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.

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).

The Individualized Genetic Barrier Predicts Treatment Response in a Large Cohort of HIV-1 Infected Patients.

The success of combination antiretroviral therapy is limited by the evolutionary escape dynamics of HIV-1. We used Isotonic Conjunctive Bayesian Networks (I-CBNs), a class of probabilistic graphical models, to describe this process. We employed partial order constraints among viral resistance mutations, which give rise to a limited set of mutational pathways, and we modeled phenotypic drug resistance as monotonically increasing along any escape pathway. Using this model, the individualized genetic barrier (IGB) to each drug is derived as the probability of the virus not acquiring additional mutations that confer resistance. Drug-specific IGBs were combined to obtain the IGB to an entire regimen, which quantifies the virus' genetic potential for developing drug resistance under combination therapy. The IGB was tested as a predictor of therapeutic outcome using between 2,185 and 2,631 treatment change episodes of subtype B infected patients from the Swiss HIV Cohort Study Database, a large observational cohort. Using logistic regression, significant univariate predictors included most of the 18 drugs and single-drug IGBs, the IGB to the entire regimen, the expert rules-based genotypic susceptibility score (GSS), several individual mutations, and the peak viral load before treatment change. In the multivariate analysis, the only genotype-derived variables that remained significantly associated with virological success were GSS and, with 10-fold stronger association, IGB to regimen. When predicting suppression of viral load below 400 cps/ml, IGB outperformed GSS and also improved GSS-containing predictors significantly, but the difference was not significant for suppression below 50 cps/ml. Thus, the IGB to regimen is a novel data-derived predictor of treatment outcome that has potential to improve the interpretation of genotypic drug resistance tests.

Bayesian Networks for the Age Classification of Living Individuals: a Study on Transition Analysis

Over the past few decades, age estimation of living persons has represented a challenging task for many forensic services worldwide. In general, the process for age estimation includes the observation of the degree of maturity reached by some physical attributes, such as dentition or several ossification centers. The estimated chronological age or the probability that an individual belongs to a meaningful class of ages is then obtained from the observed degree of maturity by means of various statistical methods. Among these methods, those developed in a Bayesian framework offer to users the possibility of coherently dealing with the uncertainty associated with age estimation and of assessing in a transparent and logical way the probability that an examined individual is younger or older than a given age threshold. Recently, a Bayesian network for age estimation has been presented in scientific literature; this kind of probabilistic graphical tool may facilitate the use of the probabilistic approach. Probabilities of interest in the network are assigned by means of transition analysis, a statistical parametric model, which links the chronological age and the degree of maturity by means of specific regression models, such as logit or probit models. Since different regression models can be employed in transition analysis, the aim of this paper is to study the influence of the model in the classification of individuals. The analysis was performed using a dataset related to the ossifications status of the medial clavicular epiphysis and results support that the classification of individuals is not dependent on the choice of the regression model.

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.

Recognition judgments and the performance of the recognition heuristic depend on the size of the reference class

In a series of three experiments, participants made inferences about which one of a pair of two objects scored higher on a criterion. The first experiment was designed to contrast the prediction of Probabilistic Mental Model theory (Gigerenzer, Hoffrage, & Kleinbölting, 1991) concerning sampling procedure with the hard-easy effect. The experiment failed to support the theory's prediction that a particular pair of randomly sampled item sets would differ in percentage correct; but the observation that German participants performed practically as well on comparisons between U.S. cities (many of which they did not even recognize) than on comparisons between German cities (about which they knew much more) ultimately led to the formulation of the recognition heuristic. Experiment 2 was a second, this time successful, attempt to unconfound item difficulty and sampling procedure. In Experiment 3, participants' knowledge and recognition of each city was elicited, and how often this could be used to make an inference was manipulated. Choices were consistent with the recognition heuristic in about 80% of the cases when it discriminated and people had no additional knowledge about the recognized city (and in about 90% when they had such knowledge). The frequency with which the heuristic could be used affected the percentage correct, mean confidence, and overconfidence as predicted. The size of the reference class, which was also manipulated, modified these effects in meaningful and theoretically important ways.

