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Statistics and Computing

, Volume 15, Issue 4, pp 315–327 | Cite as

A case study in non-centering for data augmentation: Stochastic epidemics

  • Peter NealEmail author
  • Gareth Roberts
Article

Abstract

In this paper, we introduce non-centered and partially non-centered MCMC algorithms for stochastic epidemic models. Centered algorithms previously considered in the literature perform adequately well for small data sets. However, due to the high dependence inherent in the models between the missing data and the parameters, the performance of the centered algorithms gets appreciably worse when larger data sets are considered. Therefore non-centered and partially non-centered algorithms are introduced and are shown to out perform the existing centered algorithms.

Keywords

stochastic epidemic models bernoulli random graphs non-centered and partially non-centered MCMC algorithms data augmentation 

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References

  1. Amit Y. 1991. On rates of convergence of stochastic relaxation for Gaussian and non-Gaussian distributions. J. Multivariate Analysis 38: 82–99.CrossRefGoogle Scholar
  2. Andersson H. 1999. Epidemic models and social networks. Math. Scientist 24: 128–147.Google Scholar
  3. Bailey N.T.J. 1975. The Mathematical Theory of Infectious Diseases and its Applications, 2nd edn, Griffin, LondonGoogle Scholar
  4. Ball F.G. 1986. A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models. Adv. Appl. Prob. 18: 289–310.Google Scholar
  5. Ball F.G., Mollison D., and Scalia-Tomba G. 1997. Epidemics with two levels of mixing. Ann. Appl. Prob. 7: 46–89.CrossRefGoogle Scholar
  6. Britton T. and O'Neill P.D. 2002. Bayesian inference for stochastic epidemics in populations with random social structure. Scan. J. Statist. 29: 375–390.CrossRefGoogle Scholar
  7. Cáceres V.M., Kim D.K., Bresee J.S., Horan J., Noel J.S., Ando T., Steed C.J., Weems J.J., Monroe S.S., and Gibson J.J. 1998. A viral gastroenteritis outbreak associated with person-to-person spread among hospital staff. Infection Control and Hospital Epidemiology 19(3): 162–167.PubMedGoogle Scholar
  8. Christensen O., Roberts G.O., and Sköld M. 2003. Robust MCMC methods for spatial GLMMs. Submitted for publication.Google Scholar
  9. Gelman A., Roberts G.O., and Gilks W.R. 1996. Efficient Metropolis jumping rules. Bayesian Statist. 5: 599–608.Google Scholar
  10. Geyer C.J. 1992. Practical markov chain monte carlo (with discussion). Stat. Science 7: 473–511.Google Scholar
  11. Keeling M.J., Woolhouse M.E.J., Shaw D.J., Matthews L., Chase-Topping M., Haydon D.T., Cornell S.J., Kappey J., Wilesmith J., and Grenfell B.T. 2001. Dynamics of the 2001 UK foot and mouth epidemic: stochasic dispersal in a heterogeneous landscape. Science 294: 813–817.CrossRefPubMedGoogle Scholar
  12. Meng X.-L. and van Dyk D. 1997. The EM algorithm—an old folk song sung to a fast new tune (with discussion). J. R. Statist. Soc. B 59: 511–567.Google Scholar
  13. Neal P.J. and Roberts G.O. 2004. Statistical inference and model selection for the 1861 hagelloch measles epidemic. Biostat. 5: 249–261.CrossRefGoogle Scholar
  14. O'Neill P.D. and Becker N.G. 2001. Inference for an epidemic when susceptibility varies. Biostat. 2: 99–108.CrossRefGoogle Scholar
  15. O'Neill P.D. and Roberts G.O. 1999. Bayesian inference for partially observed stochastic epidemics. J. R. Statist. Soc. A 162: 121–129.CrossRefGoogle Scholar
  16. Papaspiliopoulos O., Roberts G.O., and Sköld M. 2003. Non-centered parameterisations for hierarchical models and data augmentation. In: J.M. Bernardo, M.J. Bayarri, J.O. Berger, A.P. Dawid, D. Heckerman, A.F.M. Smith and M. West, (Eds.) Bayesian Statistics 7 Oxford University Press, pp. 307–326.Google Scholar
  17. Roberts G.O. and Rosenthal J.S. 2001. Optimal scaling for various Metropolis-Hastings algorithms. Statist. Science 16: 351–367.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Mathematics DepartmentUMISTManchesterUK
  2. 2.Department of Mathematics and StatisticsFylde College, Lancaster UniversityLancasterUK

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