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Performing Bayesian analysis in Stata using WinBUGS Tom Palmer, John Thompson & Santiago Moreno Department of Health Sciences, University of Leicester, UK 13 th UK Stata Users Group Meeting, 10 September 2007 Tom Palmer (Leicester) Running WinBUGS from Stata 1 / 24

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  • Performing Bayesian analysis in Stata using WinBUGS

    Tom Palmer, John Thompson & Santiago Moreno

    Department of Health Sciences,University of Leicester, UK

    13th UK Stata Users Group Meeting,10 September 2007

    Tom Palmer (Leicester) Running WinBUGS from Stata 1 / 24

  • Outline

    1 The Bayesian approach & WinBUGS

    2 The winbugsfromstata package

    3 How to run an analysis

    4 Summary & developments

    Tom Palmer (Leicester) Running WinBUGS from Stata 2 / 24

  • The Bayesian approach

    Bayes Theorem

    Posterior Likelihood prior

    Direct probability statements - not frequentist - subjective

    Complex posterior marginal distributions - estimation via simulation

    Markov chain Monte Carlo (MCMC) methods

    Tom Palmer (Leicester) Running WinBUGS from Stata 3 / 24

  • The Bayesian approach

    Bayes Theorem

    Posterior Likelihood prior

    Direct probability statements - not frequentist - subjective

    Complex posterior marginal distributions - estimation via simulation

    Markov chain Monte Carlo (MCMC) methods

    Tom Palmer (Leicester) Running WinBUGS from Stata 3 / 24

  • The Bayesian approach

    Bayes Theorem

    Posterior Likelihood prior

    Direct probability statements - not frequentist - subjective

    Complex posterior marginal distributions - estimation via simulation

    Markov chain Monte Carlo (MCMC) methods

    Tom Palmer (Leicester) Running WinBUGS from Stata 3 / 24

  • The Bayesian approach

    Bayes Theorem

    Posterior Likelihood prior

    Direct probability statements - not frequentist - subjective

    Complex posterior marginal distributions - estimation via simulation

    Markov chain Monte Carlo (MCMC) methods

    Tom Palmer (Leicester) Running WinBUGS from Stata 3 / 24

  • WinBUGS

    Bayesian statistics using Gibbs sampling

    MRC Biostatistics unithttp://www.mrc-bsu.cam.ac.uk/bugs

    Health Economics, Medical Statistics

    Disadvantages: data management, post-processing of results, graphics

    Tom Palmer (Leicester) Running WinBUGS from Stata 4 / 24

    http://www.mrc-bsu.cam.ac.uk/bugs

  • WinBUGS

    Bayesian statistics using Gibbs sampling

    MRC Biostatistics unithttp://www.mrc-bsu.cam.ac.uk/bugs

    Health Economics, Medical Statistics

    Disadvantages: data management, post-processing of results, graphics

    Tom Palmer (Leicester) Running WinBUGS from Stata 4 / 24

    http://www.mrc-bsu.cam.ac.uk/bugs

  • WinBUGS

    Bayesian statistics using Gibbs sampling

    MRC Biostatistics unithttp://www.mrc-bsu.cam.ac.uk/bugs

    Health Economics, Medical Statistics

    Disadvantages: data management, post-processing of results, graphics

    Tom Palmer (Leicester) Running WinBUGS from Stata 4 / 24

    http://www.mrc-bsu.cam.ac.uk/bugs

  • WinBUGS

    Bayesian statistics using Gibbs sampling

    MRC Biostatistics unithttp://www.mrc-bsu.cam.ac.uk/bugs

    Health Economics, Medical Statistics

    Disadvantages: data management, post-processing of results, graphics

    Tom Palmer (Leicester) Running WinBUGS from Stata 4 / 24

    http://www.mrc-bsu.cam.ac.uk/bugs

  • The winbugsfromstata package

    Stata interface to WinBUGS [Thompson et al., 2006]http://www2.le.ac.uk/departments/health-sciences/extranet/

    BGE/genetic-epidemiology/gedownload/information

    Tom Palmer (Leicester) Running WinBUGS from Stata 5 / 24

    http://www2.le.ac.uk/departments/health-sciences/extranet/BGE/genetic-epidemiology/gedownload/informationhttp://www2.le.ac.uk/departments/health-sciences/extranet/BGE/genetic-epidemiology/gedownload/information

