Bayesian Methods for High-dimensional and Correlated Data

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The accelerated development of many high-throughput biotechnologies has made it affordable to collect measurements of high-dimensional molecular changes in cells, such as expressions of genes, which are called features generally, and often called signatures in the literature of life sciences. Scientists are interested in discovering relevant features associated with a categorical response variable, such as cancer onset or progression. The numbers of such candidate features at our disposal are often as large as millions. The high dimension in candidate features presents great challenges to statisticians because we are much more likely to find noise rather than signals. In addition, these features have complex structures. I will work to develop and apply Bayesian statistical methodologies based on MCMC (Markov chain Monte Carlo) computing and heavy-tailed priors to identify relevant feature subsets associated with a response of interest, and to other research problems in life sciences that use high-throughput data. The outcomes from this research will include new statistical software packages (with new algorithms) for solving bioinformatics and neuroinformatics problems. These software packages are expected to facilitate new scientific discoveries, which will potentially lead to advances in diagnosis and prognosis of many complex human diseases, particularly cancers. I also propose to extend existing model evaluation methods so that they are applicable to complex Bayesian models for correlated data, such as spatial and temporal data, which often arise from epidemiological, ecological, and environmental studies. I expect that the extended model evaluation methods will be more reliable tools for evaluating models for correlated data. Better model evaluation results will not only help us choose the best model, but also guide us to improve existing models and then develop better models. Therefore, the extended model evaluation methods for correlated data will assist investigators working in epidemiological, ecological, and environmental studies to develop or choose appropriate models for their data sets, and then draw reliable conclusions and make better predictions based on their model fitting results.