Abstract
Under the Bayesian framework, we develop a novel method for assessing the goodness of fit for the SIR (susceptible-infective-removed) stochastic epidemic model. This method seeks to determine whether or not one can identify the infectious period distribution based only on a set of partially observed data using a posterior predictive distribution approach. Our criterion for assessing the model’s goodness of fit is based on the notion of Bayesian residuals.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Andersson, H., Britton, T.: Stochastic Epidemic Models and Their Statistical Analysis, vol. 4. Springer, New York (2000)
Bailey, N.T.J.: The Mathematical Theory of Infectious Diseases and Its Applications. Charles Griffin & Company, London (1975)
Britton, T., O’Neill, P.D.: Bayesian inference for stochastic epidemics in populations with random social structure. Scand. J. Stat. 29(3), 375–390 (2002)
Gelfand, A.E.: Model determination using sampling-based methods. In: Gilks, W.R., Richardson, S., Spiegelhalter, D.J. (eds.) Markov Chain Monte Carlo in Practice, pp. 145–161. Springer, New York (1996)
Kypraios, T.: Efficient Bayesian inference for partially observed stochastic epidemics and a new class of semi-parametric time series models. Ph.D. thesis, Lancaster University (2007)
Neal, P., Roberts, G.O.: A case study in non-centering for data augmentation: stochastic epidemics. Stat. Comput. 15(4), 315–327 (2005)
O’Neill, P.D.: Introduction and snapshot review: relating infectious disease transmission models to data. Stat. Med. 29(20), 2069–2077 (2010)
O’Neill, P.D., Roberts, G.O.: Bayesian inference for partially observed stochastic epidemics. J. Roy. Stat. Soc. Ser. A (Stat. Soc.) 162(1), 121–129 (1999)
Streftaris, G., Gibson, G.J.: Bayesian inference for stochastic epidemics in closed populations. Stat. Model. 4(1), 63–75 (2004)
Streftaris, G., Gibson, G.J.: Non-exponential tolerance to infection in epidemic systems–modeling, inference, and assessment. Biostatistics 13(4), 580–593 (2012)
Acknowledgements
The first author is supported by a scholarship from Taif University, Taif, Saudi Arabia.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Alharthi, M., O’Neill, P., Kypraios, T. (2015). Identifying the Infectious Period Distribution for Stochastic Epidemic Models Using the Posterior Predictive Check. In: Frühwirth-Schnatter, S., Bitto, A., Kastner, G., Posekany, A. (eds) Bayesian Statistics from Methods to Models and Applications. Springer Proceedings in Mathematics & Statistics, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-16238-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-16238-6_9
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16237-9
Online ISBN: 978-3-319-16238-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)