Graphical probabilistic analysis of the combination of items of evidence

Unlike the evaluation of single items of scientific evidence, the formal study and analysis of the jointevaluation of several distinct items of forensic evidence has to date received some punctual, ratherthan systematic, attention. Questions about the (i) relationships among a set of (usually unobservable)propositions and a set of (observable) items of scientific evidence, (ii) the joint probative valueof a collection of distinct items of evidence as well as (iii) the contribution of each individual itemwithin a given group of pieces of evidence still represent fundamental areas of research. To somedegree, this is remarkable since both, forensic science theory and practice, yet many daily inferencetasks, require the consideration of multiple items if not masses of evidence. A recurrent and particularcomplication that arises in such settings is that the application of probability theory, i.e. the referencemethod for reasoning under uncertainty, becomes increasingly demanding. The present paper takesthis as a starting point and discusses graphical probability models, i.e. Bayesian networks, as frameworkwithin which the joint evaluation of scientific evidence can be approached in some viable way.Based on a review of existing main contributions in this area, the article here aims at presentinginstances of real case studies from the author's institution in order to point out the usefulness andcapacities of Bayesian networks for the probabilistic assessment of the probative value of multipleand interrelated items of evidence. A main emphasis is placed on underlying general patterns of inference,their representation as well as their graphical probabilistic analysis. Attention is also drawnto inferential interactions, such as redundancy, synergy and directional change. These distinguish thejoint evaluation of evidence from assessments of isolated items of evidence. Together, these topicspresent aspects of interest to both, domain experts and recipients of expert information, because theyhave bearing on how multiple items of evidence are meaningfully and appropriately set into context.

Two-dimensional probabilistic inversion of plane-wave electromagnetic data: Methodology, model constraints and joint inversion with electrical resistivity data

Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints.

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.

DNA evidence, probabilistic evaluation and collaborative tests.

Forensic scientists working in 12 state or private laboratories participated in collaborative tests to improve the reliability of the presentation of DNA data at trial. These tests were motivated in response to the growing criticism of the power of DNA evidence. The experts' conclusions in the tests are presented and discussed in the context of the Bayesian approach to interpretation. The use of a Bayesian approach and subjective probabilities in trace evaluation permits, in an easy and intuitive manner, the integration into the decision procedure of any revision of the measure of uncertainty in the light of new information. Such an integration is especially useful with forensic evidence. Furthermore, we believe that this probabilistic model is a useful tool (a) to assist scientists in the assessment of the value of scientific evidence, (b) to help jurists in the interpretation of judicial facts and (c) to clarify the respective roles of scientists and of members of the court. Respondents to the survey were reluctant to apply this methodology in the assessment of DNA evidence.

Combining probabilistic land-use change and tree population dynamics modelling to simulate responses in mountain forests

Altitudinal tree lines are mainly constrained by temperature, but can also be influenced by factors such as human activity, particularly in the European Alps, where centuries of agricultural use have affected the tree-line. Over the last decades this trend has been reversed due to changing agricultural practices and land-abandonment. We aimed to combine a statistical land-abandonment model with a forest dynamics model, to take into account the combined effects of climate and human land-use on the Alpine tree-line in Switzerland. Land-abandonment probability was expressed by a logistic regression function of degree-day sum, distance from forest edge, soil stoniness, slope, proportion of employees in the secondary and tertiary sectors, proportion of commuters and proportion of full-time farms. This was implemented in the TreeMig spatio-temporal forest model. Distance from forest edge and degree-day sum vary through feed-back from the dynamics part of TreeMig and climate change scenarios, while the other variables remain constant for each grid cell over time. The new model, TreeMig-LAb, was tested on theoretical landscapes, where the variables in the land-abandonment model were varied one by one. This confirmed the strong influence of distance from forest and slope on the abandonment probability. Degree-day sum has a more complex role, with opposite influences on land-abandonment and forest growth. TreeMig-LAb was also applied to a case study area in the Upper Engadine (Swiss Alps), along with a model where abandonment probability was a constant. Two scenarios were used: natural succession only (100% probability) and a probability of abandonment based on past transition proportions in that area (2.1% per decade). The former showed new forest growing in all but the highest-altitude locations. The latter was more realistic as to numbers of newly forested cells, but their location was random and the resulting landscape heterogeneous. Using the logistic regression model gave results consistent with observed patterns of land-abandonment: existing forests expanded and gaps closed, leading to an increasingly homogeneous landscape.

