Bayesian networks for decision making under uncertaintyHow to combine data, evidence, opinion and guesstimates to make decisions

InformationTechnology

Professor Ann Nicholson

Deputy DeanFaculty of Information TechnologyMonash University

SourcesofUncertainty

• Solution:ProbabilityTheory

Ignorance PhysicalrandomnessComplexity

Thereasoningprocess1.Startwithabeliefina

proposition“Theimportedmangois

infestedwithapest”“Thepatienthaslung

cancer”“Theapplicantwillpayback

theloan”“Salesofaproductwill

increase”

“Beliefs”• Veryunlikely• 1%chance• Oddsof100to1• 0.01probabilityFrom• Gutfeeling• Expertopinion• Data

Thereasoningprocess1.Startwithabeliefina

proposition“Theimportedmangois

infestedwithapest”“Thepatienthaslung

cancer”“Theapplicantwillpayback

theloan”“Salesofaproductwill

increase”

2. New information becomes available

“Itisfromacountrywherethepestisendemic”

“Thepatientisasmokerandhasacough”

“Theapplicantdefaultedonaprevious loan”

“Somemodelsarerecalledforsafetyreasons”

3.Updateyourbeliefs But how?

Probabilitytheoryforrepresentinguncertainty

• Propositionsareeithertrueorfalse“Patienthascancer”

• Assignsanumericaldegreeofbeliefbetween0and1topropositionsP(“Patienthascancer”)=0.001prior probability (unconditional)

• WecannowrepresenttheimpactofevidenceonbeliefP(“Patienthascancer|positivemammogram”) =0.8• Conditional probability• Or,posterior probability(bywayofBayes’theorem)

TheBayesianapproach

TheRev.ThomasBayes1702?-1761

• Represent uncertaintybyprobabilities

• UseBayes’theorem:h=hypothesise=evidence

P(h|e) = P(e|h) × P(h)P(e)

Startingbelief=‘prior’

Newbelief

EstimatingRisk

Scenario: Anathleteistestedforsteroiduseandthetestcomesbackpositive.Youknowthat:• Onein100competitors arethoughttotake

steroids• Thetestisn’talwaysaccurate

Falsepositiverate:10%Falsenegativerate:20%

Q.Whatistheprobabilitytheathlete isadrugcheat?

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’TheoremforEstimatingRisk

Ingeneral,peoplecan’tdoBayesTheorem (well)offhand!

≈ 0.075 (7.5%)

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

BayesianNetworks

• Developed bygraphicalmodeling&AIcommunities in1980sforprobabilisticreasoningunderuncertainty

• Manysynonyms– Bayesnets,Bayesianbeliefnetworks,directedacyclicgraphs,probabilisticnetworks

Judea Pearl 2012 Turing

Award

ProbabilisticGraphicalModels

…andquantifytheuncertainty

…capturetheprocessstructure(notblackbox)

Foratargetsystem…

Whyusemodels?• Increases understanding• Supportsdecisionmaking• Usenewdataandevaluationtoimproveovertime

NativeFishExample

Alocalriverwithtree-linedbanks isknowntocontainnativefishpopulations,whichneedtobeconserved.Partsoftheriver passthroughcroplands,andpartsaresusceptible todrought conditions.Pesticides areknowntobeusedonthecrops.Rainfall helpsnativefishpopulationsbymaintainingwaterflow,whichincreaseshabitatsuitabilityaswellasconnectivity betweendifferenthabitatareas.Howeverraincanalsowashpesticides thataredangerous tofishfromthecroplandsintotheriver.Thereisconcern thatthetrees andnativefishwillbeaffectedbydroughtconditionsandcroppesticides.Seehttp://bayesianintelligence.com/publications/TR2010_3_NativeFish.pdf

BayesianNetworks- Definition

Agraph inwhichthefollowingholds:

1. Asetofrandomvariables=nodes innetwork

2. Asetofdirectedarcs connectspairsofnodes

Structure represents the causal process.(Anything missing?)

BayesianNetworks- DefinitionAgraph inwhichthe

followingholds:1. Asetofrandom

variables=nodes innetwork

2. Asetofdirectedarcsconnectspairsofnodes

3. Eachnode hasaconditionalprobability table(CPT)thatquantifies theeffects theparentnodeshaveonthechild node

4. Itisadirectedacyclicgraph(DAG), i.e.nodirectedcycles

Each row sums to 1

WORST CASEBEST CASE

Beforeyouknowanything(noevidence)

(Screen shots from the Netica BN software)

Diagnosis

Effects

Causes

Prediction

Effects

Causes

Whatnext?

• Havemodel• Haveestimatesofposteriorprobabilities

Q.Howdoweusetheseprobabilities toinformdecisions (aboutactionorinterventions)?

