Modeling crime scenarios in a Bayesian Network

Legal cases involve reasoning with evidence and with the development of a software support tool in mind, a formal foundation for evidential reasoning is required. Three approaches to evidential reasoning have been prominent in the literature: argumentation, narrative and probabilistic reasoning. In this paper a combination of the latter two is proposed. In recent research on Bayesian networks applied to legal cases, a number of legal idioms have been developed as recurring structures in legal Bayesian networks. A Bayesian network quantifies how various variables in a case interact. In the narrative approach, scenarios provide a context for the evidence in a case. A method that integrates the quantitative, numerical techniques of Bayesian networks with the qualitative, holistic approach of scenarios is lacking. In this paper, a method is proposed for modeling several scenarios in a single Bayesian network. The method is tested by doing a case study. Two new idioms are introduced: the scenario idiom and the merged scenarios idiom. The resulting network is meant to assist a judge or jury, helping to maintain a good overview of the interactions between relevant variables in a case and preventing tunnel vision by comparing various scenarios

Representing and Evaluating Legal Narratives with Subscenarios in a Bayesian network

In legal cases, stories or scenarios can serve as the context for a crime when reasoning with evidence. In order to develop a scientifically founded technique for evidential reasoning, a method is required for the representation and evaluation of various scenarios in a case. In this paper the probabilistic technique of Bayesian networks is proposed as a method for modeling narrative, and it is shown how this can be used to capture a number of narrative properties. Bayesian networks quantify how the variables in a case interact. Recent research on Bayesian networks applied to legal cases includes the development of a list of legal idioms: recurring substructures in legal Bayesian networks. Scenarios are coherent presentations of a collection of states and events, and qualitative in nature. A method combining the quantitative, probabilistic approach with the narrative approach would strengthen the tools to represent and evaluate scenarios. In a previous paper, the development of a design method for modeling multiple scenarios in a Bayesian network was initiated. The design method includes two narrative idioms: the scenario idiom and the merged scenarios idiom. In this current paper, the method of Vlek, et al. (2013) is extended with a subscenario idiom and it is shown how the method can be used to represent characteristic features of narrative

Sensitivity of inferences in forensic genetics to assumptions about founding genes

Many forensic genetics problems can be handled using structured systems of discrete variables, for which Bayesian networks offer an appealing practical modeling framework, and allow inferences to be computed by probability propagation methods. However, when standard assumptions are violated--for example, when allele frequencies are unknown, there is identity by descent or the population is heterogeneous--dependence is generated among founding genes, that makes exact calculation of conditional probabilities by propagation methods less straightforward. Here we illustrate different methodologies for assessing sensitivity to assumptions about founders in forensic genetics problems. These include constrained steepest descent, linear fractional programming and representing dependence by structure. We illustrate these methods on several forensic genetics examples involving criminal identification, simple and complex disputed paternity and DNA mixtures.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS235 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Calculating and understanding the value of any type of match evidence when there are potential testing errors

It is well known that Bayes’ theorem (with likelihood ratios) can be used to calculate the impact of evidence, such as a ‘match’ of some feature of a person. Typically the feature of interest is the DNA profile, but the method applies in principle to any feature of a person or object, including not just DNA, fingerprints, or footprints, but also more basic features such as skin colour, height, hair colour or even name. Notwithstanding concerns about the extensiveness of databases of such features, a serious challenge to the use of Bayes in such legal contexts is that its standard formulaic representations are not readily understandable to non-statisticians. Attempts to get round this problem usually involve representations based around some variation of an event tree. While this approach works well in explaining the most trivial instance of Bayes’ theorem (involving a single hypothesis and a single piece of evidence) it does not scale up to realistic situations. In particular, even with a single piece of match evidence, if we wish to incorporate the possibility that there are potential errors (both false positives and false negatives) introduced at any stage in the investigative process, matters become very complex. As a result we have observed expert witnesses (in different areas of speciality) routinely ignore the possibility of errors when presenting their evidence. To counter this, we produce what we believe is the first full probabilistic solution of the simple case of generic match evidence incorporating both classes of testing errors. Unfortunately, the resultant event tree solution is too complex for intuitive comprehension. And, crucially, the event tree also fails to represent the causal information that underpins the argument. In contrast, we also present a simple-to-construct graphical Bayesian Network (BN) solution that automatically performs the calculations and may also be intuitively simpler to understand. Although there have been multiple previous applications of BNs for analysing forensic evidence—including very detailed models for the DNA matching problem, these models have not widely penetrated the expert witness community. Nor have they addressed the basic generic match problem incorporating the two types of testing error. Hence we believe our basic BN solution provides an important mechanism for convincing experts—and eventually the legal community—that it is possible to rigorously analyse and communicate the full impact of match evidence on a case, in the presence of possible error

Comprehensive Security Framework for Global Threats Analysis

Cyber criminality activities are changing and becoming more and more professional. With the growth of financial flows through the Internet and the Information System (IS), new kinds of thread arise involving complex scenarios spread within multiple IS components. The IS information modeling and Behavioral Analysis are becoming new solutions to normalize the IS information and counter these new threads. This paper presents a framework which details the principal and necessary steps for monitoring an IS. We present the architecture of the framework, i.e. an ontology of activities carried out within an IS to model security information and User Behavioral analysis. The results of the performed experiments on real data show that the modeling is effective to reduce the amount of events by 91%. The User Behavioral Analysis on uniform modeled data is also effective, detecting more than 80% of legitimate actions of attack scenarios

Learning Vine Copula Models For Synthetic Data Generation

A vine copula model is a flexible high-dimensional dependence model which uses only bivariate building blocks. However, the number of possible configurations of a vine copula grows exponentially as the number of variables increases, making model selection a major challenge in development. In this work, we formulate a vine structure learning problem with both vector and reinforcement learning representation. We use neural network to find the embeddings for the best possible vine model and generate a structure. Throughout experiments on synthetic and real-world datasets, we show that our proposed approach fits the data better in terms of log-likelihood. Moreover, we demonstrate that the model is able to generate high-quality samples in a variety of applications, making it a good candidate for synthetic data generation