Statistical Inference for Large-Scale Structured Data with Dependence and Non-Stationarity

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This project aims to address some challenging research problems, with a common theme of exploiting spatial-temporal dependence and non-stationarity in large-scale structured data, emerging from scientific studies in biology, genetics, astronomy, economics, neuroscience, geophysics, and meteorology among others. New tools will be developed for stochastic modeling, computational algorithms, and statistical inference applied to medical imaging data such as functional magnetic resonance imaging, neuron spike trains, genome-wide association studies, and building faster file access systems. It is anticipated that these new developments will allow scientists to efficiently analyze data with significantly increased flexibility and accuracy, and thus will have direct impacts on these applications to science, public health, and information technology. The research will also be integrated with educational practice through development of a seminar course on new statistical methods for analyzing spatially and temporally correlated imaging data. The project focuses on adequate accommodation of three fundamentally different types of spatial-temporal dependence structures. The research results aim to bridge the gap between the limited theory and methodology currently available and the broad and challenging scientific problems encountered in many applied fields. Motivated by fMRI data analysis, Project 1 explores a new semi-parametric inference procedure applicable to a broad class of "non-stationary non-Gaussian temporally dependent" error processes for time-course data collected at a given spatial point. A new test statistic will be developed, and its asymptotic properties will be established. Large-scale multiple testing tasks often exhibit dependence, and accounting for the dependence among individual non-Gaussian test statistics is an important, challenging, but unsolved problem in statistics. Motivated by challenges in detection of activated brain regions from fMRI studies and assessing association between single-nucleotide polymorphisms and a disease from GWAS studies, Project 2 proposes a new multiple testing framework for a diverging number of "correlated chi-squared test statistics with an arbitrary dependence structure." Motivated by applications in multiple neural spike train recordings with dependence in both time and space, Project 3 develops new integrative methods for learning the "sparse network structured dependence" among nodes underlying a wide class of multivariate point process data with non-stationary event times.