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A. Gelman and D. R. Rubin, “A Single Series from the Gibbs Sampler Provides a False Sense of Security,” In: J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, Eds., Bayesian Statistics 4, Oxford University Press, Oxford, 1992, pp. 625-631.

has been cited by the following article:

• TITLE: Non-Homogeneous Poisson Processes Applied to Count Data: A Bayesian Approach Considering Different Prior Distributions

  AUTHORS: Lorena Vicini, Luiz K. Hotta, Jorge A. Achcar

  KEYWORDS: Non-Homogeneous Poisson Processes; Bayesian Analysis; Markov Chain Monte Carlo Methods and Simulation; Prior Distribution

  JOURNAL NAME: Journal of Environmental Protection, Vol.3 No.10, October 31, 2012

  ABSTRACT: This article discusses the Bayesian approach for count data using non-homogeneous Poisson processes, considering different prior distributions for the model parameters. A Bayesian approach using Markov Chain Monte Carlo (MCMC) simulation methods for this model was first introduced by [1], taking into account software reliability data and considering non-informative prior distributions for the parameters of the model. With the non-informative prior distributions presented by these authors, computational difficulties may occur when using MCMC methods. This article considers different prior distributions for the parameters of the proposed model, and studies the effect of such prior distributions on the convergence and accuracy of the results. In order to illustrate the proposed methodology, two examples are considered: the first one has simulated data, and the second has a set of data for pollution issues at a region in Mexico City.