Bayesian decision networks for risk assessment and decision supportorHow to combine data, evidence, opinion and guesstimates to make decisions

Information Technology

Professor Ann NicholsonFaculty of Information TechnologyMonash University (Melbourne, Australia)

Probabilistic Graphical Models

…and quantifythe uncertainty

… capture the processstructure (not black box)

For atarget system…

Why use models?• Increases understanding• Supports decision making• Use new data and evaluation to improve over time

The reasoning process1. Start with a belief in a

proposition“The proportion of people

with insufficient calorie intake is 10-20%”

“There will be a locust plague this summer”

“Wheat prices will fall next year”

“Unemployment is high”

“Beliefs”• Very unlikely• 1% chance• Odds of 100 to 1• 0.01 probabilityFrom• Gut feeling• Expert opinion• Data

The reasoning process1. Start with a belief in a

proposition“The proportion of people

with vitamin deficiencies is 10-20%”

“There will be a locust plague this summer”

“Wheat prices will fall next year”

“Unemployment is high”

2. New information becomes available

“Child mortality rates in region X are double region average ”

“Large egg nests observed”

“Country X is expecting record harvests”

“Food bank numbers are twice average”

3. Update your beliefs But how?

The Bayesian approach

The Rev. Thomas Bayes1702?-1761

• Represent uncertainty by probabilities

• Use Bayes’ theorem: h = hypothesis e = evidence

P(h|e) = P(e|h) × P(h) P(e)

Starting belief=‘prior’

New belief

Suppose:• h = “the athlete is taking steroids”• e = “test result is positive”And:• P(h) = 0.01 (one in 100 people)• P(e|h) = 0.8 (true positive rate)• P(e|not h) = 0.1 (false positive rate)

What is P(h|e)?

Bayes’ Theorem for Estimating Risk

In general, people can’t do Bayes Theorem (well) off hand!

≈ 0.075 (7.5%)

And how do we scale up to X1, X2, ….. X100, …. X1000 ??

Bayesian Networks

• Developed by graphical modeling & AI communities in 1980s for probabilistic reasoning under uncertainty

• Many synonyms– Bayes nets, Bayesian belief

networks, directed acyclic graphs, probabilistic networks

Judea Pearl 2012 Turing

Award

Native Fish Example

A local river with tree-lined banks is known to contain native fish populations, which need to be conserved. Parts of the river pass through croplands, and parts are susceptible to drought conditions. Pesticides are known to be used on the crops. Rainfall helps native fish populations by maintaining water flow, which increases habitat suitability as well as connectivity between different habitat areas. However rain can also wash pesticides that are dangerous to fish from the croplands into the river. There is concern that the trees and native fish will be affected by drought conditions and crop pesticides.See http://bayesianintelligence.com/publications/TR2010_3_NativeFish.pdf

What are Bayesian networks?A graph in which the

following holds:1. A set of random

variables = nodes in network

2. A set of directed arcs connects pairs of nodes

3. It is a directed acyclic graph (DAG), i.e. no directed cycles

4. Each node has a conditional probability table or distribution (CPT or CPD) that quantifies the effects the parent nodes have on the child node

• Node = variable• Arc represents dependencies• Structure represents the causal

process (qualitative)

BN parameters (quantative aspect)

A graph in which the following holds:

1. A set of random variables = nodes in network

2. A set of directed arcs connects pairs of nodes

3. It is a directed acyclic graph (DAG), i.e. no directed cycles

4. Each node has a conditional probability table or distribution (CPT or CPD) that quantifies the effects the parent nodes have on the child node

2 states

3 states

Each row sums to 1

CPT

What next?

• We now have a model!

Q. How do we use the model to compute new probabilities?

A. we have clever efficient algorithms that do lots of applications of Bayes’ theorem

Reasoning with Bayesian networks

Evidence: observation of specific state Task: given some evidence, what are the new posterior probabilities for query node(s) ?

Intercausal reasoning

Flu

Mixed reasoningDiagnosis

Effect

Cause

Prediction

Effect

Cause

Demo – Native Fish

Before you know anything (no evidence)

Predictive reasoning (cause to effect): Case 1“What if?”

Effects

Causes

Predictive reasoning (cause to effect): Case 2

Effects

Causes

Predictive reasoning (cause to effect): Case 3

Effects

Causes

Diagnosis (effect to cause)

Effects

Causes

Prediction – “what if”

Effects

Causes

What next?

