Introduction to WinBUGS

Transcription

1 Introduction to WinBUGS Joon Jin Song Department of Statistics Texas A&M University Introduction: BUGS BUGS: Bayesian inference Using Gibbs Sampling Bayesian Analysis of Complex Statistical Models using MCMC techniques MRC Biostatistics unit in Cambridge, UK (1995) Graphical Modeling Introduction: WinBUGS Similar to Classical BUGS Menu Control of Session An interactive Windows Version of Classical BUGS Easy to Copy and Paste to other packages How to obtain WinBUGS Version 1.4 is available, but it is restricted version for educational purpose. To remove the restriction, go to and fill in registration form How to install WinBUGS Create WinBUG14 directory within Program File in your computer Copy or download WinBUGS14.exe to WinBUGS14 directory Double click on WinBUGS14.exe and follow the instructions in the dialog box Create shortcut for WinBUGS14.exe and drag this shortcut to the desktop Double click on WinBUGS14.exe to run WinBUGS14 Fill in registration form and receive an which contain key to remove the restriction

2 Start WinBUGS14 and open a new empty window Copy key code from received and paste it to new empty window From the Tools menu pick the Decode option and click on the Decode All to install the key Quit and restart WinBUGS14 to start using the full version A Simple Example Consider a set of 5 observed (x,y), (1,1), (2,3), (3,3), (4,3), (5,5). We shall fit a simpler linear regression of Y on x, Y i ~ N(, τ ) α ~ N (0,1.0 E 6) µ i µ = α + β ( x) i x i β ~ N (0,1.0 E 6) τ ~ Gamma(0.001,0.001) model # Declare Model Command { # Start for (i in 1:N) { # Loop i to N Y[i]~dnorm(mu[i],tau) # Y i ~ N( µ i, τ ) mu[i]<-alpha+beta*(x[i]-mean(x[])) # µ i = α + β ( x i x) } # End Loop sigma<-1/sqrt(tau) alpha~dnorm(0,1.0e-6) # α ~ N (0,1.0 E 6) beta~dnorm(0,1.0e-6) # β ~ N (0,1.0 E 6) tau~dgamma(1.0e-3,1.0e-3) # τ ~ Gamma(0.001,0.001) } # End Start WinBUGS Select New from menu File Write the Model command

3 Data and Initial Values Running WinBUGS Data: list(x=c(1,2,3,4,5),y=c(1,3,3,3,5),n=5) Init: list(alpha=0,beta=0,tau=1) Open Specification from Model Menu Highlight the Model Command and select Check Model in Specification Tool Load Data If syntax is correct, Model is syntactically correct message is shown in bottom of WinBUGS Highlight the word list in data and select load data If data are loaded, data loaded is shown in bottom left hand corner.

4 Compile Select compile and check model complied in bottom left hand corner Load Initial Values Select load inits and check model is initialized in bottom left hand side Generating Initial Values list(alpha=0,tau=1): incomplete specification of initial values Monitoring Parameters Select Samples in Inference Menu Monitoring Parameters Write name of monitored parameters and click set Update the Model Select Update from menu Model

5 Update the Model The number of updates between redrawing the screen The number of MCMC updates to be carried out Summarizing the Posterior Plots the values against iteration number To select a subset of the stored sample for analysis Plots out a complete trace for the variables The samples from every kth iteration will be stored To select an over-relaxed form MCMC This box will be ticked while the Metropolis or slicesampling MCMC is in its initial tuning Remove the stored values Summary statistics ASCII representation of the monitored values Plots out the running mean with running 95% confidence intervals against iteration number Plots a smoothed kernel estimate Plots the autocorrelation function of the variable Calculate the Gelman-Rubin statistics Summary Statistics MCMC Time Series Click stats after selecting parameters Click history in Sample Monitor Tool Kernel Density Burn In Click density in Sample Monitor Tool Model has been updated Store all values by updating Specify Burn In on beg in Sample Monitor Tool