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WinBUGSby Haitao Chu

• Presented as part of the Statistical Software
  Interest Groups seminar series. Visit
  www.sph.emory.edu/bios/ssig/ for more
  information.
• April 15, 2003

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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

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What is BUGS?
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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 Marys, London.

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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.

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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.

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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/webres
  ource.shtml

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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

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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.

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How do we install WinBUGS?

• Obtaining the key for unrestricted use by
  registration at
• http//www.mrc-bsu.cam.ac.uk/bugs/winbugs/registe
  r.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.

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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

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The pumps data
PUMP ti xi
1 94.5 5
2 15.7 1
3 62.9 5
4 126 14
5 5.24 3
6 31.4 19
7 1.05 1
8 1.05 1
9 2.1 4
10 10.5 22

• ti the length of operation time of the pump (in
  1000s of hours).
• xi the number of failures

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Gamma-Poisson hierarchical model
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Model specification through DoodleBUGS

• Nodes
• Constants, denoted by rectangles
• 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

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Model specification through DoodleBUGS
Stochastic node
Stochastic dependence
Constant node
logical function
Deterministic node
Plate
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Model specification through BUGS language
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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)

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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

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Tutorial Batch mode submission

• Files required
• The script itself, S/Haitao Chu/WinBUGS/pumps/pum
  psbatch.odc
• Model file, S/Haitao Chu/WinBUGS/pumps/pumpsmodel
  .txt
• Data file, S/Haitao Chu/WinBUGS/pumps/pumpsdata.t
  xt
• 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

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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

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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

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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.

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

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What kind of sampling method does WinBUGS
implement?
Sampling methods are used in the following
hierarchies Continuous target distribution Conju
gate 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
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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

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The End

• Thank you very much for attending and
  participating in this Statistical Software
  Interest Group seminar
• More volunteers!