Bayesian Melding Estimation of a Stochastic SEIR Model

One of the main problems in estimating stochastic SEIR models is that the data are not completely observed. In this case, the estimation is usually done by least squares or by MCMC. The Bayesian melding method is proposed to estimate SEIR models and to evaluate the likelihood in the presence of incomplete data. The method is illustrated by estimating a model for HIV/TB interaction in the population of a prison.

[1]  Rodney Carlos Bassanezi,et al.  An Approach to Estimating the Transmission Coefficients for AIDS and for Tuberculosis Using Mathematical Models , 2003 .

[2]  A. Raftery,et al.  Inference for Deterministic Simulation Models: The Bayesian Melding Approach , 2000 .

[3]  D. Rubin,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[4]  O. Ferreira,et al.  Tuberculosis and HIV infection among female inmates in São Paulo, Brazil: a prospective cohort study. , 1996, Journal of acquired immune deficiency syndromes and human retrovirology : official publication of the International Retrovirology Association.

[5]  D. Rubin Using the SIR algorithm to simulate posterior distributions , 1988 .

[6]  Philip D O'Neill,et al.  A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods. , 2002, Mathematical biosciences.

[7]  Adrian E. Raftery,et al.  Inference from a Deterministic Population Dynamics Model for Bowhead Whales , 1995 .

[8]  W. Wong,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[9]  Richard J Boys,et al.  Bayesian inference for stochastic epidemic models with time-inhomogeneous removal rates , 2007, Journal of mathematical biology.

[10]  R. Bassanezi,et al.  THE ATTRACTING BASINS AND THE ASSESSMENT OF THE TRANSMISSION COEFFICIENTS FOR HIV AND M. TUBERCULOSIS INFECTIONS AMONG WOMEN INMATES , 2002 .

[11]  E. Massad,et al.  Modeling the interaction between aids and tuberculosis , 1993 .

[12]  Adrian E. Raftery,et al.  Probabilistic projections of HIV prevalence using Bayesian melding. , 2007, 0709.0421.

[13]  Joseph N S Eisenberg,et al.  Statistical estimation of parameters in a disease transmission model: analysis of a Cryptosporidium outbreak , 2002, Statistics in medicine.

[14]  Gavin J. Gibson,et al.  Bayesian inference for stochastic epidemics in closed populations , 2004 .

[15]  A E Ades,et al.  Markov Chain Monte Carlo Estimation of a Multiparameter Decision Model: Consistency of Evidence and the Accurate Assessment of Uncertainty , 2002, Medical decision making : an international journal of the Society for Medical Decision Making.

[16]  Norman T. J. Bailey,et al.  The Mathematical Theory of Infectious Diseases , 1975 .

[17]  G. Roberts,et al.  Statistical inference and model selection for the 1861 Hagelloch measles epidemic. , 2004, Biostatistics.

[18]  B. Finkenstädt,et al.  Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention: Ebola as a Case Study , 2006, Biometrics.

[19]  J. Hyman,et al.  The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda. , 2004, Journal of theoretical biology.

[20]  Denise Kirschner,et al.  A Model to Predict Cell-Mediated Immune Regulatory Mechanisms During Human Infection with Mycobacterium tuberculosis1 , 2001, The Journal of Immunology.

[21]  A. J. Hall Infectious diseases of humans: R. M. Anderson & R. M. May. Oxford etc.: Oxford University Press, 1991. viii + 757 pp. Price £50. ISBN 0-19-854599-1 , 1992 .

[22]  G. Roberts,et al.  Bayesian inference for partially observed stochastic epidemics , 1999 .

[23]  D. Kirschner,et al.  The human immune response to Mycobacterium tuberculosis in lung and lymph node. , 2004, Journal of theoretical biology.

[24]  C. Rogier,et al.  Bayesian analysis of an epidemiologic model of Plasmodium falciparum malaria infection in Ndiop, Senegal. , 2000, American journal of epidemiology.