WinBUGS DemoWinBUGS Demo

Saghir A. BashirSaghir A. Bashir Amgen Ltd, Cambridge, U.K.Amgen Ltd, Cambridge, U.K.

Email: saghir_bashir@hotmail.comEmail: saghir_bashir@hotmail.com

44thth January 2001 January 2001

OutlineOutline

IntroductionIntroduction BUGS and WinBUGSBUGS and WinBUGS Graphical ModelsGraphical Models DoodleBUGSDoodleBUGS Example - SimulationExample - Simulation Power calculationPower calculation SummarySummary

IntroductionIntroduction

Bayesian Inference Using Gibbs SamplingBayesian Inference Using Gibbs Sampling• BUGSBUGS

Analysis of Complex ModelsAnalysis of Complex Models

Bayesian MethodsBayesian Methods

Markov Chain Monte Carlo IntegrationMarkov Chain Monte Carlo Integration• Useful when no closed form existsUseful when no closed form exists

Classic BUGSClassic BUGS

Declarative Language Declarative Language • Similar to Splus Similar to Splus

Complex Statistical ModelsComplex Statistical Models• Missing dataMissing data• Measurement ErrorMeasurement Error• No closed form for LikelihoodNo closed form for Likelihood

Graphical ModellingGraphical Modelling

Flexible compared to Flexible compared to

approximationsapproximations

WinBUGSWinBUGS

Similar to Classic BUGSSimilar to Classic BUGS• Plus new methodological developmentsPlus new methodological developments

Graphical representation of modelGraphical representation of model• DoodleBUGSDoodleBUGS

Menu Control of sessionMenu Control of session

Cut and paste to other packagesCut and paste to other packages

BUGS and WinBUGSBUGS and WinBUGS

No data management facilityNo data management facility• Why reinvent the wheel?Why reinvent the wheel?

““Easy” interface with other Easy” interface with other packagespackages• R and SplusR and Splus• Stata Stata (S. Bashir)(S. Bashir)

Simple analysis of outputSimple analysis of output

Working with BUGSWorking with BUGS

Output AnalysisOutput Analysis

R/SplusSTATA

Prepare Data

Prepare Data

EditorStats packageSpread sheet

BUGS Analysis

BUGS Analysis

WinBUGSBUGS

Graphical ModelsGraphical Models

Complex multivariate probability Complex multivariate probability modelsmodels• RepresentationRepresentation• VisualisationVisualisation

Graphs...Graphs...• simplify complex modelssimplify complex models• communicate structure of the problemcommunicate structure of the problem• provide basis for computationprovide basis for computation

WinBUGSWinBUGS

BUGS languageBUGS language

DoodleBUGSDoodleBUGS• Used for the purposed of this Demo.Used for the purposed of this Demo.

WinBUGS is currently free from:WinBUGS is currently free from:• http://www.mrc-bsu.cam.ac.uk/bugs/http://www.mrc-bsu.cam.ac.uk/bugs/• Register to get full version accessRegister to get full version access

DoodleBUGSDoodleBUGS

Start WinBUGSStart WinBUGS Select “Select “DoodleDoodle” from menu bar” from menu bar

DoodleBUGS - BasicsDoodleBUGS - Basics

Select “Select “New…New…” ”

Press “Press “okok”” You have a window to “Doodle” in.You have a window to “Doodle” in.

NodesNodes

Creating a node Creating a node • Mouse clickMouse click in Doodle Window in Doodle Window

Deleting a node: Deleting a node: CTRL + DelCTRL + Del

Nodes can beNodes can be• Stochastic Stochastic

• LogicalLogical

• Constant (rectangle)Constant (rectangle)

Node TypesNode Types

Example - SimulationExample - Simulation

LetLet• r1 ~ Bin (0.25, 250)r1 ~ Bin (0.25, 250)• r2 ~ Bin (0.35, 150)r2 ~ Bin (0.35, 150)

Calculate p: common proportion for r1 & r2Calculate p: common proportion for r1 & r2

p = (r1+r2)/400p = (r1+r2)/400

Classical p = 0.2875 Classical p = 0.2875

DoodleBUGSDoodleBUGS

Start with r1 ~ Bin(0.25, 250) Start with r1 ~ Bin(0.25, 250) (stochastic node)(stochastic node)

DoodleBUGSDoodleBUGS

Add r2 ~ Bin(0.35, 150)Add r2 ~ Bin(0.35, 150) (stochastic node)(stochastic node)

Logical NodesLogical Nodes Add p as a logical nodeAdd p as a logical node

• To define a logical node click on “To define a logical node click on “typetype” for choices.” for choices.

