Statistics, science and statistical science

About this book

As science continues to evolve in both style and scope, increasingly facilitated by the availability of large-scale computing power, so do the statistical challenges arising in many scientific disciplines. This dissertation provides a number developments in statistical computation that are designed for a wide range of potential applications; but are particularly targeted at those in the physical sciences. In addition to the general methodology, we also present a statistical application in astrophysics. In Chapter 1 we present a new algorithm, the Interwoven Expectation-Maximization Algorithm (IEM), designed to accelerate statistical computation in a wide range of settings. The algorithm combines classical ideas such as sufficiency and ancillarity with the rich body of literature on data augmentation. We detail the extensive connections to existing algorithms and provide both theoretical and empirical results that show the excellent performance of IEM. Using insight from the design and implementation of the IEM algorithm, in chapter 2 we present an example of statistical modeling in a complex physical science setting. Our framework for analyzing stellar populations allows for the integration of scientific knowledge and data: providing the opportunity to investigate new structures within existing data. Statistical computation in this application is complicated by the 'black box' likelihood, for which we develop a general and efficient algorithm applicable to similar settings. We conclude in chapter 3 with an example that provides a rare opportunity for a 'fair' comparison between a selection of very different semi-parametric models. By finding a unique parametric model that intersects the classes of three semi-parametric models we investigate the efficiency and robustness of different estimators and the implications for the ordering of semi-parametric estimators.