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 useable 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).

Probabilistic graphical models to deal with age estimation of living persons

Due to the rise of criminal, civil and administrative judicial situations involving people lacking valid identity documents, age estimation of living persons has become an important operational procedure for numerous forensic and medicolegal services worldwide. The chronological age of a given person is generally estimated from the observed degree of maturity of some selected physical attributes by means of statistical methods. However, their application in the forensic framework suffers from some conceptual and practical drawbacks, as recently claimed in the specialised literature. The aim of this paper is therefore to offer an alternative solution for overcoming these limits, by reiterating the utility of a probabilistic Bayesian approach for age estimation. This approach allows one to deal in a transparent way with the uncertainty surrounding the age estimation process and to produce all the relevant information in the form of posterior probability distribution about the chronological age of the person under investigation. Furthermore, this probability distribution can also be used for evaluating in a coherent way the possibility that the examined individual is younger or older than a given legal age threshold having a particular legal interest. The main novelty introduced by this work is the development of a probabilistic graphical model, i.e. a Bayesian network, for dealing with the problem at hand. The use of this kind of probabilistic tool can significantly facilitate the application of the proposed methodology: examples are presented based on data related to the ossification status of the medial clavicular epiphysis. The reliability and the advantages of this probabilistic tool are presented and discussed.

A Bayesian approach for pervasive estimation of breaststroke velocity using a wearable IMU

A ubiquitous assessment of swimming velocity (main metric of the performance) is essential for the coach to provide a tailored feedback to the trainee. We present a probabilistic framework for the data-driven estimation of the swimming velocity at every cycle using a low-cost wearable inertial measurement unit (IMU). The statistical validation of the method on 15 swimmers shows that an average relative error of 0.1 ± 9.6% and high correlation with the tethered reference system (rX,Y=0.91 ) is achievable. Besides, a simple tool to analyze the influence of sacrum kinematics on the performance is provided.

Time-lapse and probabilistic inversion strategies for plane-wave electromagnetic data.

