Silvia Bozza

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.

Decision analysis in forensic science.

Forensic scientists are routinely faced with the problems of making decisions under circumstances of uncertainty (i.e., to perform or not perform a test). A decision making model in forensic science is proposed, illustrated with an example from the field of forensic genetics. The approach incorporates available evidence and associated uncertainties with the assessment of utilities (or desirability of the consequences). The paper examines a general example for which identification will be made of the decision maker, the possible actions, the uncertain states of nature, the possible source of evidence and the kind of utility assessments required. It is argued that a formal approach can help to clarify the decision process and give a coherent means of combining elements to reach a decision.

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).

Handwriting Evidence Evaluation Based on the Shape of Characters: Application of Multivariate Likelihood Ratios*,†

Abstract:  A novel Bayesian methodology has been developed to quantitatively assess handwriting evidence by means of a likelihood ratio (LR) designed for multivariate data. This methodology is presented and its applicability is shown through a simulated case of a threatening anonymous text where a suspect is apprehended. The shape of handwritten characters a, d, o, and q of the threatening text was compared with characters of the true writer, and then with two other writers, one with similar and one with dissimilar characters shape compared to the true writer. In each of these three situations, 100 draws of characters were made and the resulting distributions of LR were established to consider the natural handwriting variation. LR values supported the correct hypothesis in every case. This original Bayesian methodology provides a coherent and rigorous tool for the assessment of handwriting evidence, contributing undoubtedly to integrate the field of handwriting examination into science.

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.

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.