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Geometric ergodicity of the Gibbs sampler for the Poisson change-point model

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  • Fitzpatrick, Matthew

Abstract

Poisson change-point models have been widely used for modelling inhomogeneous time-series of count data. There are a number of methods available for estimating the parameters in these models using iterative techniques such as MCMC. Many of these techniques share the common problem that there does not seem to be a definitive way of knowing the number of iterations required to obtain sufficient convergence. In this paper, we show that the Gibbs sampler of the Poisson change-point model is geometrically ergodic. Establishing geometric ergodicity is crucial from a practical point of view as it implies the existence of a Markov chain central limit theorem, which can be used to obtain standard error estimates. We prove that the transition kernel is a trace-class operator, which implies geometric ergodicity of the sampler. We then provide a useful application of the sampler to a model for the quarterly driver fatality counts for the state of Victoria, Australia.

Suggested Citation

  • Fitzpatrick, Matthew, 2014. "Geometric ergodicity of the Gibbs sampler for the Poisson change-point model," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 55-61.
    • Handle: RePEc:eee:stapro:v:91:y:2014:i:c:p:55-61
    DOI: 10.1016/j.spl.2014.04.008
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    References listed on IDEAS

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    1. Bradley P. Carlin & Alan E. Gelfand & Adrian F. M. Smith, 1992. "Hierarchical Bayesian Analysis of Changepoint Problems," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 389-405, June.
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    1. de Bessa, Iury Valente & Palhares, Reinaldo Martinez & D'Angelo, Marcos Flávio Silveira Vasconcelos & Chaves Filho, João Edgar, 2016. "Data-driven fault detection and isolation scheme for a wind turbine benchmark," Renewable Energy, Elsevier, vol. 87(P1), pages 634-645.

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