RiskAssessment– thedecision-theoreticview

Risk=Likelihood xConsequence

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

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

Decision nodes

Utility nodes(cost/benefits)

Decisionnetwork=BN+decisions+utilities

Ourmethodology1:Buildamodel• E.g.Variables:patient’sdetails,

diseases, symptoms,interventions

• Costs/benefits:eg.$,QALY

Test

ReviewStructure

Parameters

Experts

DataLiterature

2:Embedmodelindecisionsupporttool• Diagnosis• Prognosis• Treatment• Riskassessment• Prevention

Design

Build

Review

Revise

Bayesiannetworksforfogforecasting(CollaborationwithAus Bur.ofMeteorology)

Phase1:(Boneh etal,2015)Inusebyweather forecastersinMelbourne since2006

Willtherebeafogbefore9amtomorrowmorning?

Bayesiannetworksforfogforecasting

Stage2:2013-15Researchproject(prototype)(Boneh etal.Inpreparation)• Explicittemporalmodelling,predictingtimeofonsetandclearance

CaseStudy:ModellingWillows(inSt.John’sRiverBasin,Florida)

Plant and seed collectionArtificial Islands

Transplanting

Changes in water depthMay 2010 Artificial Ponds

Greenhouse exptsGrazing

Evaluating germination

Experimental research program 2009-2011

DBNExample:ModellingWillows(inSt.John’sRiverBasin,Florida)(Wilkinsonetal.,2013)

Next state

State transitions

Current state

Scenarios

Yearling

Unoccupied

Sapling

Adult

Burnt Adult

Willow life-history stage transitions

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

Architecture of the Integrated Management Tool

GIS data

ST-DOOBN:State-

TransitionDynamic OO

Bayesian Network

Seed Production & Dispersal Spatial OO Bayesian Network

(Chee et al., 2016)

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

ApplicationofBNsforcomplexenvironmentalmanagement:WesternGrasslandsReserves

(DSEProject2012-2013)(Sinclairetal.,InPreparation)

• 10,000hatoberestoredtonativegrasslands over10-20years

• Task:buildadynamicBNtoevaluate“what-if”scenariosover20years– arangeofmanagementstrategies

– foravarietyoflandtypes– explicitlyrepresentingcostsandenvironmentalvalues

BNsforRiskassessmentforLogExportsinNZ

CollaborationwithSCION(NZtimberresearch)

Potentia l s ink popula tion preva lence(s cript/BN 2.2.5)

Activity(BN 2.2.4)

Flight conditions(BN 2.2.2)

Deadwood (s imula tion 2.1.3)

Dis pers a l ke rne l(s imula tion 2.1.2)

Meteorology(GIS 1.1.1)

Fores try his tory(GIS 1.1.3)

Topography(GIS 1.1.2)

Pes t dis tribution(GIS 1.1.5)

Source popula tion preva lence(GIS 1.3.3)

Source popula tion preva lence (BN 2.2.3)

Potentia l s ink popula tion preva lence(GIS 1.3.5)

Tempera ture dependentdeve lopment

(s imula tion 2.1.1)

Tempera ture dependentdeve lopment(GIS 1.2.1)

Loca l popula tion preva lence(BN 2.2.6)

Loca l popula tion preva lence(GIS 1.3.6)

Flight condtions(GIS 1.3.2

Activity(GIS 1.3.4)

Deadwood(GIS 1.2.3)

Dis pers a l ke rne l(GIS 1.2.2)

Log pes t preva lence(Script 2.3.2)

Log pes t preva lence(DB 1.4.2)

Log ba tch pes t preva lence(Script 2.3.3)

Log ba tch pes t preva lence(DB 1.4.3)

Fores try his tory(log tag DB 1.1.6)

Fores t productivity(GIS 1.1.4)

Mature adults(BN 2.2.1)

Mature adults (GIS 1.3.1)

Pes t infes ta tion ra te(BN 2.3.1)

Pes t infes ta tion ra te(DB 1.4.1)

BayesWatch:BNsforanomalydetectionintracking (CollaborationwithDSTO)(Mascaro etal.,2014)

• Task:Detectanomalousbehaviour ofvessels, cars,pedestrians

• OriginallyusedAISdatafromvessels inSydneyHarbour

• ApplyBNlearningtobuildmodelsofbehaviour

• Combines TimeseriesBN+TrackSummary BN

• Usemetricstoassessanomalous tracks

Modellingbushfireprevention&suppression(Penmanetal.,2015)

(ScreenshotfromtheGeNIe BNsoftware)

MedicalRiskAssessment:HeartDisease(Nicholsonetal.,2008;Floresetal.,2011)

SimpleBNmodel:NZapplesImportRiskAssessment(Wintle etal.,2014).Exampleof‘what-if’reasoning

Australia’s assumptions NZ assumptions

NZApplesBN(Wintle etal.,2014)Explicithandlingofquantities(ofproduct)

(Screen shot from the AgenaRisk BN software)

Bayesianmodellingoverview

BNModels

DataMining(CaMML,

Chordalysis,Snob)

ExpertElicitation

Existingmodels

Evaluation

Decisionsupporttools

Advancedmodelling

(dynamic/timeseries,objectoriented)

Current research• FullOOBN

frameworkandmethodology

• Learningmodelswithunobservedvariables

• OnlineDelphi-basedexpertelicitation

• Visualisationofprobabilisticoutputs