Bursts modelling Using WinBUGS
Tim Watson
May 2012
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•Bayesian analysis software Using Gibbs Sampling for Windows.
•DoodleBugs – a graphical directed acyclic graph (DAG)
•Many add-ons, utilities, and variations of the package are alsoavailable (e.g. GeoBUGS-for spatial modelling, and PKBUGS-forpharmacokinetic)
•Can be run from other software packages, e.g. R.
•library(R2WinBUGS)
•Connecting to data
•Business as usual
What is WinBUGS?
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Exploratory Data Analysis
Linear Model
Log-LinearModel
Maybe somenon-linearity?
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•Define the model
•Load the data
•Specify the number of MCMC chains
•Compile the model
•Load values to initialise the algorithm
•Update the MCMC
•Sample parameters of interest
Running a statistical model in WinBUGS
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Note: WinBUGS uses precision instead ofvariance to specify a normal distribution!
Model 1Linear Regression in WinBUGS
model {
#specify likelihood
for( i in 1 : N ) {
Bursts[i] ~ dnorm(mu[i],tau)
}
for( i in 1 : N ) {
mu[i] <- alpha + beta * frost[i]
}
#specify priors
alpha ~ dnorm( 0.0,1.0E-6)
beta ~ dnorm( 0.0,1.0E-6)
tau ~ dgamma(0.001,0.001)
sigma <- sqrt(1 / tau)
}
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Results
R output
Estimate Std. Error t value Pr(>|t|)
(Intercept) 460.460 26.686 17.255 < 2e-16 ***
Nr.Air.Frost.Days 25.616 3.504 7.312 2.19e-09 ***
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Model 2Poisson Regression in WinBUGS
model {
for( i in 1 : N ) {
Bursts[i] ~ dpois(mu[i])
}
for( i in 1 : N ) {
log(mu[i]) <- alpha + beta * frost[i]
}
alpha ~ dnorm( 0.0,1.0E-6)
beta ~ dnorm( 0.0,1.0E-6)
}
R output
Estimate Std. Error z value Pr(>|z|)
(Intercept) 6.155015 0.007951 774.10 <2e-16 ***
Nr.Air.Frost.Days 0.038524 0.000861 44.74 <2e-16 ***
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Real word data (missing data) - Model 2b
•Missing data are easily handled
•Missing observations are treated asunknown parameters
•Missing values are denoted by “NA”
•Missing responses are no problem;they are simply estimated
•A missing explanatory variablemust either be replaced, or elsegiven some prior distribution
•Elicitation
model;
{
for( i in 1 : N ) {
Bursts[i] ~ dpois(mu[i])
}
for( i in 1 : N ) {
log(mu[i]) <- alpha + beta * frost[i]
}
alpha ~ dnorm( 0.0,1.0E-6)
beta ~ dnorm( 0.0,1.0E-6)
frost[1]~dunif(0,20)
frost[2]~dunif(0,20)
frost[4]~dunif(0,20)
}
list(Bursts = c(581, 504, NA, 403, 395, 484, 531,
338, 599, 611, 396, 1038, 990, 887, 722, 446, 510,
666, NA, 453, 300, 435, 532, NA, 1433, 626, 792,
499, 339, 247, 646, 367, 494, 372, 752, 924, 781, 599,
482, 438, 570, 533, 494, 715, 555, 370, 614, 524, 501,
851, 472), frost = c(NA, NA, 5.7, NA, 0.1, 0.1, 0, 0, 0, 2,
3.8, 15.3, 14.8, 11, 6.3, 2.5, 0.1, 0, 0, 0, 0, 0.9, 0.5, 13.2,
18.9, 15.4, 12.3, 5.1, 2.3, 0, 0, 0, 0.2, 2.7, 9.4, 23.1, 15.2,
3.8, 9.9, 0.3, 0.2, 0.2, 0, 0, 0, 0.4, 1.1, 4.1, 7.8, 11.1, 2.8
),N=51)
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Poisson Regression with some Missing observations inWinBUGS
Frost missing
Bursts missing
frost =c(4.1,10.1,5.8)
burst=c(504,664,1433)
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Month effect - Model 4
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•BUGS language quite straightforward to learn.
•Doodle Bugs even easier.
•Handles missing data easily.
•Very fast especially when the initialising values are closer to thestationary distribution.
•Can fit a wide variety of statistical models.
•Convenient in running multiple MCMC chains.
•Automated in R and other tools (including Excel)
•library(R2WinBUGS)
•library(Rexcel)
Why WinBUGS?
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•Need to understand what you are doing
•Saving the data in the appropriate format can be very challengingespecially large data set.
•Algorithm can easily crash especially when priors are not wellspecified or due to unrealistic initialising values.
•Algorithm can be very slow especially when dealing withhierarchical model.
•Needs to know the model to be fitted as every distribution have tobe defined.
Negatives about WinBUGS
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•Limitation in plotting capability.
•Learning BUGS syntax (though very similar to other packages suchas R, S-PLUS).
•Using extreme priors especially non-informative priors can causethe algorithm to crash.
Challenges with WinBUGS