Bayesian Inference and High-D space Characterization with application in Paleoclimatology and Biology Lin, Luan creator 2012 xv, 148 p. born digital Thesis (Ph.D. -- Brown University (2012) Lawrence, Charles Director Herbert, Timothy Reader Thompson, William Reader Brown University. Applied Mathematics sponsor theses bayesian inference clustering hmm rna secondary structure alignment RPB 20121023 engEnglishThis thesis is a mathematical study of paleoclimatology and computational biology.<br/><br/> <br/><br/> Part I gives an introduction and overview of this dissertation.<br/><br/> <br/><br/> Part II presents the applications of hidden Markov model in paleoclimatology study.<br/><br/> <br/><br/> Chapter 1 employs a two state hidden Markov model with multivariate emission to challenge the assumption that ENSO-like variability dominated Peru margin oceanography on decadal and longer time scales over the Holocene epoch. The HMM result shows that two regimes of variability dominate, one shows strong correlations between surface and subsurface proxies while the other does not.<br/><br/> <br/><br/> Chapter 2 is another application of hidden Markov model in paleoclimatology. A pair hidden Markov model is built to implement the alignments between pairs of stratigraphic records and provide uncertainty analysis. In addition to the most probable alignment, centroid alignment is also investigated.<br/><br/> <br/><br/> Part III focuses on characterization of high dimensional space.<br/><br/> <br/><br/> Chapter 3 develops an iterative algorithm to characterize the high dimensional spaces by identifying the most informative variables through mutual information based criteria. Application to the posterior space of RNA secondary structure is presented. <br/><br/> <br/><br/> Chapter 4 proposes a novel model based clustering algorithm based on $L_p$ distance in the situations where not only samples but also corresponding densities/probabilities (or subject to a normalization constant) are available. We demonstrate the abilities of this approach by experimenting via Gaussian Mixture Models.<br/><br/> <br/><br/> Part IV makes some conclusions and suggests future directions.10.7301/Z03J3B8CIn CopyrightCollection is open for research.dissertations