In this research, Bayesian two-stage D-D optimal designs for mixture experiments with or without process variables under model uncertainty are developed. A Bayesian optimality criterion is used in the first stage to minimize the determinant of the posterior variances of the parameters. The second stage design is then generated according to an optimality procedure that collaborates with the improved model from first stage data. Our results show that the Bayesian two-stage D-D optimal design is more efficient than both the Bayesian one-stage D-optimal design and the non-Bayesian one-stage D-optimal design in most cases. We also use simulations to investigate the ratio between the sample sizes for two stages and to observe least sample size for the first stage. On the other hand, we discuss D-optimal second or higher order designs, and show that Ds-optimal designs are a reasonable alternative to D-optimal designs. / Ph. D.

This dissertation proposes a model of word stress in a derivational version of Optimality Theory (OT) called Harmonic Serialism (HS; Prince and Smolensky 1993/2004, McCarthy 2000, 2006, 2010a). In this model, the metrical structure of a word is derived through a series of optimizations in which the 'best' metrical foot is chosen according to a ranking of violable constraints. Like OT, HS models cross-linguistic typology under the assumption that every constraint ranking should correspond to an attested language. Chapter 2 provides an argument for modeling stress typology in HS by showing that the serial model correctly rules out stress patterns that display non-local interactions, while a parallel OT model with the same constraints and representations fails to make such a distinction. Chapter 3 discusses two types of primary stress---autonomous and parasitic---and argues that limited parallelism in the assignment of primary stress is warranted by a consideration of attested typology. Stress systems in which the primary stress appears to behave autonomously from secondary stresses require that primary stress assignment be simultaneous with a foot's construction. As a result, a provision to allow primary stress to be reassigned during a derivation is necessary to account for a class of stress systems in which primary stress is parasitic on secondary stresses. Chapter 4 takes up two issues in the definition of constraints on primary stress, including a discussion of how primary stress alignment should be formulated and the identification of vacuous satisfaction as a cause of problematic typological predictions. It is proposed that all primary stress constraints be redefined according to non-vacuous schemata, which eliminate the problematic predictions when implemented within HS. Finally, chapter 5 considers the role of representational assumptions in typological predictions with comparisons between HS and parallel OT. The primary conclusion of this chapter is that constituent representations (i.e., feet) are necessary in HS to account for rhythmic stress patterns in a typologically restrictive way.

Pursuit-evasion games are the subject of a variety of research initiatives seeking to provide some level of autonomy to mobile, robotic vehicles with on-board controllers. Applications of these controllers include defense topics such as unmanned aerial vehicle (UAV) and unmanned underwater vehicle (UUV) navigation for threat surveillance, assessment, or engagement. Controllers implementing pursuit-evasion algorithms are also used for improving everyday tasks such as driving in traffic when used for collision avoidance maneuvers. Currently, pursuit-evasion tactics are incorporated into the control by solving the Hamilton-Jacobi-Isaacs (HJI) equation explicitly, simplifying the solution using approximate dynamic programming, or using a purely finite-horizon approach. Unfortunately, these methods are either subject to difficulties of long computational times or having no guarantees of succeeding in the pursuit-evasion game. This leads to more difficulties of implementing these tactics on-line in a real robotic scenario where the opposing agent may not be known before the maneuver is required. This dissertation presents a novel method of solving the HJI equation by partitioning the state space into regions of local, finite horizon control laws. As a result, the HJI equation can be reduced to solving the Hamilton-Jacobi-Bellman equation recursively as information is received about an opposing agent. Adding complexity to the problem structure results in a decreased calculation time to allow pursuit-evasion tactics to be calculated on-board an agent during a scenario. The algorithms and implementation methods are given explicitly and illustrated with an example of two robotic vehicles in a collision avoidance maneuver. / Ph. D.

Scheduling decisions in soft real-time environments are based on a utility function. The goal of such schedulers is to use a best-effort approach to maximize the utility function and ensure graceful degradation at overloads. Utility Accrual (UA) schedulers use heuristics to maximize the accrued utility. Heuristic-based scheduling do not always yield the optimal schedule even if there exists one because they do not explore the entire search space of task orderings. In distributed systems, local UA schedulers use the same heuristics along with deadline decomposition for task segments. At present, there has been no evaluation and analysis of the degree to which these polynomial-time, heuristic algorithms succeed in maximizing the total utility accrued. We implemented a preemptive, off-line static scheduling algorithm that performs an exhaustive search of all the possible task orderings to yield the optimal schedules. We simulated two important online dynamic UA schedulers, DASA-ND and LBESA for different system loads, task models, utility and load distribution patterns, and compared their performance with their corresponding optimal schedules. Our experimental analysis indicates that for most scenarios, both DASA-ND and LBESA create optimal schedules. When task utilities are equal or form a geometric sequence with an order of magnitude difference in their utility values, UA schedulers show more than 90% probability of being optimal for single-node workloads. Even though deadline decomposition substantially improves the optimality of both DASA-ND and LBESA under different scenarios for distributed workloads, it can adversely affect the scheduling decisions for some task sets we considered. / Master of Science

