Bayesian networks and the evaluation of scientific evidence in forensic science

Résumé Ce travail de thèse étudie des moyens de formalisation permettant d'assister l'expert forensique dans la gestion des facteurs influençant l'évaluation des indices scientifiques, tout en respectant des procédures d'inférence établies et acceptables. Selon une vue préconisée par une partie majoritaire de la littérature forensique et juridique - adoptée ici sans réserve comme point de départ - la conceptualisation d'une procédure évaluative est dite 'cohérente' lors qu'elle repose sur une implémentation systématique de la théorie des probabilités. Souvent, par contre, la mise en oeuvre du raisonnement probabiliste ne découle pas de manière automatique et peut se heurter à des problèmes de complexité, dus, par exemple, à des connaissances limitées du domaine en question ou encore au nombre important de facteurs pouvant entrer en ligne de compte. En vue de gérer ce genre de complications, le présent travail propose d'investiguer une formalisation de la théorie des probabilités au moyen d'un environment graphique, connu sous le nom de Réseaux bayesiens (Bayesian networks). L'hypothèse principale que cette recherche envisage d'examiner considère que les Réseaux bayesiens, en concert avec certains concepts accessoires (tels que des analyses qualitatives et de sensitivité), constituent une ressource clé dont dispose l'expert forensique pour approcher des problèmes d'inférence de manière cohérente, tant sur un plan conceptuel que pratique. De cette hypothèse de travail, des problèmes individuels ont été extraits, articulés et abordés dans une série de recherches distinctes, mais interconnectées, et dont les résultats - publiés dans des revues à comité de lecture - sont présentés sous forme d'annexes. D'un point de vue général, ce travail apporte trois catégories de résultats. Un premier groupe de résultats met en évidence, sur la base de nombreux exemples touchant à des domaines forensiques divers, l'adéquation en termes de compatibilité et complémentarité entre des modèles de Réseaux bayesiens et des procédures d'évaluation probabilistes existantes. Sur la base de ces indications, les deux autres catégories de résultats montrent, respectivement, que les Réseaux bayesiens permettent également d'aborder des domaines auparavant largement inexplorés d'un point de vue probabiliste et que la disponibilité de données numériques dites 'dures' n'est pas une condition indispensable pour permettre l'implémentation des approches proposées dans ce travail. Le présent ouvrage discute ces résultats par rapport à la littérature actuelle et conclut en proposant les Réseaux bayesiens comme moyen d'explorer des nouvelles voies de recherche, telles que l'étude de diverses formes de combinaison d'indices ainsi que l'analyse de la prise de décision. Pour ce dernier aspect, l'évaluation des probabilités constitue, dans la façon dont elle est préconisée dans ce travail, une étape préliminaire fondamentale de même qu'un moyen opérationnel.

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 particle's 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.

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

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.

A new poly(ortho ester)-based drug delivery system as an adjunct treatment in filtering surgery.

PURPOSE: Pharmacologic modulation of wound healing after glaucoma filtering surgery remains a major clinical challenge in ophthalmology. Poly(ortho ester) (POE) is a bioerodible and biocompatible viscous polymer potentially useful as a sustained drug delivery system that allows the frequency of intraocular injections to be reduced. The purpose of this study was to determine the efficacy of POE containing a precise amount of 5-fluorouracil (5-FU) in an experimental model of filtering surgery in the rabbit. METHODS: Trabeculectomy was performed in pigmented rabbit eyes. An ointmentlike formulation of POE containing 1% wt/wt 5-FU was injected subconjunctivally at the site of surgery, during the procedure. Intraocular pressure (IOP), bleb persistence, and ocular inflammatory reaction were monitored until postoperative day 30. Quantitative analysis of 5-FU was performed in the anterior chamber. Histologic analysis was used to assess the appearance of the filtering fistula and the polymer's biocompatibility. RESULTS: The decrease in IOP from baseline and the persistence of the filtering bleb were significantly more marked in the 5-FU-treated eyes during postoperative days 9 through 28. Corneal toxicity triggered by 5-FU was significantly lower in the group that received 5-FU in POE compared with a 5-FU tamponade. Histopathologic evaluation showed that POE was well tolerated, and no fibrosis occurred in eyes treated with POE containing 5-FU. CONCLUSIONS: In this rabbit model of trabeculectomy, the formulation based on POE and containing a precise amount of 5-FU reduced IOP and prolonged bleb persistence in a way similar to the conventional method of a 5-FU tamponade, while significantly reducing 5-FU toxicity.

