On the Markov Chain Monte Carlo Convergence Diagnostic of Bayesian Bernoulli Mixture Regression Model for Bidikmisi Scholarship Classification

  • Nur IriawanEmail author
  • Kartika Fithriasari
  • Brodjol Sutijo Suprih Ulama
  • Irwan Susanto
  • Wahyuni Suryaningtyas
  • Anindya Apriliyanti Pravitasari
Conference paper


The Bidikmisi scholarship program is an education assistance program by the government of Indonesia which aims to achieve equitable access and learning opportunities at University. Bidikmisi acceptance status having a binary type (i.e. 0 and 1) produces a structure of Bernoulli mixture model with two components. The characteristics of each component can be identified through the Bernoulli mixture regression modeling by involving the covariates of Bidikmisi scholarship grantees. The estimating parameter of Bernoulli mixture regression model was performed using Bayesian-Markov Chain Monte Carlo (MCMC) approach. One of the challenges in using Bayesian-MCMC algorithm is determining the convergence of the sampler to the posterior distribution which is typically assessed using diagnostics tools. In this paper, we present that the diagnostics tools such as Geweke method, Gelman-Rubin method, Raftery-Lewis method and Heidelberger-Welch method can give different results to conclude MCMC convergence. The improvement of convergence indicators occurs on Gelman-Rubin method and Heidelberger-Welch method when the number of iterations is increased.


Markov chain monte carlo Convergence diagnostic Bernoulli mixture regression Bayesian computation Bidikmisi 



The Authors are grateful to DRPM-Kemenristekdikti Indonesia which supported this research under PUPT research grant no. 608/PKS/ITS/2017.


  1. 1.
    Iriawan, N.: Pemodelan dan Analisis Data-Driven. ITS Press, Surabaya (2012)Google Scholar
  2. 2.
    Nadif, M., Govaert, G.: Clustering for binary data and mixture models-choice of the model. Appl. Stoch. Mod. Bus. Ind. 13, 269–278 (1997).;2-7CrossRefzbMATHGoogle Scholar
  3. 3.
    Grun, B., Leisch, F.: Finite mixtures of generalized linear regression models. In: Shalabh, C.H. (ed.) Recent Advances in Linear Models and Related Areas, pp. 205–230. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Alkan, N.: Assessing convergence diagnostic tests for bayesian cox regression. Comm. Stat. Sim. Comp. 46(4), 3201–3212 (2017).
  5. 5.
    Gelman, A., Rubin, D.: Inference from iterative simulation using multiple sequences. Stat. Sci. 7(4), 457–511 (1992).
  6. 6.
    Geweke, J.: Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: Bernardo, J.M., Smith, A.F.M., Dawid, A.P., Berger, J.O. (eds.) Bayesian Statistics 4, pp. 169–193. Oxford University Press, New York (1992)Google Scholar
  7. 7.
    Raftery, A.E., Lewis, S.M.: How many iterations in the gibbs sampler? In: Bernardo, J.M., Smith, A.F.M., Dawid, A.P., Berger, J.O. (eds.) Bayesian Statistics 4, pp. 762–773. Oxford University Press, New York (1992)Google Scholar
  8. 8.
    Heidelberger, P., Welch, P.D.: Simulation run length control in the presence of an initial transient. Oper. Res. 31(6), 1109–1144 (1983).
  9. 9.
    Lunn, D., Spiegelhalter, D., Thomas, A., Best, N.: The BUGS project: evolution, critique and future directions (with discussion). Stat. Med. 28(25), 3049–3082 (2009).
  10. 10.
    Plummer, M., Best, N., Cowles, K., Vines, K.: CODA: convergence diagnosis and output analysis for MCMC. R News 6(1), 7–11 (2006)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Nur Iriawan
    • 1
    Email author
  • Kartika Fithriasari
    • 1
  • Brodjol Sutijo Suprih Ulama
    • 2
  • Irwan Susanto
    • 1
  • Wahyuni Suryaningtyas
    • 1
  • Anindya Apriliyanti Pravitasari
    • 1
  1. 1.Department of StatisticsInstitut Teknologi Sepuluh NopemberSurabayaIndonesia
  2. 2.Department of Business StatisticsInstitut Teknologi Sepuluh NopemberSurabayaIndonesia

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