L'utilisation efficace des systèmes géothermaux, la séquestration du CO2 pour limiter le changement climatique et la prévention de l'intrusion d'eau salée dans les aquifères costaux ne sont que quelques exemples qui démontrent notre besoin en technologies nouvelles pour suivre l'évolution des processus souterrains à partir de la surface. Un défi majeur est d'assurer la caractérisation et l'optimisation des performances de ces technologies à différentes échelles spatiales et temporelles. Les méthodes électromagnétiques (EM) d'ondes planes sont sensibles à la conductivité électrique du sous-sol et, par conséquent, à la conductivité électrique des fluides saturant la roche, à la présence de fractures connectées, à la température et aux matériaux géologiques. Ces méthodes sont régies par des équations valides sur de larges gammes de fréquences, permettant détudier de manières analogues des processus allant de quelques mètres sous la surface jusqu'à plusieurs kilomètres de profondeur. Néanmoins, ces méthodes sont soumises à une perte de résolution avec la profondeur à cause des propriétés diffusives du champ électromagnétique. Pour cette raison, l'estimation des modèles du sous-sol par ces méthodes doit prendre en compte des informations a priori afin de contraindre les modèles autant que possible et de permettre la quantification des incertitudes de ces modèles de façon appropriée. Dans la présente thèse, je développe des approches permettant la caractérisation statique et dynamique du sous-sol à l'aide d'ondes EM planes. Dans une première partie, je présente une approche déterministe permettant de réaliser des inversions répétées dans le temps (time-lapse) de données d'ondes EM planes en deux dimensions. Cette stratégie est basée sur l'incorporation dans l'algorithme d'informations a priori en fonction des changements du modèle de conductivité électrique attendus. Ceci est réalisé en intégrant une régularisation stochastique et des contraintes flexibles par rapport à la gamme des changements attendus en utilisant les multiplicateurs de Lagrange. J'utilise des normes différentes de la norme l2 pour contraindre la structure du modèle et obtenir des transitions abruptes entre les régions du model qui subissent des changements dans le temps et celles qui n'en subissent pas. Aussi, j'incorpore une stratégie afin d'éliminer les erreurs systématiques de données time-lapse. Ce travail a mis en évidence l'amélioration de la caractérisation des changements temporels par rapport aux approches classiques qui réalisent des inversions indépendantes à chaque pas de temps et comparent les modèles. Dans la seconde partie de cette thèse, j'adopte un formalisme bayésien et je teste la possibilité de quantifier les incertitudes sur les paramètres du modèle dans l'inversion d'ondes EM planes. Pour ce faire, je présente une stratégie d'inversion probabiliste basée sur des pixels à deux dimensions pour des inversions de données d'ondes EM planes et de tomographies de résistivité électrique (ERT) séparées et jointes. Je compare les incertitudes des paramètres du modèle en considérant différents types d'information a priori sur la structure du modèle et différentes fonctions de vraisemblance pour décrire les erreurs sur les données. Les résultats indiquent que la régularisation du modèle est nécessaire lorsqu'on a à faire à un large nombre de paramètres car cela permet d'accélérer la convergence des chaînes et d'obtenir des modèles plus réalistes. Cependent, ces contraintes mènent à des incertitudes d'estimations plus faibles, ce qui implique des distributions a posteriori qui ne contiennent pas le vrai modèledans les régions ou` la méthode présente une sensibilité limitée. Cette situation peut être améliorée en combinant des méthodes d'ondes EM planes avec d'autres méthodes complémentaires telles que l'ERT. De plus, je montre que le poids de régularisation des paramètres et l'écart-type des erreurs sur les données peuvent être retrouvés par une inversion probabiliste. Finalement, j'évalue la possibilité de caractériser une distribution tridimensionnelle d'un panache de traceur salin injecté dans le sous-sol en réalisant une inversion probabiliste time-lapse tridimensionnelle d'ondes EM planes. Etant donné que les inversions probabilistes sont très coûteuses en temps de calcul lorsque l'espace des paramètres présente une grande dimension, je propose une stratégie de réduction du modèle ou` les coefficients de décomposition des moments de Legendre du panache de traceur injecté ainsi que sa position sont estimés. Pour ce faire, un modèle de résistivité de base est nécessaire. Il peut être obtenu avant l'expérience time-lapse. Un test synthétique montre que la méthodologie marche bien quand le modèle de résistivité de base est caractérisé correctement. Cette méthodologie est aussi appliquée à un test de trac¸age par injection d'une solution saline et d'acides réalisé dans un système géothermal en Australie, puis comparée à une inversion time-lapse tridimensionnelle réalisée selon une approche déterministe. L'inversion probabiliste permet de mieux contraindre le panache du traceur salin gr^ace à la grande quantité d'informations a priori incluse dans l'algorithme. Néanmoins, les changements de conductivités nécessaires pour expliquer les changements observés dans les données sont plus grands que ce qu'expliquent notre connaissance actuelle des phénomenès physiques. Ce problème peut être lié à la qualité limitée du modèle de résistivité de base utilisé, indiquant ainsi que des efforts plus grands devront être fournis dans le futur pour obtenir des modèles de base de bonne qualité avant de réaliser des expériences dynamiques. Les études décrites dans cette thèse montrent que les méthodes d'ondes EM planes sont très utiles pour caractériser