  • The winbugsfromstata package

    Tom Palmer (Leicester) Running WinBUGS from Stata 6 / 24

  • How to run an analysis

    Tom Palmer (Leicester) Running WinBUGS from Stata 7 / 24

  • help winbugs

    Tom Palmer (Leicester) Running WinBUGS from Stata 8 / 24

  • Example analysis: Schools

    Schools example [Goldstein et al., 1993],[Spiegelhalter et al., 2004]

    Between-school variation in exam results from inner London schools

    Standardized mean scores (Y ) 1,978 pupils, 38 schools

    LRT: London Reading Test, VR: verbal reasoning, Gender intake ofschool, denomination of school

    Tom Palmer (Leicester) Running WinBUGS from Stata 9 / 24

  • Example analysis: Schools

    Schools example [Goldstein et al., 1993],[Spiegelhalter et al., 2004]

    Between-school variation in exam results from inner London schools

    Standardized mean scores (Y ) 1,978 pupils, 38 schools

    LRT: London Reading Test, VR: verbal reasoning, Gender intake ofschool, denomination of school

    Tom Palmer (Leicester) Running WinBUGS from Stata 9 / 24

  • Example analysis: Schools

    Schools example [Goldstein et al., 1993],[Spiegelhalter et al., 2004]

    Between-school variation in exam results from inner London schools

    Standardized mean scores (Y ) 1,978 pupils, 38 schools

    LRT: London Reading Test, VR: verbal reasoning, Gender intake ofschool, denomination of school

    Tom Palmer (Leicester) Running WinBUGS from Stata 9 / 24

  • Example analysis: Schools

    Schools example [Goldstein et al., 1993],[Spiegelhalter et al., 2004]

    Between-school variation in exam results from inner London schools

    Standardized mean scores (Y ) 1,978 pupils, 38 schools

    LRT: London Reading Test, VR: verbal reasoning, Gender intake ofschool, denomination of school

    Tom Palmer (Leicester) Running WinBUGS from Stata 9 / 24

  • Data for the Schools example

    -2024-2024-2024-2024-2024-2024-40-2002040-40-2002040-40-2002040-40-2002040-40-2002040-40-2002040-40-20020401234567891011121314151617181920212223242526272829303132333435363738girlboyYLRTGraphs by school

    Tom Palmer (Leicester) Running WinBUGS from Stata 10 / 24

  • The model

    Hierarchical model; specified the mean and variance

    Model:

    Yij N(ij , ij)ij = 1j + 2jLRT ij + 3jVR1ij + 1LRT

    2ij + 2VR2ij

    + 3Girl ij + 4Gschj + 5Bschj + 6CEschj + 7RCschj + 8Oschj

    log ij = + LRT ij

    Tom Palmer (Leicester) Running WinBUGS from Stata 11 / 24

  • The model

    Hierarchical model; specified the mean and variance

    Model:

    Yij N(ij , ij)ij = 1j + 2jLRT ij + 3jVR1ij + 1LRT

    2ij + 2VR2ij

    + 3Girl ij + 4Gschj + 5Bschj + 6CEschj + 7RCschj + 8Oschj

    log ij = + LRT ij

    Tom Palmer (Leicester) Running WinBUGS from Stata 11 / 24

  • WinBUGS model statement

    model{for(p in 1 : N){Y[p] ~ dnorm(mu[p], tau[p])mu[p]

