Description
- Abstract:
- This thesis is a mathematical and statistical study of conditional modeling and conditional inference. Two applications are covered: (1) Stock Prices and the Statistics of their Returns; and (2) Computer Vision.Part (I) introduces the major methodologies for modeling and analyzing extremely high-dimensional data and overviews the two applications covered in this thesis.Part (II) is about the statistical analysis of stock returns. Chapter 1 reviews the discoveries of Hwang et al., and discusses their connections to the classical geometric Brownian motion and related models. Chapter 2 introduces combinatorial methods for exploring the temporal dependency between returns, and it gives strong statistical evidence against the standard models and many of their variations. Chapter 3 examines stochastic volatility and other modifications of Black-Scholes, and finds that these models would require very frequent high-amplitude departures from homogeneity to fit the data. Chapter 4 concludes with a summary, a discussion, and some challenges.Part (III) is another application of conditional modeling, pattern recognition in computer vision. Chapter 5 introduces a probabilistic framework for modeling hierarchy, reusability, and conditional data models. A sufficient condition for the existence of non-Markovian distributions in a hierarchical system is provided, and the convergence of an iterative perturbation scheme for achieving these desired distributions is proven. Chapter 6 studies conditional modeling methods in order to finesse the complexity of the high dimensional data. The approximate sampling method of the generative model is proposed, based on the choices of background image patches. Chapter 7 shows that essentially optimal ROC performance can be attained through a computationally feasible sequential decision analysis. Chapter 8 includes X-ray image classification experiments with a composition system. Chapter 9 makes some conclusions and suggests future directions.
- Notes:
- Thesis (Ph.D. -- Brown University (2010)
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Citation
Chang, Lo-Bin,
"Conditional Modeling and Conditional Inference"
(2010).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0B856DP
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Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....