et suivre les variations temporelles du sous-sol sur de larges échelles. Les présentes approches améliorent l'évaluation des modèles obtenus, autant en termes d'incorporation d'informations a priori, qu'en termes de quantification d'incertitudes a posteriori. De plus, les stratégies développées peuvent être appliquées à d'autres méthodes géophysiques, et offrent une grande flexibilité pour l'incorporation d'informations additionnelles lorsqu'elles sont disponibles. -- The efficient use of geothermal systems, the sequestration of CO2 to mitigate climate change, and the prevention of seawater intrusion in coastal aquifers are only some examples that demonstrate the need for novel technologies to monitor subsurface processes from the surface. A main challenge is to assure optimal performance of such technologies at different temporal and spatial scales. Plane-wave electromagnetic (EM) methods are sensitive to subsurface electrical conductivity and consequently to fluid conductivity, fracture connectivity, temperature, and rock mineralogy. These methods have governing equations that are the same over a large range of frequencies, thus allowing to study in an analogous manner processes on scales ranging from few meters close to the surface down to several hundreds of kilometers depth. Unfortunately, they suffer from a significant resolution loss with depth due to the diffusive nature of the electromagnetic fields. Therefore, estimations of subsurface models that use these methods should incorporate a priori information to better constrain the models, and provide appropriate measures of model uncertainty. During my thesis, I have developed approaches to improve the static and dynamic characterization of the subsurface with plane-wave EM methods. In the first part of this thesis, I present a two-dimensional deterministic approach to perform time-lapse inversion of plane-wave EM data. The strategy is based on the incorporation of prior information into the inversion algorithm regarding the expected temporal changes in electrical conductivity. This is done by incorporating a flexible stochastic regularization and constraints regarding the expected ranges of the changes by using Lagrange multipliers. I use non-l2 norms to penalize the model update in order to obtain sharp transitions between regions that experience temporal changes and regions that do not. I also incorporate a time-lapse differencing strategy to remove systematic errors in the time-lapse inversion. This work presents improvements in the characterization of temporal changes with respect to the classical approach of performing separate inversions and computing differences between the models. In the second part of this thesis, I adopt a Bayesian framework and use Markov chain Monte Carlo (MCMC) simulations to quantify model parameter uncertainty in plane-wave EM inversion. For this purpose, I present a two-dimensional pixel-based probabilistic inversion strategy for separate and joint inversions of plane-wave EM and electrical resistivity tomography (ERT) data. I compare the uncertainties of the model parameters when considering different types of prior information on the model structure and different likelihood functions to describe the data errors. The results indicate that model regularization is necessary when dealing with a large number of model parameters because it helps to accelerate the convergence of the chains and leads to more realistic models. These constraints also lead to smaller uncertainty estimates, which imply posterior distributions that do not include the true underlying model in regions where the method has limited sensitivity. This situation can be improved by combining planewave EM methods with complimentary geophysical methods such as ERT. In addition, I show that an appropriate regularization weight and the standard deviation of the data errors can be retrieved by the MCMC inversion. Finally, I evaluate the possibility of characterizing the three-dimensional distribution of an injected water plume by performing three-dimensional time-lapse MCMC inversion of planewave EM data. Since MCMC inversion involves a significant computational burden in high parameter dimensions, I propose a model reduction strategy where the coefficients of a Legendre moment decomposition of the injected water plume and its location are estimated. For this purpose, a base resistivity model is needed which is obtained prior to the time-lapse experiment. A synthetic test shows that the methodology works well when the base resistivity model is correctly characterized. The methodology is also applied to an injection experiment performed in a geothermal system in Australia, and compared to a three-dimensional time-lapse inversion performed within a deterministic framework. The MCMC inversion better constrains the water plumes due to the larger amount of prior information that is included in the algorithm. The conductivity changes needed to explain the time-lapse data are much larger than what is physically possible based on present day understandings. This issue may be related to the base resistivity model used, therefore indicating that more efforts should be given to obtain high-quality base models prior to dynamic experiments. The studies described herein give clear evidence that plane-wave EM methods are useful to characterize and monitor the subsurface at a wide range of scales. The presented approaches contribute to an improved appraisal of the obtained models, both in terms of the incorporation of prior information in the algorithms and the posterior uncertainty quantification. In addition, the developed strategies can be applied to other geophysical methods, and offer great flexibility to incorporate additional information when available.

