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.

Neural networks complemented with genetic algorithms and fuzzy systems for predicting nitrogenous effluent variables in wastewater treatment plants

This work focuses on the prediction of the two main nitrogenous variables that describe the water quality at the effluent of a Wastewater Treatment Plant. We have developed two kind of Neural Networks architectures based on considering only one output or, in the other hand, the usual five effluent variables that define the water quality: suspended solids, biochemical organic matter, chemical organic matter, total nitrogen and total Kjedhal nitrogen. Two learning techniques based on a classical adaptative gradient and a Kalman filter have been implemented. In order to try to improve generalization and performance we have selected variables by means genetic algorithms and fuzzy systems. The training, testing and validation sets show that the final networks are able to learn enough well the simulated available data specially for the total nitrogen

Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.

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.

Efficiency of informational transfer in regular and complex networks

We analyze the process of informational exchange through complex networks by measuring network efficiencies. Aiming to study nonclustered systems, we propose a modification of this measure on the local level. We apply this method to an extension of the class of small worlds that includes declustered networks and show that they are locally quite efficient, although their clustering coefficient is practically zero. Unweighted systems with small-world and scale-free topologies are shown to be both globally and locally efficient. Our method is also applied to characterize weighted networks. In particular we examine the properties of underground transportation systems of Madrid and Barcelona and reinterpret the results obtained for the Boston subway network.

Models of social networks based on social distance attachment

We propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance. Social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space. We derive analytical results (corroborated by extensive numerical simulations), showing that the model reproduces the main statistical characteristics of real social networks: large clustering coefficient, positive degree correlations, and the emergence of a hierarchy of communities. The model is confronted with the social network formed by people that shares confidential information using the Pretty Good Privacy (PGP) encryption algorithm, the so-called web of trust of PGP.

Extensor carpi ulnaris accessory tendinous slips (ECUATS): MRI features at 3.0T and correlation with tendinosis : 49

Purpose: To assess the visibility and the features of ECUATS on 3.0-T MRI studies, and evaluate their correlation with tendinosis. Methods and materials: Our retrospective study was approved by IRB, with waiver of informed consent. Fifty wrist MRI and 48 MR arthrographies from 98 patients (55 males, 43 females, mean age 42.3 years) performed between January and November 2009 on 3.0-T units were reviewed. Images (transverse T1, T2, FS Gd T1 and VIBE) were independently analyzed by two radiologists, and a consensus reached with a third reader in case of disagreement. The visibility of ECUATS was assessed on each available transverse sequence. When present, ECUATS' origins, diameters and insertions were noted. ECU tendinosis was also evaluated. Inter-rater agreement was assessed using Cohen's Kappa coefficient. Results: ECUATS observed prevalence was 23.5% (23/98). ECUATS were more frequently noted on the VIBE sequence, with a good inter-rater agreement (Kappa = 0.72). Origins were noted in 95.7% of cases: 3 were at the level of, and 20 distal to ECU subsheath. Insertions were seen in 43.5%: 2 were on 5th metacarpal bone, 8 on extensor apparatus of 5th finger. ECUATS mean shortest and longest diameters were 0.54 and 0.85 mm respectively. ECU tendinosis was statistically more frequently noted in patients with ECUATS (p <0.05). Conclusion: ECUATS are readily visible on 3.0-T MRI studies, especially on transverse GRE VIBE images. ECU tendinosis is more frequently noted in patients bearing ECUATS.

Empirical study of correlated survival times for recurrent events with proportional hazards margins and the effect of correlation and censoring.

Background: In longitudinal studies where subjects experience recurrent incidents over a period of time, such as respiratory infections, fever or diarrhea, statistical methods are required to take into account the within-subject correlation. Methods: For repeated events data with censored failure, the independent increment (AG), marginal (WLW) and conditional (PWP) models are three multiple failure models that generalize Cox"s proportional hazard model. In this paper, we revise the efficiency, accuracy and robustness of all three models under simulated scenarios with varying degrees of within-subject correlation, censoring levels, maximum number of possible recurrences and sample size. We also study the methods performance on a real dataset from a cohort study with bronchial obstruction. Results: We find substantial differences between methods and there is not an optimal method. AG and PWP seem to be preferable to WLW for low correlation levels but the situation reverts for high correlations. Conclusions: All methods are stable in front of censoring, worsen with increasing recurrence levels and share a bias problem which, among other consequences, makes asymptotic normal confidence intervals not fully reliable, although they are well developed theoretically.

Detection and chemical profiling of medicine counterfeits by Raman spectroscopy and chemometrics

Raman spectroscopy combined with chemometrics has recently become a widespread technique for the analysis of pharmaceutical solid forms. The application presented in this paper is the investigation of counterfeit medicines. This increasingly serious issue involves networks that are an integral part of industrialized organized crime. Efficient analytical tools are consequently required to fight against it. Quick and reliable authentication means are needed to allow the deployment of measures from the company and the authorities. For this purpose a method in two steps has been implemented here. The first step enables the identification of pharmaceutical tablets and capsules and the detection of their counterfeits. A nonlinear classification method, the Support Vector Machines (SVM), is computed together with a correlation with the database and the detection of Active Pharmaceutical Ingredient (API) peaks in the suspect product. If a counterfeit is detected, the second step allows its chemical profiling among former counterfeits in a forensic intelligence perspective. For this second step a classification based on Principal Component Analysis (PCA) and correlation distance measurements is applied to the Raman spectra of the counterfeits.

Correlation of Locally-Based Performance of Asphalts with Their Physicochemical Parameters, Progress Report 2, HR-298, 1989

This project was undertaken to study the relationships between the performance of locally available asphalts and their physicochemical properties under Iowa conditions with the ultimate objective of development of a locally and performance-based asphalt specification for durable pavements. Physical and physicochemical tests were performed on three sets of asphalt samples including: (a) twelve samples from local asphalt suppliers and their TFOT residues, (b) six core samples of known service records, and (c) a total of 79 asphalts from 10 pavement projects including original, lab aged and recovered asphalts from field mixes, as well as from lab aged mixes. Tests included standard rheological tests, HP-GPC and TMA. Some specific viscoelastic tests (at 5 deg C) were run on b samples and on some a samples. DSC and X-ray diffraction studies were performed on a and b samples. Furthermore, NMR techniques were applied to some a, b and c samples. Efforts were made to identify physicochemical properties which are correlated to physical properties known to affect field performance. The significant physicochemical parameters were used as a basis for an improved performance-based trial specification for Iowa to ensure more durable pavements.

Correlation of physical and chemical attributes of soil with sugarcane yield

The objective of this work was to evaluate the correlation between sugarcane yield and some physical and chemical attributes of soil. For this, a 42‑ha test area in Araras, SP, Brazil, was used. Soil properties were determined from samples collected at the beginning of the 2003/2004 harvest season, using a regular 100x100 m grid. Yield assessment was done with a yield monitor (Simprocana). Correlation analyses were performed between sugarcane yield and the following soil properties: pH, pH CaCl2, N, C, cone index, clay content, soil organic matter, P, K, Ca, Mg, H+AL, cation exchange capacity, and base saturation. Correlation coefficients were respectively ‑0.05, ‑0.29, 0.33, 0.41, ‑0.27, 0.22, 0.44, ‑0.24, trace, ‑0.06, 0.01, 0.32, 0.14, and 0.04. Correlations of chemical and physical attributes of soil with sugarcane yield are weak, and, per se, they are not able to explain sugarcane yield variation, which suggests that other variables, besides soil attributes, should be analysed.