  • Do-file for the example

    // winbugsfromstata demo, 16august2007cd "Z:/conferences/stata.users.uk.2007/schools"wbdecode, file(Schoolsdata.txt) clear

    wbscript, sav(c(pwd)/script.txt, replace) ///model(c(pwd)/Schoolsmodel.txt) ///data(c(pwd)/Schoolsdata.txt) ///inits(c(pwd)/Schoolsinits.txt) ///coda(c(pwd)/out) ///burn(500) update(1000) ///set(beta gamma phi theta) dic ///log(c(pwd)/winbugslog.txt) ///quit

    wbrun , sc(c(pwd)/script.txt) ///win(Z:/winbugs/WinBUGS14/WinBUGS14.exe)

    clearset memory 500mwbcoda, root(out) clear

    wbstats gamma* beta* phi theta

    wbtrace beta_1 gamma_1 phi thetawbdensity beta_1 gamma_1 phi thetawbac beta_1 gamma_1 phi thetawbhull beta_1 beta_2 gamma_2, peels(1 5 10 25)

    wbgeweke beta_1 gamma_1 phi theta

    wbdic using winbugslog.txt

    Tom Palmer (Leicester) Running WinBUGS from Stata 13 / 24

  • wbrun screenshot 1

    Tom Palmer (Leicester) Running WinBUGS from Stata 14 / 24

  • wbrun screenshot 2

    Tom Palmer (Leicester) Running WinBUGS from Stata 15 / 24

  • Stata output

    wbstats output

    . wbstats gamma* beta* phi thetaParameter n mean sd sem median 95% CrIgamma_1 500 -0.715 0.103 0.0179 -0.715 ( -0.951, -0.523 )gamma_2 500 0.031 0.010 0.0005 0.031 ( 0.010, 0.052 )gamma_3 500 0.967 0.105 0.0225 0.972 ( 0.750, 1.168 )beta_1 500 0.000 0.000 0.0000 0.000 ( 0.000, 0.000 )beta_2 500 0.433 0.072 0.0099 0.435 ( 0.284, 0.576 )beta_3 500 0.173 0.048 0.0031 0.172 ( 0.085, 0.271 )beta_4 500 0.151 0.141 0.0230 0.164 ( -0.156, 0.392 )beta_5 500 0.091 0.105 0.0150 0.087 ( -0.094, 0.318 )beta_6 500 -0.279 0.183 0.0279 -0.290 ( -0.618, 0.108 )beta_7 500 0.170 0.105 0.0158 0.169 ( -0.029, 0.380 )beta_8 500 -0.109 0.209 0.0376 -0.124 ( -0.485, 0.357 )phi 500 -0.003 0.003 0.0002 -0.003 ( -0.009, 0.003 )theta 500 0.579 0.032 0.0016 0.579 ( 0.513, 0.649 )

    regress 2: 0.030, 95% C.I. (0.026, 0.034)

    Tom Palmer (Leicester) Running WinBUGS from Stata 16 / 24

  • Stata output

    wbstats output

    . wbstats gamma* beta* phi thetaParameter n mean sd sem median 95% CrIgamma_1 500 -0.715 0.103 0.0179 -0.715 ( -0.951, -0.523 )gamma_2 500 0.031 0.010 0.0005 0.031 ( 0.010, 0.052 )gamma_3 500 0.967 0.105 0.0225 0.972 ( 0.750, 1.168 )beta_1 500 0.000 0.000 0.0000 0.000 ( 0.000, 0.000 )beta_2 500 0.433 0.072 0.0099 0.435 ( 0.284, 0.576 )beta_3 500 0.173 0.048 0.0031 0.172 ( 0.085, 0.271 )beta_4 500 0.151 0.141 0.0230 0.164 ( -0.156, 0.392 )beta_5 500 0.091 0.105 0.0150 0.087 ( -0.094, 0.318 )beta_6 500 -0.279 0.183 0.0279 -0.290 ( -0.618, 0.108 )beta_7 500 0.170 0.105 0.0158 0.169 ( -0.029, 0.380 )beta_8 500 -0.109 0.209 0.0376 -0.124 ( -0.485, 0.357 )phi 500 -0.003 0.003 0.0002 -0.003 ( -0.009, 0.003 )theta 500 0.579 0.032 0.0016 0.579 ( 0.513, 0.649 )

    regress 2: 0.030, 95% C.I. (0.026, 0.034)

    Tom Palmer (Leicester) Running WinBUGS from Stata 16 / 24

  • Stata output

    wbgeweke output

    . wbgeweke beta_1Parameter: beta_1 first 10.0% (n=50) vs last 50.0% (n=250)Means (se) 0.0003 ( 0.0000) 0.0003 ( 0.0000)Autocorrelations 0.3736 0.4114Mean Difference (se


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