The Neotropical region is the most biologically diverse region on the planet. The region encompasses a variety of ecosystems and has long been the target of researchers interested in patterns of species diversity and distribution. More recently, molecular data have been incorporated into methods for reconstructing the historical relationships among geographical areas and their biotas. Molecular phylogenetics has provided insights into diversification patterns and the influence of Late Cenozoic events on the evolutionary history of the region. Nevertheless, considering the vast extent and complexity of the region, more studies are needed to fully appreciate the patterns of biogeography and the mechanisms that generate and maintain its biodiversity. Therefore, in Chapter 1 I employed molecular methods to reconstruct the phylogenetic relationships of the subfamily Sigmodontinae, which is the most diverse and widespread radiation of Neotropical rodents. I was able to evaluate controversial hypotheses about the paleogeographic scenarios implicated to explain the biogeography of sigmodontines. Advances in sequencing technology and analytical approaches have revolutionized the role of historical biogeography in elucidating the spatial and temporal context of diversification, and the integrative field of phylogeography was fundamental to the development of biogeography at the intraspecific level. However, the potential of phylogeography to unravel diverse historical scenarios in a tractable statistical framework has been largely unexplored for the Neotropics as a whole. In order to integrate more robust hypothesis testing to elucidate the evolutionary history of Amazonia's biota, I devoted Chapter 2 to a review of Amazonian phylogeography that I anticipate will improve the basis for interpreting the patterns and processes of diversification in Amazonia. Chapter 3 is a thorough species account of spiny rats of the genus Proechimys, which is poorly known taxonomically despite its diversity and widespread distribution in the Neotropics. This taxonomic revision will benefit researchers interested in using such information with coalescent-based methods of species delimitation aimed at an integrative and stable taxonomy. Lastly, Chapter 4 deals with the phylogeography of P. roberti. This species occurs in southeastern Amazonia and the Cerrado of central Brazil. I employed a dense taxon sampling and used coalescent-based methods to demonstrate that rivers and topography have a causal link to the geographic structure of P. roberti populations. In my dissertation, I used a combination of molecular genetics tools to provide a better understanding of the biogeography and evolution of some of the most diverse groups of Neotropical mammals. My dissertation interacts in many levels with my future research interests. These present and future efforts hold promise for unraveling the evolutionary history of the Neotropical region and its biota, and will assist in conservation decisions aiming at preserving its unparalleled biodiversity.

This study compared the results of his chi square text of independence and the corrected chi square statistic against Fisher's exact probability test (the hypergeometric distribution) in contection with sampling from a finite population. Data were collected by advancing the minimum call size from zero to a maximum which resulted in a tail area probability of 20 percent for sample sizes from 10 to 100 by varying increments. Analysis of the data supported the rejection of the null hypotheses regarding the general rule-of-thumb guidelines concerning sample size, minimum cell expected frequency and the continuity correction factor. it was discovered that the computation using Yates' correction factor resulted in values which were so overly conservative (i.e. tail area porobabilities that were 20 to 50 percent higher than Fisher's exact test) that conclusions drawn from this calculation might prove to be inaccurate. Accordingly, a new correction factor was proposed which eliminated much of this discrepancy. Its performance was equally consistent with that of the uncorrected chi square statistic and at times, even better.

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Multiplex networks describe a set of entities, with multiple relationships among them, as a collection of networks over a common vertex set. Multiplex networks naturally describe complex systems where units connect across different modalities whereas single network data only permits a single relationship type. Joint spectral embedding methods facilitate analysis of multiplex network data by simultaneously mapping vertices in each network to points in Euclidean space, entitled node embeddings, where statistical inference is then performed. This mapping is performed by spectrally decomposing a matrix that summarizes the multiplex network. Different methods decompose different matrices and hence yield different node embeddings. This dissertation analyzes a class of joint spectral embedding methods which provides a foundation to compare these different approaches to multiple network inference. We compare joint spectral embedding methods in three ways. First, we extend the Random Dot Product Graph model to multiplex network data and establish the statistical properties of node embeddings produced by each method under this model. This analysis facilitates a full bias-variance analysis of each method and uncovers connections between these methods and methods for dimensionality reduction. Second, we compare the accuracy of algorithms which utilize these different node embeddings in a variety of multiple network inference tasks including community detection, vertex anomaly detection, and graph hypothesis testing. Finally, we perform a time and space complexity analysis of each method and present a case study in which we analyze interactions between New England sports fans on the social news aggregation and discussion website, Reddit. These findings provide a theoretical and practical guide to compare joint spectral embedding techniques and highlight the benefits and drawbacks of utilizing each method in practice.