• Have model• Have estimates of posterior probabilities

Q. How do we use these probabilities to inform decisions (about action or interventions)?

Risk Assessment – the decision-theoretic view

Risk = Likelihood x Consequence

P(Outcome|Action,Evidence) Utility(Outcome|Action)

Decision making is about reducing risk or “maximising expected utility”

Decision nodes

Utility nodes(cost/benefits)

Decision network = BN + decisions + utilities

Our methodology

1: Build a model• E.g. Variables: patient’s details,

diseases, symptoms, interventions

• Costs/benefits: eg. $, QALY

Test

ReviewStructure

Parameters

Experts

DataLiterature

2: Embed model in decision support tool• Diagnosis• Prognosis• Treatment• Risk assessment• Prevention

Design

Build

Review

Revise

Advantage of BNs?• Explicit & sound representation of uncertainty• Visualisation of causal process

– not a “black box”

• Powerful reasoning engine• Can be built from a combination of:

– Data (observational or simulated)– Expert opinion– Equations from the literature

• Can be extended with decision and utility nodes (“Bayesian decision networks”)

• Many ecological and environmental applications (risk assessment, management, monitoring)

Challenges for BNs?

1. Some BN software handle only discrete variables

2. Complex BNs are not easy to build, validate or understand

3. BNs don’t allow cycles, so can’t model feedback loops?

1. Winbugs (handles cts variables) or AgenaRisk (dynamic discretization)

2. “Divide-and-conquer”Use sub-networks (GeNIe) or object-oriented BNs (Hugin, AgenaRisk)

3. Model with dynamic Bayesian networks (DBNs) (Netica, GeNIE, Hugin, etc)

• Biosecurity• Ecological and Environmental Management• Bushfire management• Health• Weather• Asset management• [and lots more](If any particular application matches your area of interest, come and talk to me!”

Real-world applications of BN technology

Example: Biosecurity Risk Assessment

Biosecurity (Import Risk Assessment)

Exposure pathways based on WTO framework

Each pathway for each pest for each product-source pair assessed separately. Obvious similarities to food security pathways

Simple BN model of NZ apples Import Risk Assessment (IRA):

Example of ‘what-if’ reasoning

Australia’s assumptions NZ assumptions

Model of causal process

More or less complex models for each stage in pathway

Model of mitigation actions

NZ Apples BN (AgenaRisk version)Explicit handling of quantities (of product)

Control Point BNs (CP-BNs)(Mengersen et al, 2012)

For export pathways, structured, rather than ad hoc use of BNs

NZ “B3: Better Border Biosecurity(NZ Inst. for Plant & Food research)

• Single pest – multiple pathways

BNs for Risk assessment for Log Exports in NZ

Collaboration with SCION (NZ timber research)

Potential sink population prevalence(script/BN 2.2.5)

Activity(BN 2.2.4)

Flight conditions(BN 2.2.2)

Deadwood (simulation 2.1.3)

Dispersal kernel(simulation 2.1.2)

Meteorology(GIS 1.1.1)

Forestry history(GIS 1.1.3)

Topography(GIS 1.1.2)

Pest distribution(GIS 1.1.5)

Source population prevalence(GIS 1.3.3)

Source population prevalence (BN 2.2.3)

Potential sink population prevalence(GIS 1.3.5)

Temperature dependentdevelopment

(simulation 2.1.1)

Temperature dependentdevelopment(GIS 1.2.1)

Local population prevalence(BN 2.2.6)

Local population prevalence(GIS 1.3.6)

Flight condtions(GIS 1.3.2

Activity(GIS 1.3.4)

Deadwood(GIS 1.2.3)

Dispersal kernel(GIS 1.2.2)

Log pest prevalence(Script 2.3.2)

Log pest prevalence(DB 1.4.2)

Log batch pest prevalence(Script 2.3.3)

Log batch pest prevalence(DB 1.4.3)

Forestry history(log tag DB 1.1.6)

Forest productivity(GIS 1.1.4)

Mature adults(BN 2.2.1)

Mature adults (GIS 1.3.1)

Pest infestation rate(BN 2.3.1)

Pest infestation rate(DB 1.4.1)

North Australia Biosecurity (NAB)BN and Support Tool

NAB: Infection Point

Amalgamate all pests entering destination

Is it enough pests to trigger an establishment?

How effective are measures taken to eradicate established population?

How much is enough to establish?

Outputs from pathways sub-models

Pest Present (t+1) = (Pest Present (t) or Establish?) and not Bernoulli(Eradication Efficacy)

Examples: Environmental Management

Goulburn catchment native fish model (2004)-5 sub-networksWater QualityFlowStructural HabitatBiological Interactions

-2 query nodesFish AbundanceFish Diversity

-23 sites 6 reaches

-2 temporal scales 1 and 5 year changes

Object-oriented BNs

An extension to basic BNs that allow• HieracFor hierarchical decomposition

Hydraulic Habitat

Structural Habitat

Water Quality

Biological Interactions

Species DiversityOutcomes

Single site model

Object-oriented BNs

• For spatial modeling (linked to GIS)

Site 1 Site 2 Site 3

Site 4

Site 7

Site 6

Site 8

Site 6

Site 9

Dynamic Bayesian networks (DBN)

