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.

Modelling dependence in a ratemaking procedure with multivariate Poisson regression models

When actuaries face with the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce different regression models in order to relax the independence assumption, including zero-inflated models to account for excess of zeros and overdispersion. These models have been largely ignored to multivariate Poisson date, mainly because of their computational di±culties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claims. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models and their zero-inflated versions.

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the raph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group.

Chemical profiling of different hashish seizures by gas chromatography-mass spectrometry and statistical methodology: a case report

Limited information is available regarding the methodology required to characterize hashish seizures for assessing the presence or the absence of a chemical link between two seizures. This casework report presents the methodology applied for assessing that two different police seizures were coming from the same block before this latter one was split. The chemical signature was extracted using GC-MS analysis and the implemented methodology consists in a study of intra- and inter-variability distributions based on the measurement of the chemical profiles similarity using a number of hashish seizures and the calculation of the Pearson correlation coefficient. Different statistical scenarios (i.e., a combination of data pretreatment techniques and selection of target compounds) were tested to find the most discriminating one. Seven compounds showing high discrimination capabilities were selected on which a specific statistical data pretreatment was applied. Based on the results, the statistical model built for comparing the hashish seizures leads to low error rates. Therefore, the implemented methodology is suitable for the chemical profiling of hashish seizures.

What do we gain from simplicity versus complexity in species distribution models?

Species distribution models (SDMs) are widely used to explain and predict species ranges and environmental niches. They are most commonly constructed by inferring species' occurrence-environment relationships using statistical and machine-learning methods. The variety of methods that can be used to construct SDMs (e.g. generalized linear/additive models, tree-based models, maximum entropy, etc.), and the variety of ways that such models can be implemented, permits substantial flexibility in SDM complexity. Building models with an appropriate amount of complexity for the study objectives is critical for robust inference. We characterize complexity as the shape of the inferred occurrence-environment relationships and the number of parameters used to describe them, and search for insights into whether additional complexity is informative or superfluous. By building 'under fit' models, having insufficient flexibility to describe observed occurrence-environment relationships, we risk misunderstanding the factors shaping species distributions. By building 'over fit' models, with excessive flexibility, we risk inadvertently ascribing pattern to noise or building opaque models. However, model selection can be challenging, especially when comparing models constructed under different modeling approaches. Here we argue for a more pragmatic approach: researchers should constrain the complexity of their models based on study objective, attributes of the data, and an understanding of how these interact with the underlying biological processes. We discuss guidelines for balancing under fitting with over fitting and consequently how complexity affects decisions made during model building. Although some generalities are possible, our discussion reflects differences in opinions that favor simpler versus more complex models. We conclude that combining insights from both simple and complex SDM building approaches best advances our knowledge of current and future species ranges.

Indirect likelihood inference

Given a sample from a fully specified parametric model, let Zn be a given finite-dimensional statistic - for example, an initial estimator or a set of sample moments. We propose to (re-)estimate the parameters of the model by maximizing the likelihood of Zn. We call this the maximum indirect likelihood (MIL) estimator. We also propose a computationally tractable Bayesian version of the estimator which we refer to as a Bayesian Indirect Likelihood (BIL) estimator. In most cases, the density of the statistic will be of unknown form, and we develop simulated versions of the MIL and BIL estimators. We show that the indirect likelihood estimators are consistent and asymptotically normally distributed, with the same asymptotic variance as that of the corresponding efficient two-step GMM estimator based on the same statistic. However, our likelihood-based estimators, by taking into account the full finite-sample distribution of the statistic, are higher order efficient relative to GMM-type estimators. Furthermore, in many cases they enjoy a bias reduction property similar to that of the indirect inference estimator. Monte Carlo results for a number of applications including dynamic and nonlinear panel data models, a structural auction model and two DSGE models show that the proposed estimators indeed have attractive finite sample properties.

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.

Illicit drug profiling, reflection on statistical comparisons

This paper presents reflexions about statistical considerations on illicit drug profiling and more specifically about the calculation of threshold for determining of the seizure are linked or not. The specific case of heroin and cocaine profiling is presented with the necessary details on the target profiling variables (major alkaloids) selected and the analytical method used. Statistical approach to compare illicit drug seizures is also presented with the introduction of different scenarios dealing with different data pre-treatment or transformation of variables.The main aim consists to demonstrate the influence of data pre-treatment on the statistical outputs. A thorough study of the evolution of the true positive rate (TP) and the false positive rate (FP) in heroin and cocaine comparison is then proposed to investigate this specific topic and to demonstrate that there is no universal approach available and that the calculations have to be revaluate for each new specific application.

Improving the performance of positive selection inference by filtering unreliable alignment regions.

Errors in the inferred multiple sequence alignment may lead to false prediction of positive selection. Recently, methods for detecting unreliable alignment regions were developed and were shown to accurately identify incorrectly aligned regions. While removing unreliable alignment regions is expected to increase the accuracy of positive selection inference, such filtering may also significantly decrease the power of the test, as positively selected regions are fast evolving, and those same regions are often those that are difficult to align. Here, we used realistic simulations that mimic sequence evolution of HIV-1 genes to test the hypothesis that the performance of positive selection inference using codon models can be improved by removing unreliable alignment regions. Our study shows that the benefit of removing unreliable regions exceeds the loss of power due to the removal of some of the true positively selected sites.

Children Order Statistical Bulletin 2005 (PDF 278 KB)

Statistical information based on the Children Order returns for NI up to 31st March 2005

Statistical evaluation of the influence of writing postures on on-line signatures. Study of the impact of time.

The aim of this study is to investigate the influence of unusual writing positions on a person's signature, in comparison to a standard writing position. Ten writers were asked to sign their signature six times, in each of four different writing positions, including the standard one. In order to take into consideration the effect of the day-to-day variation, this same process was repeated over 12 sessions, giving a total of 288 signatures per subject. The signatures were collected simultaneously in an off-line and on-line acquisition mode, using an interactive tablet and a ballpoint pen. Unidimensional variables (height to width ratio; time with or without in air displacement) and time-dependent variables (pressure; X and Y coordinates; altitude and azimuth angles) were extracted from each signature. For the unidimensional variables, the position effect was assessed through ANOVA and Dunnett contrast tests. Concerning the time-dependent variables, the signatures were compared by using dynamic time warping, and the position effect was evaluated through classification by linear discriminant analysis. Both of these variables provided similar results: no general tendency regarding the position factor could be highlighted. The influence of the position factor varies according to the subject as well as the variable studied. The impact of the session factor was shown to cover the impact that could be ascribed to the writing position factor. Indeed, the day-to-day variation has a greater effect than the position factor on the studied signature variables. The results of this study suggest guidelines for best practice in the area of signature comparisons and demonstrate the importance of a signature collection procedure covering an adequate number of sampling sessions, with a sufficient number of samples per session.