<p>In this thesis, we discuss some results on the distribution of points on the sphere, asymptotically when both the number of points and the dimension of the sphere tend to infinity. We then give some applications of these results to some statistical problems and especially to hypothesis testing.</p> / Master of Science (MSc)

This dissertation focuses on exploring individual and strategic decision problems in Economics. I take a different approach in each chapter to capture various aspects of decision problems. An overview of this dissertation is provided in Chapter 1. Chapter 2 studies an individual's decision making in extensive-form games under ambiguity when the individual is ambiguous about an opponent's moves. In this chapter, a player follows Choquet Expected Utility preferences, since the standard Expected Utility cannot explain the situations of ambiguity. I raise the issue that dynamically inconsistent decision making can be derived in extensive-form games with ambiguity. To cope with this issue, this chapter provides sufficient conditions to recover dynamic consistency. Chapter 3 analyzes the strategic decision making in signaling games when a player makes an inference about hidden information from the behavioral hypothesis. The Hypothesis Testing Equilibrium (HTE) is proposed to provide an explanation for posterior beliefs from the player. The notion of HTE admits belief updates for all events including zero-probability events. In addition, this chapter introduces well-motivated modifications of HTE. Finally, Chapter 4 examines a boundedly rational individual who considers selective attributes when making a decision. It is assumed that the individual focuses on a subset of attributes that stand out from a choice set. The selective attributes model can accommodate violations of choice axioms of Independence from Irrelevant Alternative (IIA) and Regularity. / Doctor of Philosophy / This dissertation focuses on exploring individual and strategic decision problems in Economics. I take a different approach in each chapter to capture various aspects of decision problem. An overview of this dissertation is provided in Chapter 1. Chapter 2 studies an individual’s decision making in extensive-form games under ambiguity. Ambiguity describes the situation in which the information available to a decision maker is too imprecise to be summarized by a probability measure (Epstein, 1999). It is known that ambiguity causes dynamic inconsistency between ex-ante and interim decision making. This chapter provides sufficient conditions under which dynamic consistency is maintained. Chapter 3 analyzes the strategic decision making in signaling games in which there are two players: informed sender and uninformed receiver. The sender has a private information about his type and the receiver makes an inference about hidden information. This chapter suggests a notion of the Hypothesis Testing Equilibrium (HTE), which provides an alternative explanation for the receiver’s beliefs. The idea of the HTE can be used as a refinement of Perfect Bayesian Equilibrium (PBE) in signaling games to cope with the known limitations of PBE. Finally, Chapter 4 examines a boundedly rational individual who considers only salient attributes when making a decision. The individual considers an attribute only when it stands out enough in a choice set. The selective attribute model can accommodate violations of choice axioms of Independence from Irrelevant Alternative (IIA) and Regularity.

Manufacturing systems are complex entities comprised of people, processes, products, information systems and data, material processing, handling, and storage systems. Because of this complexity, systems must be modeled using a variety of views and modeling formalisms. In order to design and analyze manufacturing systems, the multiple views and models often need to be considered simultaneously. However, no single tool or computing environment currently exists that allows this to be done in an efficient and intelligible manner. New tools such as HTML and VRML present a promising approach for tackling these problems. They make possible environments where the different models can coexist and where mapping/linking between the models can be achieved. This research is concerned with developing a hybrid HTML/VRML environment for manufacturing systems modeling and analysis. Experiment was performed to compare this hybrid-modeling HTML/VRML environment to the traditional database environment in order to answer typical design/analysis questions associated with manufacturing systems, and to establish the potential advantages of this approach. Analyzing results obtained from the experiment indicated that the HTML/VRML approach might result in better understanding of a manufacturing system than the traditional database approach. / Master of Science