A Bayesian network approach to the database serch problem in criminal proceedings

Background The 'database search problem', that is, the strengthening of a case - in terms of probative value - against an individual who is found as a result of a database search, has been approached during the last two decades with substantial mathematical analyses, accompanied by lively debate and centrally opposing conclusions. This represents a challenging obstacle in teaching but also hinders a balanced and coherent discussion of the topic within the wider scientific and legal community. This paper revisits and tracks the associated mathematical analyses in terms of Bayesian networks. Their derivation and discussion for capturing probabilistic arguments that explain the database search problem are outlined in detail. The resulting Bayesian networks offer a distinct view on the main debated issues, along with further clarity. Methods As a general framework for representing and analyzing formal arguments in probabilistic reasoning about uncertain target propositions (that is, whether or not a given individual is the source of a crime stain), this paper relies on graphical probability models, in particular, Bayesian networks. This graphical probability modeling approach is used to capture, within a single model, a series of key variables, such as the number of individuals in a database, the size of the population of potential crime stain sources, and the rarity of the corresponding analytical characteristics in a relevant population. Results This paper demonstrates the feasibility of deriving Bayesian network structures for analyzing, representing, and tracking the database search problem. The output of the proposed models can be shown to agree with existing but exclusively formulaic approaches. Conclusions The proposed Bayesian networks allow one to capture and analyze the currently most well-supported but reputedly counter-intuitive and difficult solution to the database search problem in a way that goes beyond the traditional, purely formulaic expressions. The method's graphical environment, along with its computational and probabilistic architectures, represents a rich package that offers analysts and discussants with additional modes of interaction, concise representation, and coherent communication.

Uncertainty Quantification Of A Semi-Supervised Support Vector Regression Reservoir Model

Uncertainty quantification of petroleum reservoir models is one of the present challenges, which is usually approached with a wide range of geostatistical tools linked with statistical optimisation or/and inference algorithms. Recent advances in machine learning offer a novel approach to model spatial distribution of petrophysical properties in complex reservoirs alternative to geostatistics. The approach is based of semisupervised learning, which handles both ?labelled? observed data and ?unlabelled? data, which have no measured value but describe prior knowledge and other relevant data in forms of manifolds in the input space where the modelled property is continuous. Proposed semi-supervised Support Vector Regression (SVR) model has demonstrated its capability to represent realistic geological features and describe stochastic variability and non-uniqueness of spatial properties. On the other hand, it is able to capture and preserve key spatial dependencies such as connectivity of high permeability geo-bodies, which is often difficult in contemporary petroleum reservoir studies. Semi-supervised SVR as a data driven algorithm is designed to integrate various kind of conditioning information and learn dependences from it. The semi-supervised SVR model is able to balance signal/noise levels and control the prior belief in available data. In this work, stochastic semi-supervised SVR geomodel is integrated into Bayesian framework to quantify uncertainty of reservoir production with multiple models fitted to past dynamic observations (production history). Multiple history matched models are obtained using stochastic sampling and/or MCMC-based inference algorithms, which evaluate posterior probability distribution. Uncertainty of the model is described by posterior probability of the model parameters that represent key geological properties: spatial correlation size, continuity strength, smoothness/variability of spatial property distribution. The developed approach is illustrated with a fluvial reservoir case. The resulting probabilistic production forecasts are described by uncertainty envelopes. The paper compares the performance of the models with different combinations of unknown parameters and discusses sensitivity issues.