<p>This thesis proposes a simplification of the model for dependent Bernoulli variables presented in Cox and Snell (1989). The simplified model, referred to as the simplified Cox model, is developed for identically distributed and dependent Bernoulli variables.</p><p>Properties of the model are presented, including expressions for the loglikelihood function and the Fisher information. The special case of a bivariate symmetric model is studied in detail. For this particular model, it is found that the number of design points in a locally D-optimal design is determined by the log-odds ratio between the variables. Under mutual independence, both a general expression for the restrictions of the parameters and an analytical expression for locally D-optimal designs are derived.</p><p>Focusing on the bivariate case, score tests and likelihood ratio tests are derived to test for independence. Numerical illustrations of these test statistics are presented in three examples. In connection to testing for independence, an E-optimal design for maximizing the local asymptotic power of the score test is proposed.</p><p>The simplified Cox model is applied to a dental data. Based on the estimates of the model, optimal designs are derived. The analysis shows that these optimal designs yield considerably more precise parameter estimates compared to the original design. The original design is also compared against the E-optimal design with respect to the power of the score test. For most alternative hypotheses the E-optimal design provides a larger power compared to the original design.</p>

This thesis proposes a simplification of the model for dependent Bernoulli variables presented in Cox and Snell (1989). The simplified model, referred to as the simplified Cox model, is developed for identically distributed and dependent Bernoulli variables. Properties of the model are presented, including expressions for the loglikelihood function and the Fisher information. The special case of a bivariate symmetric model is studied in detail. For this particular model, it is found that the number of design points in a locally D-optimal design is determined by the log-odds ratio between the variables. Under mutual independence, both a general expression for the restrictions of the parameters and an analytical expression for locally D-optimal designs are derived. Focusing on the bivariate case, score tests and likelihood ratio tests are derived to test for independence. Numerical illustrations of these test statistics are presented in three examples. In connection to testing for independence, an E-optimal design for maximizing the local asymptotic power of the score test is proposed. The simplified Cox model is applied to a dental data. Based on the estimates of the model, optimal designs are derived. The analysis shows that these optimal designs yield considerably more precise parameter estimates compared to the original design. The original design is also compared against the E-optimal design with respect to the power of the score test. For most alternative hypotheses the E-optimal design provides a larger power compared to the original design.

Thesis (doctoral)--Rijksuniversiteit te Leiden, 1998. / Includes bibliographical references (p. [173]-180).

Thesis (doctoral)--Rijksuniversiteit te Leiden, 1998. / Includes bibliographical references (p. [173]-180).

Design problems involve finding optimal plans that minimize cost and maximize information about the effects of changing experimental variables on some response. Information is typically measured through statistically meaningful functions, or criteria, of a design's corresponding information matrix. The most common criteria implicitly assume equal interest in all effects and certain forms of information matrices tend to optimize them. However, these criteria can be poor assessments of a design when there is unequal interest in the experimental effects. Morgan and Wang (2010) addressed this potential pitfall by developing a concise weighting system based on quadratic forms of a diagonal matrix W that allows a researcher to specify relative importance of information for any effects. They were then able to generate a broad class of weighted optimality criteria that evaluate a design's ability to maximize the weighted information, ultimately targeting those designs that efficiently estimate effects assigned larger weight. This dissertation considers a much broader class of potential weighting systems, and hence weighted criteria, by allowing W to be any symmetric, positive definite matrix. Assuming the response and experimental effects may be expressed as a general linear model, we provide a survey of the standard approach to optimal designs based on real-valued, convex functions of information matrices. Motivated by this approach, we introduce fundamental definitions and preliminary results underlying the theory of general weighted optimality. A class of weight matrices is established that allows an experimenter to directly assign weights to a set of estimable functions and we show how optimality of transformed models may be placed under a weighted optimality context. Straightforward modifications to SAS PROC OPTEX are shown to provide an algorithmic search procedure for weighted optimal designs, including A-optimal incomplete block designs. Finally, a general theory is given for design optimization when only a subset of all estimable functions is assumed to be in the model. We use this to develop a weighted criterion to search for A-optimal completely randomized designs for baseline factorial effects assuming all high-order interactions are negligible. / Ph. D.

Multiobjective Stochastic Linear Programming is a relevant topic. As a matter of fact, many real life problems ranging from portfolio selection to water resource management may be cast into this framework. There are severe limitations in objectivity in this field due to the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice does not hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this thesis, we resort to the bounded rationality and chance-constrained principles to define satisficing solutions for Multiobjective Stochastic Linear Programming problems. These solutions are then characterized for the cases of normal, exponential, chi-squared and gamma distributions. Ways for singling out such solutions are discussed and numerical examples provided for the sake of illustration. Extension to the case of fuzzy random coefficients is also carried out. / Decision Sciences