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Fenton N.,Queen Mary, University of London | Fenton N.,Agena Ltd. | Neil M.,Queen Mary, University of London | Neil M.,Agena Ltd.
Journal of Biomedical Informatics | Year: 2010

This paper explains the role of Bayes Theorem and Bayesian networks arising in a medical negligence case brought by a patient who suffered a stroke as a result of an invasive diagnostic test. The claim of negligence was based on the premise that an alternative (non-invasive) test should have been used because it carried a lower risk. The case raises a number of general and widely applicable concerns about the decision-making process within the medical profession, including the ethics of informed consent, patient care liabilities when errors are made, and the research problem of focusing on 'true positives' while ignoring 'false positives'. An immediate concern is how best to present Bayesian arguments in such a way that they can be understood by people who would normally balk at mathematical equations. We feel it is possible to present purely visual representations of a non-trivial Bayesian argument in such a way that no mathematical knowledge or understanding is needed. The approach supports a wide range of alternative scenarios, makes all assumptions easily understandable and offers significant potential benefits to many areas of medical decision-making. © 2010 Elsevier Inc.

Marquez D.,Queen Mary, University of London | Neil M.,Queen Mary, University of London | Neil M.,Agena Ltd. | Fenton N.,Queen Mary, University of London | Fenton N.,Agena Ltd.
Reliability Engineering and System Safety | Year: 2010

This paper shows how recent Bayesian network (BN) algorithms can be used to model time to failure distributions and perform reliability analysis of complex systems in a simple unified way. The algorithms work for so-called hybrid BNs, which are BNs that can contain a mixture of both discrete and continuous variables. Our BN approach extends fault trees by defining the time-to-failure of the fault tree constructs as deterministic functions of the corresponding input components' time-to-failure. This helps solve any configuration of static and dynamic gates with general time-to-failure distributions. Unlike other approaches (which tend to be restricted to using exponential failure distributions) our approach can use any parametric or empirical distribution for the time-to-failure of the system components. We demonstrate that the approach produces results equivalent to the state of the practice and art for small examples; more importantly our approach produces solutions hitherto unobtainable for more complex examples, involving non-standard assumptions.. The approach offers a powerful framework for analysts and decision makers to successfully perform robust reliability assessment. Sensitivity, uncertainty, diagnosis analysis, common cause failures and warranty analysis can also be easily performed within this framework. © 2009 Elsevier Ltd. All rights reserved.

Constantinou A.C.,Queen Mary, University of London | Fenton N.,Queen Mary, University of London | Fenton N.,Agena Ltd. | Neil M.,Queen Mary, University of London | Neil M.,Agena Ltd.
Expert Systems with Applications | Year: 2016

When developing a causal probabilistic model, i.e. a Bayesian network (BN), it is common to incorporate expert knowledge of factors that are important for decision analysis but where historical data are unavailable or difficult to obtain. This paper focuses on the problem whereby the distribution of some continuous variable in a BN is known from data, but where we wish to explicitly model the impact of some additional expert variable (for which there is expert judgment but no data). Because the statistical outcomes are already influenced by the causes an expert might identify as variables missing from the dataset, the incentive here is to add the expert factor to the model in such a way that the distribution of the data variable is preserved when the expert factor remains unobserved. We provide a method for eliciting expert judgment that ensures the expected values of a data variable are preserved under all the known conditions. We show that it is generally neither possible, nor realistic, to preserve the variance of the data variable, but we provide a method towards determining the accuracy of expertise in terms of the extent to which the variability of the revised empirical distribution is minimised. We also describe how to incorporate the assessment of extremely rare or previously unobserved events. © 2016 Elsevier Ltd. All rights reserved.

Fenton N.,Queen Mary, University of London | Fenton N.,Agena Ltd
Science and Justice | Year: 2014

It is crucial to identify the most appropriate hypotheses if one is to apply probabilistic reasoning to evaluate and properly understand the impact of evidence. Subtle changes to the choice of a prosecution hypothesis can result in drastically different posterior probabilities to a defence hypothesis from the same evidence. To illustrate the problem we consider a real case in which probabilistic arguments assumed that the prosecution hypothesis "both babies were murdered" was the appropriate alternative to the defence hypothesis "both babies died of Sudden Infant Death Syndrome (SIDS)". Since it would have been sufficient for the prosecution to establish just one murder, a more appropriate alternative hypothesis was "at least one baby was murdered". Based on the same assumptions used by one of the probability experts who examined the case, the prior odds in favour of the defence hypothesis over the double murder hypothesis are 30 to 1. However, the prior odds in favour of the defence hypothesis over the alternative 'at least one murder' hypothesis are only 5 to 2. Assuming that the medical and other evidence has a likelihood ratio of 5 in favour of the prosecution hypothesis results in very different conclusions about the posterior probability of the defence hypothesis. © 2014 Forensic Science Society.

Fenton N.,Queen Mary, University of London | Fenton N.,Agena Ltd | Neil M.,Queen Mary, University of London | Neil M.,Agena Ltd | Hsu A.,Queen Mary, University of London
Artificial Intelligence and Law | Year: 2014

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 errors. © 2013 Springer Science+Business Media Dordrecht.

Neil M.,Queen Mary, University of London | Neil M.,Agena Ltd. | Marquez D.,Queen Mary, University of London
Engineering Applications of Artificial Intelligence | Year: 2012

We present a hybrid Bayesian network (HBN) framework to model the availability of renewable systems. We use an approximate inference algorithm for HBNs that involves dynamically discretizing the domain of all continuous variables and use this to obtain accurate approximations for the renewal or repair time distributions for a system. We show how we can use HBNs to model corrective repair time, logistics delay times and scheduled maintenance time distributions and combine these with time-to-failure distributions to derive system availability. Example models are presented and are accompanied by detailed descriptions of how repair (renewal) distributions might be modelled using HBNs. © 2010 Elsevier Ltd. All rights reserved.

Neil M.,Queen Mary, University of London | Neil M.,Agena Ltd. | Chen X.,Queen Mary, University of London | Fenton N.,Queen Mary, University of London | Fenton N.,Agena Ltd.
IEEE Transactions on Knowledge and Data Engineering | Year: 2012

Reducing the computational complexity of inference in Bayesian Networks (BNs) is a key challenge. Current algorithms for inference convert a BN to a junction tree structure made up of clusters of the BN nodes and the resulting complexity is time exponential in the size of a cluster. The need to reduce the complexity is especially acute where the BN contains continuous nodes. We propose a new method for optimizing the calculation of Conditional Probability Tables (CPTs) involving continuous nodes, approximated in Hybrid Bayesian Networks (HBNs), using an approximation algorithm called dynamic discretization. We present an optimized solution to this problem involving binary factorization of the arithmetical expressions declared to generate the CPTs for continuous nodes for deterministic functions and statistical distributions. The proposed algorithm is implemented and tested in a commercial Hybrid Bayesian Network software package and the results of the empirical evaluation show significant performance improvement over unfactorized models. © 2012 IEEE.

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