Executive Summary : | Binary and count data are common in scientific experiments, and researchers often use statistical models to draw essential inferences. However, the literature on multivariate data and spatial/spatiotemporal scenarios is limited. Advanced satellites collect high-resolution images, which are high-dimensional and not directly applicable to binary or count data. Gaussian processes (GPs) are not suitable for these data due to their high computational burden. This project aims to build scalable latent Gaussian Bayesian models for analyzing such datasets, using a stochastic partial differential equation (SPDE) model. The project assumes statistical models suitable for binary or count data and uses GPs built through SPDE to model potential rescaled parameters. The project explores the feasibility of latent GPs using a Gaussian approximation-based method called Max-and-Smooth under different data settings. The margin of approximation error will be evaluated under different data settings, and ways to reduce approximation error will be explored. An R package will be developed to include necessary functions for direct implementation by practitioners. |