We describe new nonparametric methods for (i) quantifying conditional dependence, (ii) quantifying multi-sample dissimilarity, and (iii) testing multivariate symmetry. In the first part of the thesis, we propose a kernel partial correlation (KPC) to quantify conditional dependence, and a kernel measure of dissimilarity between multiple distributions (KMD) to quantify the difference between multiple distributions. These two measures are both deterministic numbers between 0 and 1, with 0 and 1 corresponding to the two extreme cases --- KPC is 0 if and only if perfect conditional dependence holds, and 1 if and only if there is a conditional functional relationship; while KMD is 0 if and only if all the distributions that are compared are equal, and 1 if and only if these distributions are mutually singular. Both KPC and KMD can be estimated consistently using a computationally efficient graph-based method (including k-nearest neighbor graph and minimum spanning tree). For applications, KPC can be used to develop a model-free variable selection algorithm. This algorithm is provably consistent under sparsity assumptions, and shows superior performance in practice compared to existing procedures. KMD can be used to design an easily implementable test for the equality of multiple distributions, which is consistent against all alternatives where at least two distributions are not equal. A problem closely related to multi-sample testing is testing for symmetry. In the second part of the thesis, we develop distribution-free tests for multivariate symmetry (that includes central symmetry, sign symmetry, spherical symmetry, etc.) based on multivariate signs, ranks and signed-ranks defined via optimal transport (OT). One test we propose can be thought of as a multivariate generalization of Wilcoxon signed-rank (GWSR) test and shares many of the appealing properties of its one-dimensional counterparts. In particular, when testing against location shift alternatives, the GWSR test suffers from no loss in (asymptotic) efficiency, when compared to Hotelling's T2 test, despite being nonparametric and exactly distribution-free. Another test we propose is based on a combination of kernel methods and the multivariate signs and ranks defined via OT. This test is universally consistent against all alternatives, while still maintaining the distribution-free property. Furthermore, it is capable of testing a broader class of multivariate symmetry, including exchangeability, extending beyond the class of symmetry testable by GWSR.

Theory often indicates that a given response variable should be a function of certain explanatory variables yet fails to provide meaningful information as to the specific form of this function. To test the validity of a given functional form with sensitivity toward the feasible alternatives, a procedure is needed for comparing non-nested families of hypotheses. Two hypothesized models are said to be non-nested when one model is neither a restricted case nor a limiting approximation of the other. These non-nested hypotheses cannot be tested using conventional likelihood ratio procedures. In recent years, however, several new approaches have been developed for testing non-nested regression models. A comprehensive review of the procedures for the case of two linear regression models was presented. Comparisons between these procedures were made on the basis of asymptotic distributional properties, simulated finite sample performance and computational ease. A modification to the Fisher and McAleer JA-test was proposed and its properties investigated. As a compromise between the JA-test and the Orthodox F-test, it was shown to have an exact non-null distribution. Its properties, both analytically and empirically derived, exhibited the practical worth of such an adjustment. A Monte Carlo study of the testing procedures involving non-nested linear regression models in small sample situations (n ≤ 40) provided information necessary for the formulation of practical guidelines. It was evident that the modified Cox procedure, N̄ , was most powerful for providing correct inferences. In addition, there was strong evidence to support the use of the adjusted J-test (AJ) (Davidson and MacKinnon's test with small-sample modifications due to Godfrey and Pesaran), the modified JA-test (NJ) and the Orthodox F-test for supplemental information. Under non normal disturbances, similar results were yielded. An empirical study of spending patterns for household food consumption provided a practical application of the non-nested procedures in a large sample setting. The study provided not only an example of non-nested testing situations but also the opportunity to draw sound inferences from the test results. / Ph. D.