Logical FunctionsLogical Functions

Add “edges” for the logical relationshipAdd “edges” for the logical relationship

• Whilst node p is highlighted, Whilst node p is highlighted, CTRL + clickCTRL + click in “parent in “parent nodes” r1 and r2 (hollow arrows nodes” r1 and r2 (hollow arrows logical function) logical function)

Stochastic NodesStochastic Nodes

Stochastic dependenceStochastic dependence• p1 ~ N(0.25, 0.000026)p1 ~ N(0.25, 0.000026) (i.e., p1 ~ [0.24, 0.26])(i.e., p1 ~ [0.24, 0.26])• size1 = 250 (constant)size1 = 250 (constant)

• Single arrows for stochastic dependenciesSingle arrows for stochastic dependencies

Normal DistributionNormal Distribution

NoteNote the Normal distribution in BUGS is defined as the Normal distribution in BUGS is defined as N (mean, precision) where N (mean, precision) where precision = 1/varianceprecision = 1/variance

• NoteNote that we can define upper and lower bounds so that that we can define upper and lower bounds so that the proportion is between 0 and 1.the proportion is between 0 and 1.

DoodleBUGS ModelDoodleBUGS Model

Let us add these stochastic Let us add these stochastic dependencies to our “logical” modeldependencies to our “logical” model

DoodleBUGS ModelDoodleBUGS Model

What is our model?What is our model?

• r1 ~ Bin (p1, size1)r1 ~ Bin (p1, size1)

• p1 ~ N (0.25, 0.000026)p1 ~ N (0.25, 0.000026)

• size1 = 250size1 = 250

• r2 ~ Bin (p2, size2)r2 ~ Bin (p2, size2)

• p2 ~ N (0.35, 0.000026)p2 ~ N (0.35, 0.000026)

• size2 = 150size2 = 150

WinBUGS ModellingWinBUGS Modelling

Running our model in WinBUGSRunning our model in WinBUGS• Create a New document Create a New document

• Menu bar - File - NewMenu bar - File - New

A New document window will appearA New document window will appear

WinBUGS DocumentWinBUGS Document

Select your Doodle from your Doodle Select your Doodle from your Doodle WindowWindow• Menu bar - Edit - Select DocumentMenu bar - Edit - Select Document

Copy your DoodleCopy your Doodle• Menu bar - Edit - CopyMenu bar - Edit - Copy

Paste it into your New DocumentPaste it into your New Document• Menu bar - Edit - PasteMenu bar - Edit - Paste

Model DataModel Data

Before running we need to give BUGS Before running we need to give BUGS some datasome data

• Type Type list(size1=250, size2=150)list(size1=250, size2=150) at the top (or at the top (or the bottom) of your new document.the bottom) of your new document.

Running BUGSRunning BUGS

Use Use “Specification...”“Specification...” from the “ from the “ModelModel” ” option on option on Menu BarMenu Bar to run BUGS to run BUGS

Running BUGSRunning BUGS

ChecksSyntax

ChecksSyntax

StartSampler

StartSampler

Check Model

Check Model

LoadData

LoadData

CompileModel

CompileModel

Initial Values

Initial Values

UpdateSampler

UpdateSampler

Check ModelCheck Model

Select the Doodle (note the hairy Select the Doodle (note the hairy boarder)boarder)

Menu bar - Model - Check modelMenu bar - Model - Check model NoteNote the message in bottom left hand the message in bottom left hand

cornercorner

Load DataLoad Data

Highlight the word “Highlight the word “listlist””

Menu bar - Model - DataMenu bar - Model - Data Bottom left hand cornerBottom left hand corner

