No description available.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 67-69). Also available via the Internet.

In this dissertation we present new results regarding optimality of block designs with limited resources. The dissertation is organized as follows. The first chapter outlines the theory of optimal block design. The second chapter shows new work in optimal minimally connected block designs with spatial correlation structure. The third chapter details the discovery of the optimal incomplete designs with two blocks. The fourth chapter does the same for the optimal binary incomplete designs with three blocks. The fifth chapter summarizes the techniques used and new results found and lists possible future research topics. / Ph. D.

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by Koon-Sun Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 40-41). / Chapter Chapter 1 --- Introduction and Review --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Preliminaries --- p.4 / Chapter 1.3 --- A brief review of A-optimal designs --- p.8 / Chapter Chapter 2 --- D-optimal Designs --- p.13 / Chapter 2.1 --- A D-optimal design problem --- p.13 / Chapter 2.2 --- A theorem for D-optimal designs --- p.14 / Chapter Chapter 3 --- E-optimal Designs --- p.18 / Chapter 3.1 --- An E-optimal design problem --- p.18 / Chapter 3.2 --- A theorem for E-optimal designs --- p.19 / Chapter Chapter 4 --- An alternative method for computing CL vectors --- p.31 / Chapter Chapter 5 --- Conclusions --- p.36 / References --- p.40

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We consider optimal design for changepoint problems with particular attention paid to situations where the only possible change is in the mean. Optimal design for changepoint problems has only been addressed in an unpublished doctoral thesis, and in only one journal article, which was in a frequentist setting. The simplest situation we consider is that of a stochastic process that may undergo a, change at an unknown instant in some interval. The experimenter can take n measurements and is faced with one or more of the following optimal design problems: Where should these n observations be taken in order to best test for a change somewhere in the interval? Where should the observations be taken in order to best test for a change in a specified subinterval? Assuming that a change will take place, where should the observations be taken so that that one may best estimate the before-change mean as well as the after-change mean? We take a Bayesian approach, with a risk based on squared error loss, as a design criterion function for estimation, and a risk based on generalized 0-1 loss, for testing. We also use the Spezzaferri design criterion function for model discrimination, as an alternative criterion function for testing. By insisting that all observations are at least a minimum distance apart in order to ensure rough independence, we find the optimal design for all three problems. We ascertain the optimal designs by writing the design criterion functions as functions of the design measure, rather than of the designs themselves. We then use the geometric form of the design measure space and the concavity of the criterion function to find the optimal design measure. There is a straightforward correspondence between the set of design measures and the set of designs. Our approach is similar in spirit, although rather different in detail, from that introduced by Kiefer. In addition, we consider design for estimation of the changepoint itself, and optimal designs for the multipath changepoint problem. We demonstrate why the former problem most likely has a prior-dependent solution while the latter problems, in their most general settings, are complicated by the lack of concavity of the design criterion function. / Nous considérons, dans cette dissertation, les plans d'expérience bayésiens optimauxpour les problèmes de point de rupture avec changement d'espérance. Un cas de pointde rupture avec changement d'espérance à une seule trajectoire se présente lorsqu'uneséquence de données est prélevée le long d'un axe temporelle (ou son équivalent) etque leur espérance change de valeur. Ce changement, s'il survient, se produit à unendroit sur l'axe inconnu de l'expérimentateur. Cet endroit est appelé "point derupture". Le fait que la position du point de rupture soit inconnue rend les tests etl'inférence difficiles dans les situations de point de rupture à une seule trajectoire.

Thesis (Ph. D.)--University of Chicago, Dept. of Statistics, June 2002. / Includes bibliographical references (p. 123-132) Also available on the Internet.

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The optimal projection approach to solving the reduced order model problem produces two coupled, highly nonlinear matrix equations with rank conditions as constraints. Due to the resemblance of these equations to standard matrix Lyapunov equations, they are called modified Lyapunov equations. The proposed algorithms utilize probability-one homotopy theory as the main tool. It is shown that there is a family of systems (the homotopy) that make a continuous transformation from some initial system to the final system. With a carefully chosen initial problem a theorem guarantees that all the systems along the homotopy path will be asymptotically stable, controllable and observable. One method, which solves the equations in their original form, requires a decomposition of the projection matrix using the Drazin inverse of a matrix. It is shown that the appropriate inverse is a differentiable function. An effective algorithm for computing the derivative of the projection matrix that involves solving a set of Sylvester equations is given. Another class of methods considers the equations in a modified form, using a decomposition of the pseudogramians based on a contragredient transformation. Some freedom is left in making an exact match between the number of equations and the number of unknowns, thus effectively generating a family of methods. Three strategies are considered for balancing the number of equations and unknowns. This approach proved to be very successful on a number of examples. The tests have shown that using the ‘best’ method practically always leads to a solution. / Master of Science