical models. Bayesian estimation procedures are given a primary focus of attention because they allow the scientist to combine (his/her) prior knowledge about the problem of interest with newly acquired experimental data. The present paper also considers further topics such as the sensitivity of the likelihood ratio due to uncertainty in parameters and the study of likelihood ratio values obtained for members of particular populations (e.g., individuals with or without exposure to GSR).

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.

Two Items of Evidence, No Putative Source: An Inference Problem in Forensic Intelligence

ABSTRACT: Intelligence analysts commonly associate cases on the basis of similarities found in compared characteristics of scientific evidence. The present paper studies some of the inferential difficulties associated with such operations. An analysis is proposed that breaks down the reasoning process into inference to common source, and inference to case linkage. The former requires an approach to the difficulty associated with evaluating the similarities of items of evidence from different cases with no putative source being available. The latter requires consideration to be given to the relevance of evidence. Throughout the paper, probability theory is used to describe the nature of the proposed inferences. Graphical models are also introduced with the aim of providing further insight into the dependence and independence relationships assumed to hold among the various propositions considered. Notions from decision theory are used to discuss ways in which intelligence analysts may assist investigators in deciding whether or not cases should be considered as linked.

Bayesian Networks and the Value of the Evidence for the Forensic Two‐Trace Transfer Problem*

Abstract:  Forensic scientists face increasingly complex inference problems for evaluating likelihood ratios (LRs) for an appropriate pair of propositions. Up to now, scientists and statisticians have derived LR formulae using an algebraic approach. However, this approach reaches its limits when addressing cases with an increasing number of variables and dependence relationships between these variables. In this study, we suggest using a graphical approach, based on the construction of Bayesian networks (BNs). We first construct a BN that captures the problem, and then deduce the expression for calculating the LR from this model to compare it with existing LR formulae. We illustrate this idea by applying it to the evaluation of an activity level LR in the context of the two‐trace transfer problem. Our approach allows us to relax assumptions made in previous LR developments, produce a new LR formula for the two‐trace transfer problem and generalize this scenario to n traces.

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.

Helping to distinguish primary from secondary transfer events for trace DNA

DNA is routinely recovered in criminal investigations. The sensitivity of laboratory equipment and DNA profiling kits means that it is possible to generate DNA profiles from very small amounts of cellular material. As a consequence, it has been shown that DNA we detect may not have arisen from a direct contact with an item, but rather through one or more intermediaries. Naturally the questions arising in court, particularly when considering trace DNA, are of how DNA may have come to be on an item. While scientists cannot directly answer this question, forensic biological results can help in discriminating between alleged activities. Much experimental research has been published showing the transfer and persistence of DNA under varying conditions, but as of yet the results of these studies have not been combined to deal with broad questions about transfer mechanisms. In this work we use published data and Bayesian networks to develop a statistical logical framework by which questions of transfer mechanism can be approached probabilistically. We also identify a number of areas where further work could be carried out in order to improve our knowledge base when helping to address questions about transfer mechanisms. Finally, we apply the constructed Bayesian network to ground truth known data to determine if, with current knowledge, there is any power in DNA quantities to distinguish primary and secondary transfer events.

Evaluation of Forensic DNA Traces When Propositions of Interest Relate to Activities: Analysis and Discussion of Recurrent Concerns

When forensic scientists evaluate and report on the probative strength of single DNA traces, they commonly rely on only one number, expressing the rarity of the DNA profile in the population of interest. This is so because the focus is on propositions regarding the source of the recovered trace material, such as “the person of interest is the source of the crime stain.” In particular, when the alternative proposition is “an unknown person is the source of the crime stain,” one is directed to think about the rarity of the profile. However, in the era of DNA profiling technology capable of producing results from small quantities of trace material (i.e., non-visible staining) that is subject to easy and ubiquitous modes of transfer, the issue of source is becoming less central, to the point that it is often not contested. There is now a shift from the question “whose DNA is this?” to the question “how did it get there?” As a consequence, recipients of expert information are now very much in need of assistance with the evaluation of the meaning and probative strength of DNA profiling results when the competing propositions of interest refer to different activities. This need is widely demonstrated in day-to-day forensic practice and is also voiced in specialized literature. Yet many forensic scientists remain reluctant to assess their results given propositions that relate to different activities. Some scientists consider evaluations beyond the issue of source as being overly speculative, because of the lack of relevant data and knowledge regarding phenomena and mechanisms of transfer, persistence and background of DNA. Similarly, encouragements to deal with these activity issues, expressed in a recently released European guideline on evaluative reporting (Willis et al., 2015), which highlights the need for rethinking current practice, are sometimes viewed skeptically or are not considered feasible. In this discussion paper, we select and discuss recurrent skeptical views brought to our attention, as well as some of the alternative solutions that have been suggested. We will argue that the way forward is to address now, rather than later, the challenges associated with the evaluation of DNA results (from small quantities of trace material) in light of different activities to prevent them being misrepresented in court.