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

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.

[1]  F. Ball A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models , 1986, Advances in Applied Probability.

[2]  N G Becker,et al.  Inference for an epidemic when susceptibility varies. , 2001, Biostatistics.

[3]  Xiao-Li Meng,et al.  The EM Algorithm—an Old Folk‐song Sung to a Fast New Tune , 1997 .

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

[5]  M. J. Bayarri,et al.  Non-Centered Parameterisations for Hierarchical Models and Data Augmentation , 2003 .

[6]  J. Rosenthal,et al.  Optimal scaling for various Metropolis-Hastings algorithms , 2001 .

[7]  P. O’Neill,et al.  Bayesian inference for stochastic epidemics in populations with random social structure , 2002 .

[8]  S. Cornell,et al.  Dynamics of the 2001 UK Foot and Mouth Epidemic: Stochastic Dispersal in a Heterogeneous Landscape , 2001, Science.

[9]  Alexander Grey,et al.  The Mathematical Theory of Infectious Diseases and Its Applications , 1977 .

[10]  Gareth O. Roberts,et al.  Non-centred parameterisations for hierarchical models and data augmentation. , 2003 .

[11]  Charles J. Geyer,et al.  Practical Markov Chain Monte Carlo , 1992 .

[12]  J S Noel,et al.  A Viral Gastroenteritis Outbreak Associated with Person-to-Person Spread Among Hospital Staff , 1998, Infection Control & Hospital Epidemiology.

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

[14]  N. Ling The Mathematical Theory of Infectious Diseases and its applications , 1978 .

[15]  Y. Amit On rates of convergence of stochastic relaxation for Gaussian and non-Gaussian distributions , 1991 .

[16]  F. Ball,et al.  Epidemics with two levels of mixing , 1997 .