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Transcript of Slide 1 Government Actuary's Department 18 November 2014 Norman Fenton Queen Mary University of...
Slide 1
Government Actuary's Department18 November 2014
Norman FentonQueen Mary University of London
and Agena Ltd
Bayesian Networks forRisk Assessment
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
Slide 3
Our book
www.BayesianRisk.com
Slide 4
Overview of Bayes and Bayesian Networks
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?
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*0.001
1*0.001 + 0.05*0.999P(H|E) = =
0.001
0.50050.02
But we want the posterior P(H|E)
H (hypothesis)
Have a prior P(H) (“person has disease”)
We know P(E|H)
Slide 7
A Classic BN
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
Slide 9
A Classic BN: Marginals
Slide 10
Dyspnoea observed
Slide 11
Also non-smoker
Slide 12
Positive x-ray
Slide 13
..but recent visit to Asia
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)
Slide 15
Why causal Bayesian networks are needed for risk assessment
Slide 16
2 . 1 4 4 2 4 3 . 5 5N T
Irrational for risk assessment Rational for risk assessment
Problems with regression driven ‘risk assessment’
Slide 17Slide 17
‘Standard’ definition of risk
“An event that can have negative consequences”
Measured (or even defined by):
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
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)
Slide 20
Bayesian Net with causal view of risk
Meteor strikesEarth
Risk event
Meteor on collision course
with Earth
Trigger Blow up Meteor
Control
Build Underground
citiesMitigant
Loss of Life
Consequence
Slide 21
Examples and real applications in financial risk
Slide 22
Note that ‘common causes’ are easily modelled
Causal Risk Register
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
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
Slide 25
Stress testing with causal dependency
Slide 26
Stress testing with causal dependency
Slide 27
Op Risk Loss Event Model
Slide 28
Operational Risk VAR Models
Scenario dynamics
Contributing outcomes
Aggregate scenario outcome
Slide 29
Stress and Scenario ModellingPandemic
Civil Unrest
Travel Disruption
Reverse Stress
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
Slide 31
Policyholder Behaviour
Slide 32
The challenges
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
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!!!!!!!!!!!!!!!
Slide 35
A typical data-driven study
Age Delay in arrival
Injurytype
Brain scanresult
Arterialpressure
Pupildilation
Outcome (death y/n)
17 25 A N L Y N
39 20 B N M Y N
23 65 A N L N Y
21 80 C Y H Y N
68 20 B Y M Y N
22 30 A N M N Y
… … … .. … …
Slide 36
Delay in arrival
Injurytype
Brain scanresult Arterial
pressure
Pupildilation
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
Slide 37
Delay in arrival
Injurytype
Brain scanresult Arterial
pressure
Pupildilation
Age
Causal model with intervention
Dangerlevel
Outcome
TREATMENT
..crucial variables missing from the data
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), 1420-1432, Oct 2007
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
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 variableMethods not designed to cope with the presence of Discrete Causally Connected Random VariablesSolution: 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 298-319
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
Slide 42
Follow up
Try the free BN software and all the models
www.AgenaRisk.com
Get the bookwww.BayesianRisk.com
Propose case study for ERC Project BAYES-KNOWLEDGEwww.eecs.qmul.ac.uk/~norman/projects/B_Knowledge.html