Methods for High Dimensional Analysis, Multiple Testing, and Visual Exploration
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Date
2016-04-05
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Johns Hopkins University
Abstract
My thesis work focuses on aiding the practical implementation of advanced statistical methods. Chapter 2 concerns the common practice of visual exploratory data analysis, and the extent to which humans can visually detect statistical significance from plots. We find that human accuracy in detecting significance was initially poor, but improved with practice. Chapter 3 aids the implementation of bootstrap principal component analysis, by providing significant computational improvements. In a dataset of brain magnetic resonance images, the proposed method can reduce bootstrap standard error computation times from approximately 4 days to 47 minutes. Chapter 4 proposes an approximate optimization technique for adaptive clinical trials, aimed at lowering the expected sample size or expected duration of a trial.
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Keywords
Bootstrap, Adaptive Clinical Trials, Principal Component analysis, Exploratory Data Analaysis