Bayesian Period-Varying Poisson Modelling With Reduced-Rank Regression

Poisson regression models have been classical tools for estimating and predicting species abundance. However, as changes in weather conditions become more frequent and dramatic, Poisson models that can reflect varying impacts of climate variables with respect to time are needed. In this paper, we expand the application domain of Poisson regression models by developing a period-varying Poisson regression framework that can explain the varying impacts of covariates on the outcome over the course of time. The framework of period-varying Poisson regression modelling uses the notion of reduced-rank regression, which improves the accuracy of statistical inference by allowing the regression coefficient vectors to share information with each other. We establish the consistency in rank selection for the proposed method. To enable statistical inference under the low-rank constraint, we incorporate the weighted Bayesian bootstrap into our framework. The results of a simulation study are provided to demonstrate the performance of our proposed method. Finally, the period-varying Poisson regression model is applied to investigate the effect of varying climate on the mosquito population in a rural city in South Korea.