The modeling of complex data is an open challenge due to the intricate spatio-temporal dynamics, the covariate interactions and nonlinear effects as well as heterogenous grouping structure. Bayesian nonparametric models offer a compelling solution to those challenges due to their flexibility, minimal reliance on modeling assumptions and adaptability to heterogeneity while providing rigorous uncertainty estimates. In this presentation, I will talk about two Bayesian nonparametric models that handles two types of complex data.

The first project focuses on Bayesian Additive Regression Trees (BART) for Spatial Model Prediction that we call BART-SIMP. BART-SIMP is a novel combination of a Gaussian process spatial model and a BART model as a prediction framework for spatial data that allows for nonlinearities and interactions in the covariate structure. An efficient implementation is developed by combining Markov chain Monte Carlo (MCMC) with the Integrated Nested Laplace Approximation (INLA) technique. For this study, we investigate the performance of the method via simulations and use the model to predict anthropometric responses, collected via household cluster samples in Kenya.

The second project focuses on Dependent Dirichlet Process for Multivariate Hawkes Processes (MHP-DDP), which is a class of stochastic processes models for complex temporal dynamics among event sequences on multiple dimensions. Specifically, we capture the flexible excitation patterns in MHP via Dirichlet Process mixtures of scaled Beta distributions and borrow strengths across dimensions via hierarchical modeling. We develop two algorithms using Markov chain Monte Carlo (MCMC) and the stochastic variational inference (SVI) algorithm. We show that MHP-DDP outperforms the benchmark methods in terms of lower estimation error for both algorithms, with SVI being computationally more efficient than MCMC.