Spatial prediction of monthly wind speeds in complex terrain with adaptive general regression neural networks

This paper presents the general regression neural networks (GRNN) as a nonlinear regression method for the interpolation of monthly wind speeds in complex Alpine orography. GRNN is trained using data coming from Swiss meteorological networks to learn the statistical relationship between topographic features and wind speed. The terrain convexity, slope and exposure are considered by extracting features from the digital elevation model at different spatial scales using specialised convolution filters. A database of gridded monthly wind speeds is then constructed by applying GRNN in prediction mode during the period 1968-2008. This study demonstrates that using topographic features as inputs in GRNN significantly reduces cross-validation errors with respect to low-dimensional models integrating only geographical coordinates and terrain height for the interpolation of wind speed. The spatial predictability of wind speed is found to be lower in summer than in winter due to more complex and weaker wind-topography relationships. The relevance of these relationships is studied using an adaptive version of the GRNN algorithm which allows to select the useful terrain features by eliminating the noisy ones. This research provides a framework for extending the low-dimensional interpolation models to high-dimensional spaces by integrating additional features accounting for the topographic conditions at multiple spatial scales. Copyright (c) 2012 Royal Meteorological Society.

Coordination on Networks: Does Topology Matter?

Effective coordination is key to many situations that affect the well-being of two or more humans. Social coordination can be studied in coordination games between individuals located on networks of contacts. We study the behavior of humans in the laboratory when they play the Stag Hunt game - a game that has a risky but socially efficient equilibrium and an inefficient but safe equilibrium. We contrast behavior on a cliquish network to behavior on a random network. The cliquish network is highly clustered and resembles more closely to actual social networks than the random network. In contrast to simulations, we find that human players dynamics do not converge to the efficient outcome more often in the cliquish network than in the random network. Subjects do not use pure myopic best-reply as an individual update rule. Numerical simulations agree with laboratory results once we implement the actual individual updating rule that human subjects use in our laboratory experiments.

Contribution of neural networks to Alzheimer disease's progression.

The neuropathology of Alzheimer disease is characterized by senile plaques, neurofibrillary tangles and cell death. These hallmarks develop according to the differential vulnerability of brain networks, senile plaques accumulating preferentially in the associative cortical areas and neurofibrillary tangles in the entorhinal cortex and the hippocampus. We suggest that the main aetiological hypotheses such as the beta-amyloid cascade hypothesis or its variant, the synaptic beta-amyloid hypothesis, will have to consider neural networks not just as targets of degenerative processes but also as contributors of the disease's progression and of its phenotype. Three domains of research are highlighted in this review. First, the cerebral reserve and the redundancy of the network's elements are related to brain vulnerability. Indeed, an enriched environment appears to increase the cerebral reserve as well as the threshold of disease's onset. Second, disease's progression and memory performance cannot be explained by synaptic or neuronal loss only, but also by the presence of compensatory mechanisms, such as synaptic scaling, at the microcircuit level. Third, some phenotypes of Alzheimer disease, such as hallucinations, appear to be related to progressive dysfunction of neural networks as a result, for instance, of a decreased signal to noise ratio, involving a diminished activity of the cholinergic system. Overall, converging results from studies of biological as well as artificial neural networks lead to the conclusion that changes in neural networks contribute strongly to Alzheimer disease's progression.

