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Fenton and Neil's book: "Risk Assessment with Bayesian Networks"

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White Papers

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Visualising your Risks: Making sense of risks by letting them tell a story

Have you ever had to do a project risk assessment and not known where to start? Have you ever looked at a long list of risks and wondered how you could make more sense of it? You probably won't have been helped by the literature on risk assessment... [Click here for the full paper]

Measuring your Risks: Numbers that would make sense to Bruce Willis and his crew

By destroying the meteor in the film Armageddon, Bruce Willis saved the world. The probability of the meteor strike was so large, and the consequences so great, that nothing much else mattered except to try to prevent the strike... [Click here for the full paper]

Using Bayesian Networks to Model Expected and Unexpected Operational Losses

This report describes the use of Bayesian Networks (BNs) to model statistical loss distributions in financial operational risk scenarios. Its’ focus is on modelling “thick” tail, or unexpected, loss events using mixtures of appropriate loss frequency and severity distributions where these mixtures are conditioned on causal variables that model the capability or effectiveness of the underlying controls process. We conclude that BNs can help combine qualitative data from experts and quantitative data from historical loss databases in a principled way and as such they go some way to meeting the requirements of the draft Basel II Accord for an Advanced Measurement Approach (AMA). [Click here for the full paper]

Generalising Event Trees Using Bayesian Networks with a Case Study of Train Derailment (by George Bearfield and William Marsh)

Event trees are a popular technique for modelling accidents in system safety analyses. Bayesian networks are a probabilistic modelling technique representing influences between uncertain variables. Although popular in expert systems, Bayesian networks are not used widely for safety. Using a train derailment case study, we show how an event tree can be viewed as a Bayesian network, making it clearer when one event affects a later one. Since this effect needs to be understood to construct an event tree correctly, we argue that the two notations should be used together. We then show how the Bayesian Network enables the factors that influence the outcome of events to be represented explicitly. In the case study, this allowed the train derailment model to be generalised and applied in more circumstances. Although the resulting model is no longer just an event tree, the familiar event tree notation remains useful. [Click here for the full paper]

Modeling Dependable Systems using Hybrid Bayesian Networks

A hybrid Bayesian Network (BN) is one that incorporates both discrete and continuous nodes. In our extensive applications of BNs for system dependability assessment the models are invariably hybrid and the need for efficient and accurate computation is paramount. We apply a new iterative algorithm that efficiently combines dynamic discretisation with robust propagation algorithms on junction tree structures to perform inference in hybrid BNs. We illustrate its use on two example dependability problems: reliability estimation and diagnosis of a faulty sensor in a temporal system. Dynamic discretisation can be used as an alternative to analytical or Monte Carlo methods with high precision and can be applied to a wide range of dependability problems... [Click here for the full paper]

Using Bayesian Networks and Simulation for Data Fusion and Risk Analysis

Bayesian networks (BNs) were pioneered to solve problems in Artificial Intelligence (AI) and have proven successful in "intelligent" applications such as medical expert systems, speech recognition, and fault diagnosis. In practical terms, one of the major benefits from using BNs is in that probabilistic and causal relationships among variables are represented and executed as graphs and can thus be easily visualized and extended, making model building and verification easier and faster. We illustrate how BNs can be used for risk analysis by introducing a novel approach modeling causal chains containing event triggers, consequences and interventions. However, if we want to incorporate continuous (as opposed to just discrete) variables in BN models the established BN tools and methods are inadequate. This paper reports on a new, unifying, approach to modeling continuous variables in BNs, called dynamic discretization, which approximates continuous variables without recourse to the traditional approach of Monte Carlo simulation methods. We illustrate the practical usefulness of the approach with an application involving the fusion of diverse sources of temporal data for fault diagnosis, classification and prediction of system behavior.... [Click here for the full paper]

New Directions For Software Metrics

This paper is part of a talk delivered at the CIO Annual Software Process Improvement Symposium. The focus of this talk was on why the software metrics discipline had largely failed to meet up to its true objective of providing quantitative risk assessment for software managers and developers. The paper describes how a causal approach could overcome the limitations of traditional approaches to meet the true objective.  [Click here for the full paper]