For explicitly modeling changes over time (including feedback loops)

T1 T2 T3

Case Study: Modelling Willows (in St. John’s River Basin, Florida)

Plant and seed collectionArtificial Islands

Transplanting

Changes in water depthMay 2010

June 2010

March 2011

August 2010

Artificial Ponds

Greenhouse exptsGrazing

Evaluating germination

Experimental research program 2009-2011

DBN Example: Modelling Willows (in St. John’s River Basin, Florida)

Empty

Yearling

Sapling

Adult

Next state

State transitions

Current state

Scenarios

cell size = 100m x 100m (1ha)CanalsCattailGrassSedgeMarsh

SawgrassHerbaceousMarshWillowSwampMixedShrubTreeIslandHardwoodSwampOpenWater

Levees

Architecture of the Integrated Management Tool

GIS data

ST-DBN:State-

TransitionDynamic Bayesian Network

Seed Production & Dispersal

Spatial Bayesian Network

Managing Complexity: Object-oriented Modeling

Enough_Bare_Ground

Burn_Decision

Burn_Intensity

Vegetation

Summer_PPTCanal_or_Center

Soil_Type

BurnEffect_on_Willow

Spring_PPTMech_Clearing

GrowingSeason_PPT

Available_Water_Spring Available_Water_Survival

Available_Water_GrowingSeasAvailable_Water_Germination

Level of Cover (T)

Stage (T)

Proportion_Germinating Seedling_Survival_Proportion

Level of Cover (T+1)

Stage (T+1)

Seed_Availability NumberGerminating NumberSurviving

Rooted_Basal_Stem_Diameter (T)

Rooted_Basal_Stem_Diameter (T+1)

Sapling_Transition

Yearling_Transition

UnOccupied_Transition

Burnt_Adult_Transition

NonInterv_Yearling_Transition

Adult_Transition

Seed_Production

Modelling Seed Production

SeedsPerStem = I * F * SwhereI is number of inflorescencesF is the number fruits per inflorescenceS is number of seeds per fruit

SeedsPerHA = SeedsPerStem * NumberOfStemsPerHA

Application of BNs for complex environmental management: Western Grasslands Reserves

(DSE Project 2012-2013)

• 10,000 ha to be restored to native grasslands over 10-20 years

• Task: build a dynamic Object-Oriented BN to evaluate “what-if” scenarios over 20 years– a range of management

strategies– for a variety of land types– explicitly representing

costs and environmental values

NERP Tropical Ecosystems project 9.4:Conservation Planning for a Changing Coastal Zone

GIS-BN Tool

Input Layers (GIS)

Cumulative Impact Model

(BN)

Output (GIS)

Land Use Scenario (GIS)

Example: Bushfire management

Modelling bushfire prevention & suppression: Dynamic BN

House Risk Assessment Toolwhich uses a back-end BN reasoning engine:

Importance of the interface

BNs for modelling $ consequences of bushfires and costs of fire management treatments:

focus on economic aspects (not environmental)

0 1.3 2.6 3.899999999999990

0.2

0.4

0.6

0.8

1

Ember Density

Pro

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of B

urn

Template

Submodels (e.g. fire vulnerability)

Medical Risk Assessment: Coronary Heart DiseaseClinical decision support tool showing impact of

behaviour modification

Model built from data and based on existing epidemilogical models

Basic interface (research

prototype), never deployed

Power industry asset risk management (Western Power 2012-2013)

“How to build 24 Bayesian models in 9 months” (ABNMS-13)• A BN model for each kind of asset (e.g. ‘poles’)

Bayesian networks for fog forecasting(Collaboration with Aus. Bur. of Meteorology)

Incremental development, build relationship over 10 years

Stage 1: 2005-09• Static model (no explicit time)• In use by weather forecasters in

Melbourne and Perth

Stage 2: 2013-15• Explicitly temporal modelling• Predicting time of onset and

clearance

Example of rare event prediction, used to generate fog alerts

Connections to food security?

1. BNs are a great modelling tool for any individual component of Food Security (Michael’s Micro Analysis)

2. BNs allow re-use of model components, tailoring to different regions, populations, food types, etc

3. Current Research Aim: Scaling up the technical infrastructure to model full(?) system, with multiple interacting components (Michael’s Macro Analysis)

4. Additional challenge for Food Security:• Integrating the Social, Physical & Biological Science

Bayesian techniques at Monash

BN Models

Data Mining(CaMML,

Chordalysis,Snob)

Expert Elicitation

Existing models

Evaluation

Decision support

tools

Advanced modelling

(dynamic/time series, object oriented)

Current research• Scaling up to

1000s of variables

• Learning models with unobserved variables

• Combining data + expert knowledge

• Visualisation of probabilistic outputs