DATA SCIENCE WEEK

I will give a brief overview of my research followed by three detailed examples. As my first example, I describe our progress on the reconstruction of paleoclimate using different data sources. We have made a number of methodological developments that have enhanced our understanding of both climate reconstruction and its uncertainty quantification via Bayesian hierarchical models. My second example addresses one year ahead prediction of US county-specific HIV incidence rates using publicly available data that are abundant in space but scarce in time. We developed new spatially varying autoregressive models compounded with conditional autoregressive spatial correlation structures and compared their predictive ability to that of a number of linear mixed models. Motivated by my climate studies, the last example concerns new statistical methods for comparing two spatio-temporal random fields. We propose a multiple testing procedure for detecting local differences in the characteristics of two spatio-temporal random fields by explicitly taking spatial information into account. Finally, I will briefly discuss some future research interests.

Inference, such as hypothesis tests, with reasonable accuracy from extremely limited data is a challenge. In many situations it is common to have only two available sample percentile values of a response with no control on the choice of the available percentile pairs. In such situations, one may want to estimate other pertinent information about the population such as the mean, standard deviation, and eventually derive a test of the mean, based on the two available sample percentiles. We propose a test for the mean of a normal distribution based on two sample percentile values. The exact and asymptotic distributions of the proposed test statistic are investigated. The power and the robustness of the proposed test are under review.