Avoiding legal errors with simple Bayesian reasoning

The Society for Expert Witnesses made a video interview with Norman Fenton for their Annual Conference at Studley Castle. The Society was keen to get a proper explanation of the so-called “Prosecutor’s fallacy” whereby lawyers make incorrect deductions about probabilities that are known to have a profound impact on juries. The Society’s Press Officer Tom Magnum had sought out a number of statisticians and probability experts but was unable to get a simple explanation that he felt could be understood by lawyers and judges. He turned to Norman Fenton after reading an article Norman had written with Martin Neil about the subject of probability fallacies in legal reasoning.  [Click here for the full article]

Bayesian nets provide radical improvements in software defect prediction

The developers of any new complex software system will confirm that, no matter how much testing they perform, there will still be plenty of defects (or ‘bugs’) yet to be found. The hope is that, when the software is released, any defects found by end-users will have minimal impact. Hence, the decision about when to stop testing and release the software must always be balanced by the likely number (and criticality) of remaining defects ... [Click here for the full article]

Beating the bookies: How Bayesian nets predicted Spurs’ results with consistent accuracy

There must be at least 20 million people in the UK who fancy themselves as experts at predicting the results of football matches. But, as the bookmakers’ increased profits also confirm, it seems that those brave enough to put their money where their mouths are, are not especially accurate with their predictions. In fact, it has been shown that even if you do some very fancy statistical analysis of previous relevant data for each match as the basis for your predictions, you will still not be consistently accurate to beat the bookies.  [Click here for the full article]

If A is half of B why can't I conclude that B is two times A?

Suppose you known that, on average, 50% of the trucks that start out in a military campaign are fully operational at the end. Then you would be correct in deducing that, if you start with 100 trucks you will end up, on average, with 50 that are fully operational. But, what if you know that you ended a campaign with 50 operational trucks. Then is it correct to assume that, on average, you started with 100? This was a simplified version of a real problem that one of Agena's clients had to tackle and the answer (surprisingly to them) was NO. This has everything to do with the way we reason with prior assumptions (this reasoning lies at the heart of the so-called Bayesian approach to probability).  [Click here for the full article, which is one of a series looking at probability puzzles and fallacies. You can see more here. ]

Software - a risky business?

What exactly is it that makes software such an inherently risky business, and why are its costs so difficult to judge? The problem has been known about for decades, but the answer has always seemed elusive, at least until now. The Risk Assessment and Decision Analysis research group (RADAR) at Queen Mary, University of London, think they have the answer.  [Click here for the full article which was written by Peter Hearty a PhD student at Queen Mary who is funded by EPSRC and an Agena CASE award. This essay won runner-up prize in the EPSRC Essay Competition ]

Using Bayesian Networks to Predict Software Defects and Reliability

This paper reviews the use of Bayesian Networks (BNs) in predicting software defects and software reliability. The approach has been used by organisations such as Motorola, Siemens and Philips who have reported accurate predictions. However, one of the impediments to more widespread use of BNs for this type of application was that, traditionally, BN tools and algorithms suffered from an obvious “Achilles’ Heel” – they were not able to handle continuous nodes properly, if at all... Read it all here.

Predicting and preventing IT risk

This short article describes how a leading North American bank uses AgenaRisk to help predict IT risk and prevent potential business problems. Read here. CASE award. This essay won runner-up prize in the EPSRC Essay Competition ]

The 'Jury Observation Fallacy' and the use of Bayesian Networks to present Probabilistic Legal Arguments

Probability theory, especially Bayesian probability, is widely misunderstood by the general public. Lawyers are no different from ordinary members of the public in falling victim to arguments that have been known to mathematicians for decades to be fallacies. The so-called prosecutor’s fallacy and the defendant’s fallacy are two well-known examples that arise from a basic misunderstanding of conditional probability and Bayes’ Theorem. In this paper we introduce  a previously unreported fallacy, which we refer to as the jury observation fallacy.  Read it here.