The Graduate Student Seminar

is pleased to announce a lecture by

Andrea Nemeth

on

The Search for D-Optimal Weighing Designs Using Simulated Annealing

Tuesday, November 7 at 4pm in JR 202

Abstract:

We are interested in estimating the weights of $n$ objects with $m$ weighings on an imperfect one-pan scale. These weighing design problems are analyzed through the general linear model. The standard form of this model is $y=\beta W+\epsilon$, where $y$ is the data vector, $\beta$ is the unknown parameter vector, $W$ is the design matrix, and $\epsilon$ is the error vector. The accuracy of the estimates of the unknown weights is determined from the design matrix; consequently, there is interest in choosing $W$ in an optimal fashion. Under certain assumptions about the distribution of the errors of the scale, we want to find the smallest confidence region for the true weights. This goal is achieved when the determinant of the information matrix $W^TW$, is maximized, and this is called the D-optimality criterion. The D-optimal results are known for $n=2, 3, 4, 5, 6, 7$, and for $n=-1\mod 4$ when $m$ is large. In this talk I will present many of these known results, and some new results using simulated annealing, a generalization of the Monte Carlo method that has been used in various combinatorial optimization problems.

Andrea Nemeth received her undergraduate degree in mathematics from CSUN. She is an alumna of the NASA/PAIR program and currently a second year graduate student at CSUN and a FERMAT Fellow. Her talk is based on work for her thesis with Prof. Mark Schilling.