Professor, Department of StatisticsOhio State University
Exploring Latent Structure in Spatial Temporal Processes Using Process Convolutions
Bayesian process convolution models provide an appealing approach for modeling spatial temporal data. Their structure can be exploited to significantly reduce the dimensionality of a complex spatial temporal process. In addition, process convolution models can provide insight into the space-time dependence structure of the process. We illustrate a univariate version of these dynamic process convolution models using daily ozone concentration readings from 512 weather stations in the Eastern United States. Our hope is to better understand the space-time dependence in ozone concentrations over this region. The computational advantages of the model are highlighted. Dynamic process convolution models can easily be extended to model multivariate spatial time-series. Instead of specifying the cross-covariance structure directly, we construct an underlying dynamic factor model that provides insight into the covariance structure. By constructing a factor model, we further reduce the model's dimension temporally. Each of the factors evolves over time, and the data are modeled as a smoothed weighted average of these underlying factor processes. Inference procedures remain computationally tractable due to the additional reduction in the dimensionality of the model. We illustrate this model using multivariate pollutant data from the EPA's Clean Air Status and Trends Network (CASTNet). Finally, a multiresolution dynamic factor process convolution model is proposed to gain insight into the dynamics of spatial processes at different scales. In most applications, global temporal trends can be modeled at fairly coarse resolutions whereas purely spatial variation takes place at fine scales. The CASTNet data is again analyzed by adding an additional process convolution field constructed from a fine-scale, temporally independent underlying process.