Stat Colloquium: Dr. Pulong Ma

Title: Bayesian Multi-Scale Poisson Process Soft Tree Model for High-Dimensional Point Patterns
Abstract: Estimating the intensity of a spatial point process is challenging when the underlying pattern is heterogeneous and driven by a high-dimensional covariate space. Bayesian inference is further complicated by the need to repeatedly evaluate multidimensional integrals of a random intensity function. This talk introduces a Bayesian multi-scale Poisson process soft-tree model that adaptively represents intensity variation across resolutions while smoothing transitions across partition boundaries. This construction is shown to yield analytically tractable integrated intensities, thus eliminating numerical integration from likelihood evaluation even in high dimensions. A latent-allocation data augmentation technique is introduced to enable efficient posterior computation. This talk also discusses posterior consistency under infill asymptotics. Numerical examples and a wildfire application are demonstrate its advantages over existing methods.