Bayesian estimation of speciation and extinction from incomplete fossil occurrence data.

The temporal dynamics of species diversity are shaped by variations in the rates of speciation and extinction, and there is a long history of inferring these rates using first and last appearances of taxa in the fossil record. Understanding diversity dynamics critically depends on unbiased estimates of the unobserved times of speciation and extinction for all lineages, but the inference of these parameters is challenging due to the complex nature of the available data. Here, we present a new probabilistic framework to jointly estimate species-specific times of speciation and extinction and the rates of the underlying birth-death process based on the fossil record. The rates are allowed to vary through time independently of each other, and the probability of preservation and sampling is explicitly incorporated in the model to estimate the true lifespan of each lineage. We implement a Bayesian algorithm to assess the presence of rate shifts by exploring alternative diversification models. Tests on a range of simulated data sets reveal the accuracy and robustness of our approach against violations of the underlying assumptions and various degrees of data incompleteness. Finally, we demonstrate the application of our method with the diversification of the mammal family Rhinocerotidae and reveal a complex history of repeated and independent temporal shifts of both speciation and extinction rates, leading to the expansion and subsequent decline of the group. The estimated parameters of the birth-death process implemented here are directly comparable with those obtained from dated molecular phylogenies. Thus, our model represents a step towards integrating phylogenetic and fossil information to infer macroevolutionary processes.

Probabilistic age classification with Bayesian networks: a study on the ossification status of the medial clavicular epiphysis

In the past few decades, the rise of criminal, civil and asylum cases involving young people lacking valid identification documents has generated an increase in the demand of age estimation. The chronological age or the probability that an individual is older or younger than a given age threshold are generally estimated by means of some statistical methods based on observations performed on specific physical attributes. Among these statistical methods, those developed in the Bayesian framework allow users to provide coherent and transparent assignments which fulfill forensic and medico-legal purposes. The application of the Bayesian approach is facilitated by using probabilistic graphical tools, such as Bayesian networks. The aim of this work is to test the performances of the Bayesian network for age estimation recently presented in scientific literature in classifying individuals as older or younger than 18 years of age. For these exploratory analyses, a sample related to the ossification status of the medial clavicular epiphysis available in scientific literature was used. Results obtained in the classification are promising: in the criminal context, the Bayesian network achieved, on the average, a rate of correct classifications of approximatively 97%, whilst in the civil context, the rate is, on the average, close to the 88%. These results encourage the continuation of the development and the testing of the method in order to support its practical application in casework.

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.

Is the formula of Traub still up to date in antemortem blood glucose level estimation?

According to the hypothesis of Traub, also known as the 'formula of Traub', postmortem values of glucose and lactate found in the cerebrospinal fluid or vitreous humor are considered indicators of antemortem blood glucose levels. However, because the lactate concentration increases in the vitreous and cerebrospinal fluid after death, some authors postulated that using the sum value to estimate antemortem blood glucose levels could lead to an overestimation of the cases of glucose metabolic disorders with fatal outcomes, such as diabetic ketoacidosis. The aim of our study, performed on 470 consecutive forensic cases, was to ascertain the advantages of the sum value to estimate antemortem blood glucose concentrations and, consequently, to rule out fatal diabetic ketoacidosis as the cause of death. Other biochemical parameters, such as blood 3-beta-hydroxybutyrate, acetoacetate, acetone, glycated haemoglobin and urine glucose levels, were also determined. In addition, postmortem native CT scan, autopsy, histology, neuropathology and toxicology were performed to confirm diabetic ketoacidosis as the cause of death. According to our results, the sum value does not add any further information for the estimation of antemortem blood glucose concentration. The vitreous glucose concentration appears to be the most reliable marker to estimate antemortem hyperglycaemia and, along with the determination of other biochemical markers (such as blood acetone and 3-beta-hydroxybutyrate, urine glucose and glycated haemoglobin), to confirm diabetic ketoacidosis as the cause of death.

Molecular estimation of dispersal for ecology and population genetics

The dispersal process, by which individuals or other dispersing agents such as gametes or seeds move from birthplace to a new settlement locality, has important consequences for the dynamics of genes, individuals, and species. Many of the questions addressed by ecology and evolutionary biology require a good understanding of species' dispersal patterns. Much effort has thus been devoted to overcoming the difficulties associated with dispersal measurement. In this context, genetic tools have long been the focus of intensive research, providing a great variety of potential solutions to measuring dispersal. This methodological diversity is reviewed here to help (molecular) ecologists find their way toward dispersal inference and interpretation and to stimulate further developments.