Local optima networks of hard combinatorial landscapes

Combinatorial optimization involves finding an optimal solution in a finite set of options; many everyday life problems are of this kind. However, the number of options grows exponentially with the size of the problem, such that an exhaustive search for the best solution is practically infeasible beyond a certain problem size. When efficient algorithms are not available, a practical approach to obtain an approximate solution to the problem at hand, is to start with an educated guess and gradually refine it until we have a good-enough solution. Roughly speaking, this is how local search heuristics work. These stochastic algorithms navigate the problem search space by iteratively turning the current solution into new candidate solutions, guiding the search towards better solutions. The search performance, therefore, depends on structural aspects of the search space, which in turn depend on the move operator being used to modify solutions. A common way to characterize the search space of a problem is through the study of its fitness landscape, a mathematical object comprising the space of all possible solutions, their value with respect to the optimization objective, and a relationship of neighborhood defined by the move operator. The landscape metaphor is used to explain the search dynamics as a sort of potential function. The concept is indeed similar to that of potential energy surfaces in physical chemistry. Borrowing ideas from that field, we propose to extend to combinatorial landscapes the notion of the inherent network formed by energy minima in energy landscapes. In our case, energy minima are the local optima of the combinatorial problem, and we explore several definitions for the network edges. At first, we perform an exhaustive sampling of local optima basins of attraction, and define weighted transitions between basins by accounting for all the possible ways of crossing the basins frontier via one random move. Then, we reduce the computational burden by only counting the chances of escaping a given basin via random kick moves that start at the local optimum. Finally, we approximate network edges from the search trajectory of simple search heuristics, mining the frequency and inter-arrival time with which the heuristic visits local optima. Through these methodologies, we build a weighted directed graph that provides a synthetic view of the whole landscape, and that we can characterize using the tools of complex networks science. We argue that the network characterization can advance our understanding of the structural and dynamical properties of hard combinatorial landscapes. We apply our approach to prototypical problems such as the Quadratic Assignment Problem, the NK model of rugged landscapes, and the Permutation Flow-shop Scheduling Problem. We show that some network metrics can differentiate problem classes, correlate with problem non-linearity, and predict problem hardness as measured from the performances of trajectory-based local search heuristics.

Implicit methods for qualitative modeling of gene regulatory networks.

Advancements in high-throughput technologies to measure increasingly complex biological phenomena at the genomic level are rapidly changing the face of biological research from the single-gene single-protein experimental approach to studying the behavior of a gene in the context of the entire genome (and proteome). This shift in research methodologies has resulted in a new field of network biology that deals with modeling cellular behavior in terms of network structures such as signaling pathways and gene regulatory networks. In these networks, different biological entities such as genes, proteins, and metabolites interact with each other, giving rise to a dynamical system. Even though there exists a mature field of dynamical systems theory to model such network structures, some technical challenges are unique to biology such as the inability to measure precise kinetic information on gene-gene or gene-protein interactions and the need to model increasingly large networks comprising thousands of nodes. These challenges have renewed interest in developing new computational techniques for modeling complex biological systems. This chapter presents a modeling framework based on Boolean algebra and finite-state machines that are reminiscent of the approach used for digital circuit synthesis and simulation in the field of very-large-scale integration (VLSI). The proposed formalism enables a common mathematical framework to develop computational techniques for modeling different aspects of the regulatory networks such as steady-state behavior, stochasticity, and gene perturbation experiments.

Multimodal MRI analysis of structural and functional networks in the human brain : application to two clinical studies : driving abilities under THC intoxication and early white matter changes in FXTAS

