“WinBUGS” by Haitao Chu

1. “WinBUGS”by Haitao Chu Presented as part of the Statistical Software Interest Group’s seminar series. Visit www.sph.emory.edu/bios/ssig/ for more information. April 15, 2003

2. Outline • What is BUGS/WinBUGS? • Why do we want to use WinBUGS? • Where do we get WinBUGS? • How do we install WinBUGS? • How do we use WinBUGS? • Example • What kind of output can WinBUGS give us? • What kind of sampling method does WinBUGS implement? • Summary

3. What is BUGS?

4. What is BUGS? Bayesian inference Using Gibbs Sampling • is a piece of computer software for the Bayesian analysis of complex statistical models using Markov chain Monte Carlo (MCMC) methods. • It grew from a statistical research project at the MRC BIOSTATISTICAL UNIT in Cambridge, but now is developed jointly with the Imperial College School of Medicine at St Mary’s, London.

5. Classic BUGS WinBUGS (Windows Version) BUGS GeoBUGS (spatial models) PKBUGS (pharmokinetic modelling) What is BUGS? • The Classic BUGS program uses text-based model description and a command-line interface, and versions are available for major computer platforms (Sparc, Dos). However, it is not being further developed.

6. What is WinBUGS? • WinBUGS, a windows program with an option of a graphical user interface, the standard ‘point-and-click’ windows interface, and on-line monitoring and convergence diagnostics. It also supports Batch-mode running (version 1.4). • GeoBUGS, an add-on to WinBUGS that fits spatial models and produces a range of maps as output. • PKBUGS, an efficient and user-friendly interface for specifying complex population pharmacokinetic and pharmacodynamic (PK/PD) models within WinBUGS software.

7. Why do we want to use WinBUGS? • Its ability to fit complex statistical models using MCMC methods. • Its flexibility to program, two different ways to specify model • DoodleBUGS: Direct graphics • BUGS language • Free to download • A lot of examples in WinBUGS • A lot of online resources http://www.mrc-bsu.cam.ac.uk/bugs/weblinks/webresource.shtml

8. Where do we get WinBUGS • Free download http://www.mrc-bsu.cam.ac.uk/bugs. • Package needs to be downloaded • WinBUGS14.exe • Potential useful packages for convergence diagnostics • CODA (Convergence Diagnostic and Output Analysis) for S+ or R • BOA (Bayesian Output Analysis) for S+ or R

9. How do we install WinBUGS? • Downloading the file WinBUGS14.exe (also available in S:/Haitao Chu/WinBUGs) • Exit all other programs currently running (particularly if using Windows XP) • Go into Explore and double click on WinBUGS14.exe • Follow the instructions in the dialog box • You should have a new directory called WinBUGS14 within Program Files • Inside the WinBUGS14 directory is a program called WinBUGS14.exe • Drag the pretty icon to your desktop to create a shortcut. • Double click on WinBUGS14.exe to run WinBUGS14.

10. How do we install WinBUGS? • Obtaining the key for unrestricted use by registration at http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/register.shtml • Following the instructions from automatic response of your registration to remove the restrictions in WinBUGS 1.4 • check that the date of Keys.ocf file in ..\WinBUGS14\Bugs\Code\ has been updated.

11. How do we use WinBUGS? Educational Example: Pumps: conjugate Gamma-Poisson hierarchical model • The pumps data • Gamma-Poisson hierarchical model • Model specification in WinBUGS • DoodleBUGS, Direct graphics • BUGS language • Format data and specify initial values • Tutorial

12. The pumps data • ti: the length of operation time of the pump (in 1000s of hours). • xi: the number of failures

13. Gamma-Poisson hierarchical model

14. Model specification through DoodleBUGS • Nodes • Constants, denoted byrectangles • Stochastic nodes, denoted by ellipses • Deterministic nodes, logical function of other nodes • Edges • Directed links • Solid arrow: stochastic dependence • Hollow arrow: logical function • Undirected links, dashed line • representing an upper or lower bound • Plates, repeated parts of the graph Read the User Manual & Doodle help at the Help menu…

15. Model specification through DoodleBUGS Stochastic node Stochastic dependence Constant node logical function Deterministic node Plate

16. Model specification through BUGS language

17. Format data and specify initial values • Data format • S-Plus format list(t = c(94.3, 15.7, 62.9, 126, 5.24, 31.4, 1.05, 1.05, 2.1, 10.5), x = c(5, 1, 5, 14, 3, 19, 1, 1, 4, 22), N = 10) • Rectangular format Please see formatting of data at model specification at User Manual • Initial values list(alpha = 1, beta = 1) list(alpha = 10, beta = 10)

18. Tutorial: Interactive submission • Standard windows “point and click” method • Example Pumps — conjugate Gamma-Poisson hierarchical model in Example Volume I at Help menu S:/Haitao Chu/WinBUGS/pumps/pumps.odc

19. Tutorial: Batch mode submission • Files required • The script itself, S:/Haitao Chu/WinBUGS/pumps/pumpsbatch.odc • Model file, S:/Haitao Chu/WinBUGS/pumps/pumpsmodel.txt • Data file, S:/Haitao Chu/WinBUGS/pumps/pumpsdata.txt • Initial values file • S:/Haitao Chu/WinBUGS/pumps/pumpsin1.txt • S:/Haitao Chu/WinBUGS/pumps/pumpsin2.txt • Format of the files • native WinBUGS format with .odc extension • text format with .txt extension

20. Tutorial: running WinBUGS from R and other programs • From R • http://www.stat.columbia.edu/~gelman/bugsR • S:/Haitao Chu/WinBUGS/bugsR • From other programs • http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/remote14.shtml

21. What kind of output can WinBUGS give us? • Samples at Inference Menu • trace: plots the variable value against iteration number. • history: plots out a complete trace for the variable. • density: smoothed kernel density estimate for continuous variable or a histogram for discrete variable. • auto cor: auto correlation, up to lag-50 • stats: Summary statistics, pooling over the chains selected. • coda: output the monitored values to CODA or BOA

22. What kind of output can WinBUGS give us? • Samples at Inference Menu • quantiles: plots out the running mean with running 95% confidence intervals against iteration number. • bgr diag: Brooks-Gelman-Rubin convergence statistic • Brooks and Gelman (1998) • Green: the width of the central 80% interval of the pooled runs • Blue: the average width of the 80% intervals within the individual runs • Red: their ratio R (= pooled / within). • Convergence: R to 1, and with convergence of both the pooled and within interval widths to stability.

23. What kind of output can WinBUGS give us? Compare at Inference Menu Box Plot Caterpillar Plot

24. What kind of output can WinBUGS give us? • Rank at Inference Menu • stats: the distribution of the ranks of each component of the variable. • histogram: the empirical distribution of the simulated rank for each component • DIC at Inference Menu • Deviance Information Criterion

25. What kind of sampling method does WinBUGS implement? Sampling methods are used in the following hierarchies Continuous target distribution Conjugate Direct sampling using standard algorithms Log-concave Derivative-free adaptive rejection sampling Non-log-concave (restricted range) Slice sampling Non-log-concave (unrestricted range) Metropolis Discrete target distribution (I have no experience) Finite upper bound Inversion Shifted Poisson Direct sampling using standard algorithm

26. Summary • What is BUGS/WinBUGS? • Why do we want to use WinBUGS? • Where do we get WinBUGS? • How do we install WinBUGS? • How do we use WinBUGS? • What kind of output can WinBUGS give us? • What kind of sampling method does WinBUGS implement? • MCMC can be dangerous

27. The End Thank you very much for attending and participating in this Statistical Software Interest Group seminar… More volunteers!