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Slide 1 Government Actuary's Department 18 November 2014 Norman Fenton Queen Mary University of London and Agena Ltd Bayesian Networks for Risk Assessment

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Slide 2 Outline Overview of Bayes and Bayesian networks Why Bayesian networks are needed for risk assessment Examples and real applications in financial risk Challenges and the future

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Slide 3 Our book

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Slide 4 Overview of Bayes and Bayesian Networks

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Slide 5 A classic risk assessment problem A particular disease has a 1 in 1000 rate of occurrence A screening test for the disease is 100% accurate for those with the disease; 95% accurate for those without What is the probability a person has the disease if they test positive?

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Slide 6 Bayes Theorem E (evidence) Now get some evidence E (“test result positive”) P(H|E) = P(E|H)*P(H) P(E) P(E|H)*P(H) P(E|H)*P(H) + P(E|not H)*P(not H) = 1* * *0.999 P(H|E) = = But we want the posterior P(H|E) H (hypothesis) Have a prior P(H) (“person has disease”) We know P(E|H)

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Slide 7 A Classic BN

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Slide 8 Bayesian Propagation Applying Bayes theorem to update all probabilities when new evidence is entered Intractable even for small BNs Breakthrough in late 1980s - fast algorithms Tools implement efficient propagation

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Slide 9 A Classic BN: Marginals

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Slide 10 Dyspnoea observed

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Slide 11 Also non-smoker

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Slide 12 Positive x-ray

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Slide 13..but recent visit to Asia

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Slide 14 The power of BNs Explicitly model causal factors Reason from effect to cause and vice versa ‘Explaining away’ Overturn previous beliefs Make predictions with incomplete data Combine diverse types of evidence Visible auditable reasoning Can deal with high impact low probability events (we do not require massive datasets)

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Slide 15 Why causal Bayesian networks are needed for risk assessment

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Slide 16 Irrational for risk assessment Rational for risk assessment Problems with regression driven ‘risk assessment’

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Slide 17 ‘Standard’ definition of risk “An event that can have negative consequences” Measured (or even defined by):

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Slide 18..but this does not tell us tell us what we need to know Armageddon risk: Large meteor strikes the Earth The ‘standard approach’ makes no sense at all

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Slide 19 Risk using causal analysis A risk is an event that can be characterised by a causal chain involving (at least): The event itself At least one consequence event that characterises the impact One or more trigger (i.e. initiating) events One or more control events which may stop the trigger event from causing the risk event One or more mitigating events which help avoid the consequence event (for risk)

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Slide 20 Bayesian Net with causal view of risk Meteor strikes Earth Risk event Meteor on collision course with Earth Trigger Blow up Meteor Control Build Underground cities Mitigant Loss of Life Consequence

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Slide 21 Examples and real applications in financial risk

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Slide 22 Note that ‘common causes’ are easily modelled Causal Risk Register

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Slide 23 Assumes capital sum $100m and a 10-month loan Expected value of resulting payment is $12m with 95% percentile at $26m Regulator stress test: “at least 4% interest rate” Simple stress test interest payment example

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Slide 24 Expected value of resulting payment in stress testing scenario is $59m with 95% percentile at $83m Simple stress test interest payment example This model can be built in a couple of minutes with AgenaRisk

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Slide 25 Stress testing with causal dependency

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Slide 26 Stress testing with causal dependency

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Slide 27 Op Risk Loss Event Model

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Slide 28 Operational Risk VAR Models Scenario dynamics Contributing outcomes Aggregate scenario outcome

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Slide 29 Stress and Scenario Modelling Pandemic Civil Unrest Travel Disruption Reverse Stress

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Slide 30 Business Performance Holistic map of business enhances understanding of interrelationships between risks and provides candidate model structure Risk Register entries help explain uncertainty associated with business processes KPIs inform the current state of the system Business Performance Indicators serve as ex-post indicators, we can then use the model to explain the drivers underlying business outcomes

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Slide 31 Policyholder Behaviour

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Slide 32 The challenges

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Slide 33 Challenge 1: Resistance to Bayes’ subjective probabilities “.. even if I accept the calculations are ‘correct’ I don’t accept subjective priors” There is no such thing as a truly objective frequentist approach

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Slide 34 Challenge 2: Building realistic models Common method: Structure and probability tables all learnt from data only (‘machine learning’) DOES NOT WORK EVEN WHEN WE HAVE LOTS OF ‘RELEVANT’ DATA!!!!!!!!!!!!!!!

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Slide 35 A typical data-driven study AgeDelay in arrival Injury type Brain scan result Arterial pressure Pupil dilation Outcome (death y/n) 1725ANLYN 3920BNMYN 2365ANLNY 2180CYHYN 6820BYMYN 2230ANMNY ………..……

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Slide 36 Delay in arrival Injury type Brain scan result Arterial pressure Pupil dilation Age Outcome Purely data driven machine learning algorithms will be inaccurate and produce counterintuitive results e.g. outcome more likely to be OK in the worst scenarios A typical data-driven study

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Slide 37 Delay in arrival Injury type Brain scan result Arterial pressure Pupil dilation Age Causal model with intervention Danger level Outcome TREATMENT..crucial variables missing from the data

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Slide 38 Challenge 2: Building realistic models Need to incorporate experts judgment: Structure informed by experts, probability tables learnt from data Structure and tables built by experts Fenton NE, Neil M, and Caballero JG, "Using Ranked nodes to model qualitative judgements in Bayesian Networks“, IEEE TKDE 19(10), , Oct 2007

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Slide 39 Challenge 3: Handling continuous nodes Static discretisation: inefficient and devastatingly inaccurate Our developments in dynamic discretisation starting to have a revolutionary effect Neil, M., Tailor, M., & Marquez, D. (2007). “Inference in hybrid Bayesian networks using dynamic discretization”. Statistics and Computing, 17(3), 219–233. Neil, M., Tailor, M., Marquez, D., Fenton, N. E., & Hearty, P. (2008). “Modelling dependable systems using hybrid Bayesian networks”. Reliability Engineering and System Safety, 93(7), 933–939

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Slide 40 Challenge 4: Risk Aggregation Estimate sum of a collection of financial assets or events, where each asset or event is modelled as a random variable Methods not designed to cope with the presence of Discrete Causally Connected Random Variables Solution: Bayesian Factorization and Elimination (BFE) algorithm - exploits advances in BNs and is as accurate on conventional problems as competing methods. Peng Lin, Martin Neil and Norman Fenton (2014). “Risk aggregation in the presence of discrete causally connected random variables”. Annals of Actuarial Science, 8, pp

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Slide 41 Conclusions Genuine risk assessment requires causal Bayesian networks Bayesian networks now used effectively in a range of real world problems Must involve experts and not rely only on data No major remaining technical barrier to widespread

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Slide 42 Follow up Try the free BN software and all the models Get the book Propose case study for ERC Project BAYES-KNOWLEDGE

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