Les approches multimodales dans l'imagerie cérébrale non invasive sont de plus en plus considérées comme un outil indispensable pour la compréhension des différents aspects de la structure et de la fonction cérébrale. Grâce aux progrès des techniques d'acquisition des images de Resonance Magnetique et aux nouveaux outils pour le traitement des données, il est désormais possible de mesurer plusieurs paramètres sensibles aux différentes caractéristiques des tissues cérébraux. Ces progrès permettent, par exemple, d'étudier les substrats anatomiques qui sont à la base des processus cognitifs ou de discerner au niveau purement structurel les phénomènes dégénératifs et développementaux. Cette thèse met en évidence l'importance de l'utilisation d'une approche multimodale pour étudier les différents aspects de la dynamique cérébrale grâce à l'application de cette approche à deux études cliniques: l'évaluation structurelle et fonctionnelle des effets aigus du cannabis fumé chez des consommateurs réguliers et occasionnels, et l'évaluation de l'intégrité de la substance grise et blanche chez des jeunes porteurs de la prémutations du gène FMR1 à risque de développer le FXTAS (Fragile-X Tremor Ataxia Syndrome). Nous avons montré que chez les fumeurs occasionnels de cannabis, même à faible concentration du principal composant psychoactif (THC) dans le sang, la performance lors d'une tâche visuo-motrice est fortement diminuée, et qu'il y a des changements dans l'activité des trois réseaux cérébraux impliqués dans les processus cognitifs: le réseau de saillance, le réseau du contrôle exécutif, et le réseau actif par défaut (Default Mode). Les sujets ne sont pas en mesure de saisir les saillances dans l'environnement et de focaliser leur attention sur la tâche. L'augmentation de la réponse hémodynamique dans le cortex cingulaire antérieur suggère une augmentation de l'activité introspective. Une investigation des ef¬fets au niveau cérébral d'une exposition prolongée au cannabis, montre des changements persistants de la substance grise dans les régions associées à la mémoire et au traitement des émotions. Le niveau d'atrophie dans ces structures corrèle avec la consommation de cannabis au cours des trois mois précédant l'étude. Dans la deuxième étude, nous démontrons des altérations structurelles des décennies avant l'apparition du syndrome FXTAS chez des sujets jeunes, asymptomatiques, et porteurs de la prémutation du gène FMR1. Les modifications trouvées peuvent être liées à deux mécanismes différents. Les altérations dans le réseau moteur du cervelet et dans la fimbria de l'hippocampe, suggèrent un effet développemental de la prémutation. Elles incluent aussi une atrophie de la substance grise du lobule VI du cervelet et l'altération des propriétés tissulaires de la substance blanche des projections afférentes correspondantes aux pédoncules cérébelleux moyens. Les lésions diffuses de la substance blanche cérébrale peu¬vent être un marquer précoce du développement de la maladie, car elles sont liées à un phénomène dégénératif qui précède l'apparition des symptômes du FXTAS. - Multimodal brain imaging is becoming a leading tool for understanding different aspects of brain structure and function. Thanks to the advances in Magnetic Resonance imaging (MRI) acquisition schemes and data processing techniques, it is now possible to measure different parameters sensitive to different tissue characteristics. This allows for example to investigate anatomical substrates underlying cognitive processing, or to disentangle, at a pure structural level degeneration and developmental processes. This thesis highlights the importance of using a multimodal approach for investigating different aspects of brain dynamics by applying this approach to two clinical studies: functional and structural assessment of the acute effects of cannabis smoking in regular and occasional users, and grey and white matter assessment in young FMR1 premutation carriers at risk of developing FXTAS. We demonstrate that in occasional smokers cannabis smoking, even at low concentration of the main psychoactive component (THC) in the blood, strongly decrease subjects' performance on a visuo-motor tracking task, and globally alters the activity of the three brain networks involved in cognitive processing: the Salience, the Control Executive, and the Default Mode networks. Subjects are unable to capture saliences in the environment and to orient attention to the task; the increase in Hemodynamic Response in the Anterior Cingulate Cortex suggests an increase in self-oriented mental activity. A further investigation on long term exposure to cannabis, shows a persistent grey matter modification in brain regions associated with memory and affective processing. The degree of atrophy in these structures also correlates with the estimation of drug use in the three months prior the participation to the study. In the second study we demonstrate structural changes in young asymptomatic premutation carriers decades before the onset of FXTAS that might be related to two different mechanisms. Alteration of the cerebellar motor network and of the hippocampal fimbria/ fornix, may reflect a potential neurodevelopmental effect of the premutation. These include grey matter atrophy in lobule VI and modification of white matter tissue property in the corresponding afferent projections through the Middle Cerebellar Peduncles. Diffuse hemispheric white matter lesions that seem to appear closer to the onset of FXTAS and be related to a neurodegenerative phenomenon may mark the imminent onset of FXTAS.