Paolo Garbolino

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.

Evaluation of scientific evidence using Bayesian networks

Bayesian networks provide a valuable aid for representing epistemic relationships in a body of uncertain evidence. The paper proposes some simple Bayesian networks for standard analysis of patterns of inference concerning scientific evidence, with a discussion of the rationale behind the nets, the corresponding probabilistic formulas, and the required probability assessments.

A graphical model for the evaluation of cross-transfer evidence in DNA profiles

The role of graphical models in the assessment of transfer evidence is described with particular reference to the role of cross-transfer evidence. The issues involved in the determination of factors (nodes), associations (links) and probabilities to be included are discussed. Four types of subjective probabilities are of particular interest: those for transfer, persistence and recovery; innocent acquisition; relevance; innocent presence. Examples are given to illustrate the roles of various aspects of the suspects and victims lifestyle and the investigation of the evidence found on the suspect and victim in assessing the probability of ultimate issue, that the suspect committed the crime.

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.

Bayesian theory and artificial intelligence: the quarrelsome marriage

Abstract The problem of knowledge-base updating is addressed from an abstract point of view in the attempt to identify some general desiderata the updating mechanism should satisfy. They are recognized to be basically two: evaluating the local impact of new data on the single items of knowledge already stored, and propagating this effect through the knowledge-base maintaining at the same time its global coherence. It will be shown that Bayesian updating, difficult to implement, satisfies simultaneously these two requirements, and that, on the other hand, Dempster—Shafer updating, easy to implement, does not satisfy the requirement of global coherent propagation. I will point out the existence of a trade-off between coherence and effectiveness in the methods for representing uncertainty currently proposed in AI. Two kinds of learning machines, Boltzmann machines and Harmonium, will be discussed and considered as first attempts to give a non-behavioral characterization of coherence in a cognitive agent, a characterization still consistent with the behavioral (probabilistic) definition.

A comparison of some rules for probabilistic reasoning

Abstract Generalized Bayesian conditionals and Dempster-Shafers conditionals are considered as probabilistic kinematics which hold under different conditions. In particular, generalized Bayes can be applied whenever the available evidence allows to partition the frame of reference. It will be pointed out how, in this case, it is always possible to get a probability function by a belief function by means of minimum (relative) entropy kinematics.

Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science: Taroni/Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science

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The Scientification of Forensic Practice

Forensic science is traditionally defined as the science of individualization, but claim that forensic scientists are able to achieve conclusions of individualization has been criticized in recent years. Many scholars hold that perfect identification of a person or object as the source of trace or mark is unachievable and that opinions about the source are always probabilistic. From the very beginning, forensic science met statistics and probability theory, and its history provides a good case study of what Bernard Cohen has called the “probabilizing revolution” in science. The emergence of DNA typing has set up a major challenge for forensic practice, opening the door to the use of advanced statistical methods and putting in question the scientific status of traditional forensic methodologies.

Uncertainty about the true source. A note on the likelihood ratio at the activity level

This paper focuses on likelihood ratio based evaluations of fibre evidence in cases in which there is uncertainty about whether or not the reference item available for analysis - that is, an item typically taken from the suspect or seized at his home - is the item actually worn at the time of the offence. A likelihood ratio approach is proposed that, for situations in which certain categorical assumptions can be made about additionally introduced parameters, converges to formula described in existing literature. The properties of the proposed likelihood ratio approach are analysed through sensitivity analyses and discussed with respect to possible argumentative implications that arise in practice.