Propose a computationally efficient approach to construct a well-defined spatial Gaussian process (GP) with the nonstationary covariance using multiple yet simple directed acyclic graphs (DAGs), which leads to computational efficiency, flexibility, and interpretability in point-referenced geostatistical models.

Develop Bag of DAGs-Gaussian process (BDAG-GP), each DAG of which is chosen to represent a different possible dependence structure, to induce nonstationarity.

Analyze spatiotemporal variability of fine particulate matter (PM2.5) in California in which a DAG represents a prevailing wind direction causing some associated covariance in the pollutants.

Motivated by applications in point-referenced geostatistics that have measurements collected and meaningful only within a constrained domain.

Develop the Barrier Overlap-Removal Acyclic directed graph GP (BORA-GP), a scalable GP method that incorporates the constrained domain via sparsity-inducing DAGs.

Enable characterization of dependence in constrained domains by removing an edge in a DAG if a linear path between two points overlaps physical barriers.

Analyze levels of chlorophyll a along the east coast of the United States.

submitted https://arxiv.org/pdf/2009.08405.pdf

Adapted Bayesian heteroscedastic nonparametric regression to a multiple hypothesis testing framework.

Imposed a generalized latent factor model to form a non-exchangeable prior for testing.

Developed a matrix completion method for a latent matrix.

Tackled sparsity of the ToxCast data using hierarchical framework.

Enabled prediction for non-tested chemical’s activity.

Broadened the definition of activity including heteroscedasticity.