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Non-iterative sampling-based Bayesian methods for identifying changepoints in the sequence of cases of Haemolytic uraemic syndrome

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  • Tian, Guo-Liang
  • Ng, Kai Wang
  • Li, Kai-Can
  • Tan, Ming

Abstract

Diarrhoea-associated Haemolytic Uraemic syndrome (HUS) is a disease that affects the kidneys and other organs. Motivated by the annual number of cases of HUS collected in Birmingham and Newcastle of England, respectively, from 1970 to 1989, we consider Bayesian changepoint analysis with specific attention to Poisson changepoint models. For changepoint models with unknown number of changepoints, we propose a new non-iterative Bayesian sampling approach (called exact IBF sampling), which completely avoids the problem of convergence and slow convergence associated with iterative Markov chain Monte Carlo (MCMC) methods. The idea is to first utilize the sampling inverse Bayes formula (IBF) to derive the conditional distribution of the latent data given the observed data, and then to draw iid samples from the complete-data posterior distribution. For the purpose of selecting the appropriate model (or determining the number of changepoints), we develop two alternative formulae to exactly calculate marginal likelihood (or Bayes factor) by using the exact IBF output and the point-wise IBF, respectively. The HUS data are re-analyzed using the proposed methods. Simulations are implemented to validate the performance of the proposed methods.

Suggested Citation

  • Tian, Guo-Liang & Ng, Kai Wang & Li, Kai-Can & Tan, Ming, 2009. "Non-iterative sampling-based Bayesian methods for identifying changepoints in the sequence of cases of Haemolytic uraemic syndrome," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3314-3323, July.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:9:p:3314-3323
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    References listed on IDEAS

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    1. R. Henderson & J. N. S. Matthews, 1993. "An Investigation of Changepoints in the Annual Number of Cases of Haemolytic Uraemic Syndrome," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(3), pages 461-471, September.
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    Cited by:

    1. Hinoveanu, Laurentiu C. & Leisen, Fabrizio & Villa, Cristiano, 2019. "Bayesian loss-based approach to change point analysis," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 61-78.

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