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In this paper, we consider Bayesian methods for analyzing time series of count data under a Poisson regression model with a latent auto-regressive process embedded as an additive error term. We propose two different methods; the first method samples the latent variables one by one while the second method samples them jointly. The two methods are compared by simulation studies and an example employing real data. In terms of relative bias and root-mean-squared-errors, the two methods perform almost the same. However, the mixing performance of the first method is better than the second method for most of the simulation scenarios.

Bayesian methods for time series of count data