Cardiovascular risk estimation and eligibility for statin therapy using different scoring systems in Europe: a population-based study in Switzerland

BACKGROUND: Recommendations for statin use for primary prevention of coronary heart disease (CHD) are based on estimation of the 10- year CHD risk. We compared the 10-year CHD risk assessments and eligibility percentages for statin therapy using three scoring algorithms currently used in Europe. METHODS: We studied 5683 women and men, aged 35-75, without overt cardiovascular disease (CVD), in a population-based study in Switzerland. We compared the 10-year CHD risk using three scoring schemes, i.e., the Framingham risk score (FRS) from the U.S. National Cholesterol Education Program's Adult Treatment Panel III (ATP III), the PROCAM scoring scheme from the International Atherosclerosis Society (IAS), and the European risk SCORE for low-risk countries, without and with extrapolation to 60 years as recommended by the European Society of Cardiology guidelines (ESC). With FRS and PROCAM, high-risk was defined as a 10- year risk of fatal or non-fatal CHD>20% and a 10-year risk of fatal CVD≥5% with SCORE. We compared the proportions of high-risk participants and eligibility for statin use according to these three schemes. For each guideline, we estimated the impact of increased statin use from current partial compliance to full compliance on potential CHD deaths averted over 10 years, using a success proportion of 27% for statins. RESULTS: Participants classified at high-risk (both genders) were 5.8% according to FRS and 3.0% to the PROCAM, whereas the European risk SCORE classified 12.5% at high-risk (15.4% with extrapolation to 60 years). For the primary prevention of CHD, 18.5% of participants were eligible for statin therapy using ATP III, 16.6% using IAS, and 10.3% using ESC (13.0% with extrapolation) because ESC guidelines recommend statin therapy only in high-risk subjects. In comparison with IAS, agreement to identify eligible adults for statins was good with ATP III, but moderate with ESC. Using a population perspective, a full compliance with ATP III guidelines would reduce up to 17.9% of the 24′ 310 CHD deaths expected over 10 years in Switzerland, 17.3% with IAS and 10.8% with ESC (11.5% with extrapolation). CONCLUSIONS: Full compliance with guidelines for statin therapy would result in substantial health benefits, but proportions of high-risk adults and eligible adults for statin use varied substantially depending on the scoring systems and corresponding guidelines used for estimating CHD risk in Europe.

Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science

Continuing developments in science and technology mean that the amounts of information forensic scientists are able to provide for criminal investigations is ever increasing. The commensurate increase in complexity creates difficulties for scientists and lawyers with regard to evaluation and interpretation, notably with respect to issues of inference and decision. Probability theory, implemented through graphical methods, and specifically Bayesian networks, provides powerful methods to deal with this complexity. Extensions of these methods to elements of decision theory provide further support and assistance to the judicial system. Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science provides a unique and comprehensive introduction to the use of Bayesian decision networks for the evaluation and interpretation of scientific findings in forensic science, and for the support of decision-makers in their scientific and legal tasks. Includes self-contained introductions to probability and decision theory. Develops the characteristics of Bayesian networks, object-oriented Bayesian networks and their extension to decision models. Features implementation of the methodology with reference to commercial and academically available software. Presents standard networks and their extensions that can be easily implemented and that can assist in the reader's own analysis of real cases. Provides a technique for structuring problems and organizing data based on methods and principles of scientific reasoning. Contains a method for the construction of coherent and defensible arguments for the analysis and evaluation of scientific findings and for decisions based on them. Is written in a lucid style, suitable for forensic scientists and lawyers with minimal mathematical background. Includes a foreword by Ian Evett. The clear and accessible style of this second edition makes this book ideal for all forensic scientists, applied statisticians and graduate students wishing to evaluate forensic findings from the perspective of probability and decision analysis. It will also appeal to lawyers and other scientists and professionals interested in the evaluation and interpretation of forensic findings, including decision making based on scientific information.