Thesis (Ph. D.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 73-75). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 73-75). Also available on the Internet.

Proefschrift--Nederlandse Economische Hogeschool te Rotterdam. / Summary in Dutch. "Stellingen": [2] p. inserted. Bibliography: p. 118-119.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1994. / Vita. Abstract. Includes bibliographical references (leaves 133-135). Also available via the Internet.

Thesis (M. Sc.)--Carleton University, 1993. / Includes bibliographical references. Also available in electronic format on the Internet.

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (p. [195]-202).

Thesis (M. Phil.)--University of Hong Kong, 2009. / Includes bibliographical references (p. 43-48). Also available in print.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Nov. 25, 2008). PDF text:vii, 125 p. : ill. ; 29 Mb. UMI publication number: AAT 3317288. Includes bibliographical references. Also available in microfilm and microfiche formats.

This thesis deals with gradience in grammar, i.e., with the fact that some linguistic structures are not fully acceptable or unacceptable, but receive gradient linguistic judgments. The importance of gradient data for linguistic theory has been recognized at least since Chomsky's Logical Structure of Linguistic Theory. However, systematic empirical studies of gradience are largely absent, and none of the major theoretical frameworks is designed to account for gradient data. The present thesis addresses both questions. In the experimental part of the thesis (Chapters 3-5), we present a set of magnitude estimation experiments investigating gradience in grammar. The experiments deal with unaccusativity/unergativity, extraction, binding, word order, and gapping. They cover all major modules of syntactic theory, and draw on data from three languages (English, German, and Greek). In the theoretical part of thesis (Chapters 6 and 7), we use these experimental results to motivate a model of gradience in grammar. This model is a variant of Optimality Theory, and explains gradience in terms of the competition of ranked, violable linguistic constraints. The experimental studies in this thesis deliver two main results. First, they demonstrate that an experimental investigation of gradient phenomena can advance linguistic theory by uncovering acceptability distinctions that have gone unnoticed in the theoretical literature. An experimental approach can also settle data disputes that result from the informal data collection techniques typically employed in theoretical linguistics, which are not well-suited to investigate the behavior of gradient linguistic data. Second, we identify a set of general properties of gradient data that seem to be valid for a wide range of syntactic phenomena and across languages. (a) Linguistic constraints are ranked, in the sense that some constraint violations lead to a greater degree of unacceptability than others. (b) Constraint violations are cumulative, i.e., the degree of unacceptability of a structure increases with the number of constraints it violates. (c) Two constraint types can be distinguished experimentally: soft constraints lead to mild unacceptability when violated, while hard constraint violations trigger serious unacceptability. (d) The hard/soft distinction can be diagnosed by testing for effects from the linguistic context; context effects only occur for soft constraints; hard constraints are immune to contextual variation. (e) The soft/hard distinction is crosslinguistically stable. In the theoretical part of the thesis, we develop a model of gradient grammaticality that borrows central concepts from Optimality Theory, a competition-based grammatical framework. We propose an extension, Linear Optimality Theory, motivated by our experimental results on constraint ranking and the cumulativity of violations. The core assumption of our model is that the relative grammaticality of a structure is determined by the weighted sum of the violations it incurs. We show that the parameters of the model (the constraint weights), can be estimated using the least square method, a standard model fitting algorithm. Furthermore, we prove that standard Optimality Theory is a special case of Linear Optimality Theory. To test the validity of Linear Optimality Theory, we use it to model data from the experimental part of the thesis, including data on extraction, gapping, and word order. For all data sets, a high model fit is obtained and it is demonstrated that the model's predictions generalize to unseen data. On a theoretical level, our modeling results show that certain properties of gradient data (the hard/soft distinction, context effects, and crosslinguistic effects) do not have to be stipulated, but follow from core assumptions of Linear Optimality Theory.

Ph.D. / Electrical and Computer Engineering / Probabilistic inference is the problem of estimating the hidden variables (states or parameters) of a system in an optimal and consistent fashion as a set of noisy or incomplete observations of the system becomes available online. The optimal solution to this problem is given by the recursive Bayesian estimation algorithm which recursively updates the posterior density of the system state as new observations arrive. This posterior density constitutes the complete solution to the probabilistic inference problem, and allows us to calculate any "optimal" estimate of the state. Unfortunately, for most real-world problems, the optimal Bayesian recursion is intractable and approximate solutions must be used. Within the space of approximate solutions, the extended Kalman filter (EKF) has become one of the most widely used algorithms with applications in state, parameter and dual estimation. Unfortunately, the EKF is based on a sub-optimal implementation of the recursive Bayesian estimation framework applied to Gaussian random variables. This can seriously affect the accuracy or even lead to divergence of any inference system that is based on the EKF or that uses the EKF as a component part. Recently a number of related novel, more accurate and theoretically better motivated algorithmic alternatives to the EKF have surfaced in the literature, with specific application to state estimation for automatic control. We have extended these algorithms, all based on derivativeless deterministic sampling based approximations of the relevant Gaussian statistics, to a family of algorithms called Sigma-Point Kalman Filters (SPKF). Furthermore, we successfully expanded the use of this group of algorithms (SPKFs) within the general field of probabilistic inference and machine learning, both as stand-alone filters and as subcomponents of more powerful sequential Monte Carlo methods (particle filters). We have consistently shown that there are large performance benefits to be gained by applying Sigma-Point Kalman filters to areas where EKFs have been used as the de facto standard in the past, as well as in new areas where the use of the EKF is impossible.