Academic

In this talk, I will first present a Bayesian semiparametric method of jointly estimating the density function and the tail index. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the tail of the distribution getting washed away by unrelated features of a hefty bulk. The proposed Bayesian method avoids this problem by incorporating smoothness and tail regularization through a carefully specified semiparametric prior distribution, and can consistently estimate both the density function and its tail index at near minimax optimal rates of contraction. A brief real-data application will be presented to showcase the improvement of uncertainty assessment in estimating the tail index compared to thresholding methods. 

Next, I will present a hierarchical extension of the Bayesian mixture-of-experts model for the censored ocean flow cytometry data towards a better understanding of the relationship between marine microbial populations and environmental factors. The dynamics of marine phytoplankton and their relationship with the ocean environment are fundamental to oceanography and our planet Earth. The newly emerged technology allows collecting ocean data at the cell level massively in real-time onboard a moving ship — the flow cytometry data on the distribution of phytoplankton across thousands of kilometers. However, instrument limits confine the data in a restricted region, and data originally outside the region are observed bunching on the boundary. The Bayesian method imputes the censored data within a Gibbs sampler. In addition to identifying important environmental drivers, the method offers a natural uncertainty assessment of the dynamics of the time-varying relative abundance of the phytoplanktons.