Abstract not found

Several competing objectives may be relevant in the design of an experiment. The competing objectives may not be easy to characterize in a single optimality criterion. One approach to these design problems has been to weight each criterion and find the design that optimizes the weighted average of the criteria. An alternative approach has been to optimize one criterion subject to constraints on the other criteria. An equivalence theorem is presented for the Bayesian constrained design problem. Equivalence theorems are essential in verifying optimality of proposed designs, especially when, as in most nonlinear design problems, numerical optimization is required. This theorem is used to show that the results of Cook and Wong on the equivalence of the weighted and constrained problems also apply much more generally. The results are applied to Bayesian nonlinear design problems with several objectives. KEY WORDS: Bayesian design, regression, nonlinear design 1. INTRODUCTION An experimen...

Computer-generated designs in the cube are described which have the minimal (or larger) number of runs for a full quadratic response-surface design. Examples of 2-factor designs are included with 6 to 20 runs, 3-factor designs with 10 to 20 runs, 4-factor designs with 15 to 20 runs, 5-factor designs with 21 to 25 runs, 6-factor designs with 28 to 31 runs, and 7-factor designs with 36 and 39 runs. The designs were constructed by minimizing the average prediction variance, and without imposing any prior constraints -- such as a central composite structure -- on the locations of the points. Key Words. Minimal designs; cube designs; quadratic response surface; computer-generated designs; minimal variance designs. 1 Present address: AT&T Shannon Labs, Florham Park, NJ 07932-0971 1

Appearance matching methods use raw or filtered pixel brightness values to perform recognition. To expedite recognition, subspace methods are used to achieve compact representations of images. In many cases it is advantageous to recognize an image based on only a subset of its pixels, for example, when a part of an image is occluded, or to expedite recognition. Currently, such subsets are selected either randomly or using heuristics. In this paper, we derive criteria for selecting the pixel subsets through a sensitivity analysis of the subspace. Based on these criteria, we propose two practical recognition algorithms. These algorithms were tested on a large number of images with degraded or partial data. In addition to faster recognition, our algorithms yield high recognition accuracy. 1

In this paper, we present a probability model and a Markov Chain sampler for exploring expected utility surfaces in decision theory and optimal design problems. The overall goal is to exploit Markov chain techniques to address computationally intensive decision problems. Technically, we propose to generate a sample of decisions by constructing a probability model on both the problem's unknowns and the decision variables. We achieve this by augmenting the given probability model in such a way that the marginal distribution of the sampled decisions is proportional to expected utility. Analyzing the sampled decisions provides guidance to decision making. This approach has potential application to a wide class of design and decision problems. We illustrate it with applications to the design of a screening trial and to a k-armed bandit problem in clinical trials.

This thesis considers the problem of achieving better system performance through adaptive experiments. For the case of discrete design space, I propose an adaptive One-Factor-at-A-Time (OFAT) experimental design, study its properties and compare its performance to saturated fractional factorial designs. The rationale for adopting the adaptive OFAT design scheme become clear if it is imbedded in a Bayesian framework: it becomes clear that OFAT is an efficient response to step by step accrual of sample information. The Bayesian predictive distribution for the outcome by implementing OFAT and the corresponding principal moments when a natural conjugate prior is assigned to parameters that are not known with certainty are also derived. For the case of compact design space, I expand the treatment of OFAT by the

for Choice-Based Conjoint Analysis with Generic-Attribute