Languages and species both evolve by a process of repeated divergences, which can be described with the branching of a phylogenetic tree or phylogeny. Taking advantage of this fact, it is possible to study language change using computational tree building techniques developed for evolutionary biology. Mathematical approaches to the construction of phylogenies fall into two major categories: character based and distance based methods. Character based methods were used in prior work in the application of phylogenetic methods to the Indo-European family of languages by researchers at the University of Pennsylvania. Discussion of the limitations of character-based models leads to a similar presentation of distance based models. We present an adaptation of these methods to linguistic data, and the phylogenies generated by applying these methods to several modern Germanic languages and Spanish. We conclude that distance based for phylogenies are useful for historical linguistic reconstruction, and that it would be useful to extend existing tree drawing methods to better model the evolutionary effects of language contact.

<p>This dissertation is devoted to modeling complex data from the</p><p>Bayesian perspective via constructing priors with latent structures.</p><p>There are three major contexts in which this is done -- strategies for</p><p>the analysis of dynamic longitudinal data, estimating</p><p>shape-constrained functions, and identifying subgroups. The</p><p>methodology is illustrated in three different</p><p>interdisciplinary contexts: (1) adaptive measurement testing in</p><p>education; (2) emulation of computer models for vehicle crashworthiness; and (3) subgroup analyses based on biomarkers.</p><p>Chapter 1 presents an overview of the utilized latent structured</p><p>priors and an overview of the remainder of the thesis. Chapter 2 is</p><p>motivated by the problem of analyzing dichotomous longitudinal data</p><p>observed at variable and irregular time points for adaptive</p><p>measurement testing in education. One of its main contributions lies</p><p>in developing a new class of Dynamic Item Response (DIR) models via</p><p>specifying a novel dynamic structure on the prior of the latent</p><p>trait. The Bayesian inference for DIR models is undertaken, which</p><p>permits borrowing strength from different individuals, allows the</p><p>retrospective analysis of an individual's changing ability, and</p><p>allows for online prediction of one's ability changes. Proof of</p><p>posterior propriety is presented, ensuring that the objective</p><p>Bayesian analysis is rigorous.</p><p>Chapter 3 deals with nonparametric function estimation under</p><p>shape constraints, such as monotonicity, convexity or concavity. A</p><p>motivating illustration is to generate an emulator to approximate a computer</p><p>model for vehicle crashworthiness. Although Gaussian processes are</p><p>very flexible and widely used in function estimation, they are not</p><p>naturally amenable to incorporation of such constraints. Gaussian</p><p>processes with the squared exponential correlation function have the</p><p>interesting property that their derivative processes are also</p><p>Gaussian processes and are jointly Gaussian processes with the</p><p>original Gaussian process. This allows one to impose shape constraints</p><p>through the derivative process. Two alternative ways of incorporating derivative</p><p>information into Gaussian processes priors are proposed, with one</p><p>focusing on scenarios (important in emulation of computer</p><p>models) in which the function may have flat regions.</p><p>Chapter 4 introduces a Bayesian method to control for multiplicity</p><p>in subgroup analyses through tree-based models that limit the</p><p>subgroups under consideration to those that are a priori plausible.</p><p>Once the prior modeling of the tree is accomplished, each tree will</p><p>yield a statistical model; Bayesian model selection analyses then</p><p>complete the statistical computation for any quantity of interest,</p><p>resulting in multiplicity-controlled inferences. This research is</p><p>motivated by a problem of biomarker and subgroup identification to</p><p>develop tailored therapeutics. Chapter 5 presents conclusions and</p><p>some directions for future research.</p> / Dissertation

This thesis is composed of two parts. The first part pertains to tree-based models. The second part deals with multiple testing in large-scale contingency tables. Tree-based models have gained enormous popularity in statistical modeling and data mining. We propose a novel tree-pruning algorithm called frontier-based tree-pruning algorithm (FBP). The new method has an order of computational complexity comparable to cost-complexity pruning (CCP). Regarding tree pruning, it provides a full spectrum of information. Numerical study on real data sets reveals a surprise: in the complexity-penalization approach, most of the tree sizes are inadmissible. FBP facilitates a more faithful implementation of cross validation, which is favored by simulations. One of the most common test procedures using two-way contingency tables is the test of independence between two categorizations. Current test procedures such as chi-square or likelihood ratio tests provide overall independency but bring limited information about the nature of the association in contingency tables. We propose an approach of testing independence of categories in individual cells of contingency tables based on a multiple testing framework. We then employ the proposed method to identify the patterns of pair-wise associations between amino acids involved in beta-sheet bridges of proteins. We identify a number of amino acid pairs that exhibit either strong or weak association. These patterns provide useful information for algorithms that predict secondary and tertiary structures of proteins.