A case study in non-centering for data augmentation: Stochastic epidemics
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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.
Keywordsstochastic epidemic models bernoulli random graphs non-centered and partially non-centered MCMC algorithms data augmentation
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- Andersson H. 1999. Epidemic models and social networks. Math. Scientist 24: 128–147.Google Scholar
- Bailey N.T.J. 1975. The Mathematical Theory of Infectious Diseases and its Applications, 2nd edn, Griffin, LondonGoogle Scholar
- 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
- 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
- Christensen O., Roberts G.O., and Sköld M. 2003. Robust MCMC methods for spatial GLMMs. Submitted for publication.Google Scholar
- Gelman A., Roberts G.O., and Gilks W.R. 1996. Efficient Metropolis jumping rules. Bayesian Statist. 5: 599–608.Google Scholar
- Geyer C.J. 1992. Practical markov chain monte carlo (with discussion). Stat. Science 7: 473–511.Google Scholar
- 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
- 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