Compiling the ModelCompiling the Model

Menu bar - Model - CompileMenu bar - Model - Compile Bottom left hand cornerBottom left hand corner

Load Initial ValuesLoad Initial Values

Menu bar - Model - Gen initsMenu bar - Model - Gen inits Bottom left hand sideBottom left hand side

Update the ModelUpdate the Model

Menu bar - Model - UpdateMenu bar - Model - Update

1000 MCMC updates to be carried out.1000 MCMC updates to be carried out.

Burn InBurn In

Model has been updatedModel has been updated

MCMC run did not store any data.MCMC run did not store any data.• Used for the “burn in”Used for the “burn in”

Store values by “monitoring” them Store values by “monitoring” them toto• Draw inferences Draw inferences • Monitor MCMC runMonitor MCMC run

Monitoring NodesMonitoring Nodes

Monitoring p our parameter of interestMonitoring p our parameter of interest Menu bar - Inference - Samples...Menu bar - Inference - Samples...

Sample Monitor ToolSample Monitor Tool

Monitoring NodesMonitoring Nodes

Type name of node “Type name of node “pp” to monitor” to monitor Press “Press “setset””

Update & MonitorUpdate & Monitor

UpdateUpdate model again model again

1000 values “monitored” of the MCMC 1000 values “monitored” of the MCMC run for prun for p

Summary StatisticsSummary Statistics

Summary statisticsSummary statistics Select “Select “pp” from the Sample Monitor Tool” from the Sample Monitor Tool Press “Press “statsstats” (Sample Monitor Tool)” (Sample Monitor Tool)

Node statistics windowNode statistics window

Summary StatisticsSummary Statistics

Mean = 0.2873Mean = 0.2873 Median = 0.285 Median = 0.285 (usually more (usually more

stable)stable)

95% credible interval (0.245, 0.335)95% credible interval (0.245, 0.335) MCMC run size 1000MCMC run size 1000

MCMC Time SeriesMCMC Time Series

Press “Press “HistoryHistory” in Sample Monitor Tool” in Sample Monitor Tool

Kernel DensityKernel Density

Press “Press “DensityDensity” in the Sample Monitor ” in the Sample Monitor ToolTool

Kernel DensityKernel Density

Increase monitored values to 25,000Increase monitored values to 25,000

PlatesPlates

Creating a plate Creating a plate • CTRL + mouse clickCTRL + mouse click in Doodle Window in Doodle Window

• Deleting a plate: Deleting a plate: CTRL + DelCTRL + Del

Allow more complex structure, e.g.,Allow more complex structure, e.g.,• Repeated measuresRepeated measures• Hierarchical modelsHierarchical models

Extend our example to calculate powerExtend our example to calculate power• r1 and r2 from Binomial distributionr1 and r2 from Binomial distribution• Simulte r1 and r2 100 times per “update”Simulte r1 and r2 100 times per “update”• Calculate test statisticCalculate test statistic• Count number of times it falls in critical regionCount number of times it falls in critical region

PlatesPlates

HH00: p1 = p2 = p vs H: p1 = p2 = p vs H11: p1 < : p1 < p2p2

• p1 = r1/size1p1 = r1/size1 && p2 = r2/size2p2 = r2/size2

Test statisticTest statistic

Test StatisticTest Statistic

(p2 - p1)s.d.(p)

s.d.(p) = (p(1-p)(1/size1 + 1/size2))

PowerPower

DataData• list(prop1=.25, prop2=.35, list(prop1=.25, prop2=.35, size1=250,size2=150, N=100, size1=250,size2=150, N=100, alpha.val=1.96)alpha.val=1.96)

ResultsResults

Power = 57% (47%, 67%)Power = 57% (47%, 67%)

Power - HistoryPower - History

Power - DensityPower - Density

UpdatesUpdates

Updating - Bottom left hand cornerUpdating - Bottom left hand corner

After updates finishAfter updates finish

SummarySummary

BUGS is a power toolBUGS is a power tool• Bayesian AnalysisBayesian Analysis• Simulation ToolSimulation Tool

Graphical Models Graphical Models • Doodle BUGSDoodle BUGS• Simple representation of modelSimple representation of model

Easy to use!Easy to use!