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/2112.11870.pdf

Propose a computationally efficient approach to construct a class of nonstationary spatiotemporal processes 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 processes (BAGs) whose nonstationarity is induced via local mixtures of DAGs. Directed edges in DAGs are alternative and competing assumptions on directional correlation patterns in space and time.

Analyze spatiotemporal variability of fine particulate matter (PM2.5) in South Korea and California, US, in which a directed edge represents a prevailing wind direction causing some associated covariance in the pollutants.

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

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

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

Develop a matrix completion method for a latent matrix.

Tackle sparsity of the ToxCast data using hierarchical framework.

Enable prediction for non-tested chemical’s activity.

Broaden the definition of activity including heteroscedasticity.