Predictive Methods for Analyzing High-throughput Data and Spatial-Temporal Data

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The accelerated development of high-throughput sequencing biotechnologies has made it affordable to collect high-dimensional molecular-level profiles, such as gene expression, which are called features in this proposal. It is of great interest to identify relevant features associated with a phenotype (eg. cancer status, health disorder). Many researchers have advocated to apply statistical learning methods to perform predictive analysis for high-throughput data. Predictive analysis results can be used in many ways. For example, they can be used to diagnose human diseases, to predict response to a medicine (personalized medicine); they can be used to choose an optimal gene subset for further experiments by plant/animal breeders; the subset of features extracted from good predictive models can facilitate the uncovering of the biological mechanism for a phenotype. Unfortunately, the high-dimensionality causes enormous overfitting in predictive analysis even with very simple models. The chance of finding false predictive features/patterns is extremely high. Therefore, it is challenging to fight against false discovery in predictive analysis when searching for more predictive features. My research outcomes will include new tools for honestly measuring predictivity (such as error rate, AUC) of selected features, and new tools for identifying truly predictive features and for building sharper predictive models for phenotypes. I will also practice predictive analysis with specific high-throughput datasets in a variety of scientific problems related to human health and food security, which will lead to new scientific discoveries and new solutions for these areas. In science, a theory is tested by performing predictions for observations in the future. Significant discrepancies between observations and predictions suggest that the theory is incorrect or flawed. Similarly, looking at out-of-sample predictions is a straightforward method for comparing and checking goodness-of-fit (GOF) of statistical models. Today, increasingly complex models are being proposed for a variety of correlated data such as, temporal, spatial, and repeated measurements data. More widely applicable predictive methods for comparing and checking such complex models are demanded. I will work to improve predictive model comparison and checking methods for generalized linear mixed models (GLMM) for datasets with correlation structure, and to release R add-on packages to facilitate the comparison and checking of GLMM. My research outcomes will include new tools for evaluating complex Bayesian/non-Bayesian models with correlated random effects. These new model evaluation tools will be essential for researchers in epidemiology, ecology, and environmental sciences. Improved modelling of the datasets from these areas will lead to more solid data analysis conclusions, which have essential impact on policy making in economic-social problems.