Hierarchical Bayesian Spatio-Temporal Conway–Maxwell Poisson Models with Dynamic Dispersion
Modeling spatio-temporal count processes is often a challenging endeavor. That is, in many real-world applications the complexity and high-dimensionality of the data and/or process do not allow for routine model specification. For example, spatio-temporal count data often exhibit temporally varying over/underdispersion within the spatial domain. In order to accommodate such structure, while quantifying different sources of uncertainty, we propose a Bayesian spatio-temporal Conway–Maxwell Poisson (CMP) model with dynamic dispersion. Motivated by the problem of predicting migratory bird settling patterns, we propose a threshold vector-autoregressive model for the CMP intensity parameter that allows for regime switching based on climate conditions. Additionally, to reduce the inherent high-dimensionality of the underlying process, we consider nonlinear dimension reduction through kernel principal component analysis. Finally, we demonstrate the effectiveness of our approach through out-of-sample one-year-ahead prediction of waterfowl migratory patterns across the United States and Canada. The proposed approach is of independent interest and illustrates the potential benefits of dynamic dispersion in terms of superior forecasting.
This article has supplementary material online.
Key WordsCount data Empirical orthogonal functions Hierarchical model Kernel principal component analysis Nonlinear Overdispersion Threshold vector autoregressive model Underdispersion
Unable to display preview. Download preview PDF.
- Conway, R., and Maxwell, W. (1962), “A Queuing Model With State Dependent Service Rates,” Journal of Industrial Engineering, 12, 2. Google Scholar
- Hansen, H., and McKnight, D. (1964), “Emigration of Drought-Displaced Ducks to the Arctic,” in Transactions of the North American Wildlife and Natural Resources Conference, Vol. 29, pp. 119–127. Google Scholar
- Herbers, J. M. (1989), “Community Structure in North Temperate Ants: Temporal and Spatial Variation,” Oecologia, 81 (2), 201–211. Google Scholar
- Johnson, D., and Grier, J. (1988), “Determinants of Breeding Distributions of Ducks,” in Wildlife Monographs, pp. 3–37. Google Scholar
- Jolliffe, I. (2010), Principal Component Analysis, Berlin: Springer. Google Scholar
- Minka, T., Shmueli, G., Kadane, J., Borle, S., and Boatwright, P. (2003), Computing with the COM-Poisson Distribution. Pittsburgh: Department of Statistics, Carnegie Mellon University. Google Scholar
- R Development Core Team (2012), R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing. ISBN:3-900051-07-0 Google Scholar
- Shmueli, G., Minka, T., Kadane, J., Borle, S., and Boatwright, P. (2005), “A Useful Distribution for Fitting Discrete Data: Revival of the Conway–Maxwell–Poisson Distribution,” Journal of the Royal Statistical Society. Series C. Applied Statistics, 54 (1) 127–142. MathSciNetCrossRefMATHGoogle Scholar
- Van der Maaten, L., Postma, E., and Van den Herik, H. (2008). ”Dimensionality Reduction: A Comparative Review.” Online Preprint. Google Scholar
- — (2010), Handbook of Spatial Statistics, London/Boca Raton: Chapman and Hall/CRC. Google Scholar
- Wikle, C., and Hooten, M. (2006), “Hierarchical Bayesian Spatio-Temporal Models for Population Spread,” in Applications of Computational Statistics in the Environmental Sciences: Hierarchical Bayes and MCMC Methods, pp. 145–169. Google Scholar