Bayesian methodology has been widely explored and applied to broad fields due to its natural ability of uncertainty quantification, also the flexibility to model specific statistical problems and incorporate non-regular restrictions. We focus on studying Bayesian semi-parametric methods for non-standard function estimation problems motivated by real scientific applications. The frequentist properties of Gaussian process have been well studied in the last decade, however, there still are some gaps in justifying the variants of Gaussian process models applied in certain specific regression settings. One component of my research projects focuses on studying Frequentist properties of Gaussian processes in non-linear latent variable models and measurement error models. Another aspect concentrates on developing efficient algorithms and conducting theoretical investigations in Gaussian process models for the shape constrained regression, motivated by scientific studies in nuclear physics and health science.
