| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | July 7, 2014 |
| Latest Amendment Date: | May 6, 2016 |
| Award Number: | 1407518 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Gabor Szekely
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | July 15, 2014 |
| End Date: | June 30, 2018 (Estimated) |
| Total Intended Award Amount: | $211,019.00 |
| Total Awarded Amount to Date: | $211,019.00 |
| Funds Obligated to Date: |
FY 2015 = $71,474.00 FY 2016 = $104,980.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
809 S MARSHFIELD AVE M/C 551 CHICAGO IL US 60612-4305 (312)996-2862 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
Chicago IL US 60612-4305 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | STATISTICS |
| Primary Program Source: |
01001516DB NSF RESEARCH & RELATED ACTIVIT 01001617DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): | |
| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
Designed experiments form an integral part of the scientific process in many areas of research, such as the biological sciences, the health sciences, the social sciences, engineering, marketing, education, and others. A well-chosen design facilitates the collection of data that maximizes the information for the scientific questions of interest at a fixed cost, or that minimizes the cost for a desired level of information. Many experiments deal with correlated data, multiple objectives, or multiple covariates, but little is known about the identification of good designs in such settings. This project establishes how to find efficient designs for these types of problems for the most commonly used statistical models. The tools developed in this project have a tremendous potential for impact on society because designed experiments are used so often to further knowledge in many different fields. Results from the project will be made available to researchers in other areas through easy-to-use software that implements algorithms that are developed. Graduate students will be trained to become researchers in design of experiments.
The outcomes of this project constitute a major leap forward in understanding and knowledge of optimal design of experiments. Recent contributions by the principal investigators and others have had a significant impact on the advancement of optimal design of experiments for nonlinear and generalized linear models. However, these results have for the most part been limited to (i) independent data; (ii) use of a single optimality criterion; and (iii) use of a single covariate. While these results are arguably important in their own right, this project will extend methods and tools to problems with correlated data, multiple objectives, and multiple covariates. The latter could consist of a mix of covariates that can be chosen by the experimenter and covariates that, known or unknown at the design stage, cannot be controlled by the experimenter. Preliminary results indicate that this is an opportune time to make these challenging but critical steps. Building a framework for deriving and identifying optimal designs for these types of problems will provide a much needed addition to our collective design toolbox. Current results are very sparse and only for very specialized problems that are mostly motivated by mathematical feasibility. The project develops tools to select efficient designs for models and conditions that are far more realistic than those that have been considered so far.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
Design of experiments is an integral part of the scientific process in many areas of research with a direct impact on society. For example, designed experiments are essential in clinical trials for drug development; they are also critical for studying consumer preferences in marketing studies; or for quality assessment and improvement in manufacturing processes. With this NSF grant support, the PI has obtained the following results which fulfill the goal of this project.
(1) Optimal designs for nonlinear model with random block effects are systematically studied. For a large class of nonlinear models, it has been proved that any optimal design can be based on some simple structure. The corresponding general equivalence theorem was derived. This allows us to propose an efficient algorithm for deriving specific optimal designs. The application of the algorithm is demonstrated through deriving a variety of locally optimal designs and accessing their robustness under different nonlinear models.
(2) Deriving optimal designs with multiple objectives is a long-standing challenging problem with few tools available. The few existing approaches cannot provide a satisfied solution in general: either the computation is very expensive, or a satisfied solution is not guaranteed. A novel algorithm framework to address this literature gap was proposed. The convergence of this algorithm was proved. It was shown that the new algorithm can derive the true solutions with high speed in various examples. With this new algorithm framework, efficient designs for multiple objectives can be found easily and quickly.
(3) The constructing optimal/efficient discrete choice experiments (DCEs), widely applied for modeling real marketplace choices, in both fundamental and applied research, is systematically investigated. To improve the quality of designing DCEs, most researchers have drawn on optimal design theory. Because of the nonlinearity of the probabilistic choice models, to construct a proper choice design, one needs the help of efficient search algorithms, among which the coordinate-exchange algorithm (CEA) has shown itself to work very well under the widely used multinomial logit discrete choice model. However, due to the discrete nature of the choice design, there are no computationally feasible ways to verify that the resulting design is indeed optimal or efficient. An approach of evaluating the performance of the CEA for Bayesian optimal designs was proposed. This approach gives a lower bound of the efficiency of the resulting design. More important, a new algorithm based on OWEA can construct even more efficient designs at much less computation cost.
Last Modified: 10/29/2018
Modified by: Min Yang
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