Computationally intensive approaches to missing data

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Due to the explosion of computational advances and general technological innovation for gathering information, modern scientific research faces a unique challenge when faced with missing data. My research will attempt to develop new methods for analyzing data in the presence of missing observations, particularly for data that is high-dimensional in nature and addressing the question of model selection. I will employ and extend advanced nonparametric clustering methods to improve multiple imputation methods for high-dimensional categorical variables.I will show how returning the the original premise of the multiple imputation algorithm as estimation of a high-dimensional integral can help to improve the efficiency of inference with small numbers of copies through the use of adaptive quadrature methods, particularly methods that have been developed for the design of computer experiments. I will examine the use of tools for dimensionality reduction that are commonly used in machine and statistical learning (such as principal component analysis, partial least squares, neural networks, and support vector machines) to allow for generation of completed datasets that use as much relevant information as possible and practical. Finally, I will use new developments in functional data analysis (particularly generalized profile estimation) to construct a framework in which practitioners can more easily and automatically test for robustness to modelling assumptions when analyzing data with missingness.