Keywords and phrases: the posterior predictive distribution, the posterior distribution, the SIR epidemic model, major epidemic.
Received: January 12, 2022; Accepted: March 3, 2022; Published: March 24, 2022
How to cite this article: Muteb Alharthi, Bayesian analysis of the predictive distribution of the SIR models, Advances and Applications in Statistics 75 (2022), 1-21. http://dx.doi.org/10.17654/0972361722024
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] M. Alharthi, Bayesian model assessment for stochastic epidemic models, Ph.D. Thesis, University of Nottingham, 2016. [2] H. Andersson and T. Britton, Stochastic epidemic models and their statistical analysis, Volume 4, New York, Springer, 2000. [3] F. Ball, The threshold behaviour of epidemic models, Journal of Applied Probability (1983), 227-241. [4] P. Billingsley, Convergence of Probability Measures, John Wiley & Sons, 2013. [5] J. L. Doob, Application of the theory of martingales, Le calcul des Probabilites et ses Applications 1949, p. 23-27. [6] A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari and D. B. Rubin, Bayesian data analysis, CRC Press, 2013. [7] A. Gelman, X.-L. Meng and H. Stern, Posterior predictive assessment of model fitness via realized discrepancies, Statistica Sinica 6(4) (1996), 733-760. [8] R. Ghanam, E. L. Boone and A.-S. G. Abdel-Salam, Seird model for Qatar covid-19 outbreak: A case study, 2020. arXiv preprint arXiv:2005.12777. [9] F. Komaki, On asymptotic properties of predictive distributions, Biometrika 83(2) (1996), 299-313. [10] J. L. Lockett, Convergence in total variation of predictive distributions: finite horizon, Ph.D. Thesis, Dept. of Statistics, Stanford University, 1971. [11] R. H. Mena, J. X. Velasco-Hernandez, N. B. Mantilla-Beniers, G. A. Carranco-Sapiéns, L. Benet, D. Boyer and I. P. Castillo, Using posterior predictive distributions to analyse epidemic models: Covid-19 in Mexico city, Physical Biology 17(6) (2020), 065001. [12] P. D. O’Neill and G. O. Roberts, Bayesian inference for partially observed stochastic epidemics, J. Roy. Statist. Soc.: Ser. A (Statistics in Society) 162(1) (1999), 121-129. [13] L. Pellis, F. Ball, S. Bansal, K. Eames, T. House, V. Isham and P. Trapman, Eight challenges for network epidemic models, Epidemics 10 (2015), 58-62. [14] W. N. Rida, Asymptotic properties of some estimators for the infection rate in the general stochastic epidemic model, J. Roy. Statist. Soc., Ser. B (Methodological) (1991), 269-283. [15] M. Roberts, V. Andreasen, A. Lloyd and L. Pellis, Nine challenges for deterministic epidemic models, Epidemics 10 (2015), 49-53. [16] H. Scheffé, A useful convergence theorem for probability distributions, The Annals of Mathematical Statistics 18(3) (1947), 434-438. [17] L. Schwartz, On Bayes procedures, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 4(1) (1965), 10-26. [18] A. Vehtari and J. Ojanen, A survey of Bayesian predictive methods for model assessment, selection and comparison, Statistics Surveys 6 (2012), 142-228. [19] S. Watanabe, Mathematical Theory of Bayesian Statistics, CRC Press, 2018.
|