Optimal designs for nonlinear regression models without prior point parameter estimates

Authors
Prasadh, Hari
ORCID
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Other Contributors
Dunn, Stanley
Kramer, Peter Roland, 1971-
Mitchell, John E.
Xie, Wei
Issue Date
2016-05
Keywords
Decision sciences and engineering systems
Degree
PhD
Terms of Use
This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.
Full Citation
Abstract
Our methodology proposes a new class of optimality criteria that share characteristics with Maxi-min designs based on efficiency measures (Dette et al., 2006; Kitsos, 2013, p. 34; Muller and Pazman, 1998; Silvey, 1980) and Pseudo-Bayesian designs (Atkinson et al., 2007, chap. 18; Chaloner and Verdinelli, 1995). Namely, we use Monte Carlo sampling to incorporate prior information of parameters (uniform distribution used if only the range is available) and for the objective function, we employ a relative efficiency measure. However, there are two key differences. Firstly, our criterion metric is based on a Value-at-Risk (VaR) metric such as 〖VaR〗_(5%) , 〖CVaR〗_(1%), 〖MeanToVaR〗_(10%). Secondly, rather than picking the design having the best VaR objective function value (a scalar measure), we recommend evaluating the quality of competing VaR based designs across the entire relative efficiency distribution. We have empirically demonstrated consistency in the results by applying VaR methodology across three response models used in clinical, biological and engineering contexts. We believe that in light of the parameter uncertainty and the consequent nonlinear nature of the relative efficiency distribution for sampled parameter values, the VaR methodology will lead to more informed choices by the experimenter on the right design for a particular context.
Description
May 2016
School of Engineering
Department
Dept. of Industrial and Systems Engineering
Publisher
Rensselaer Polytechnic Institute, Troy, NY
Relationships
Rensselaer Theses and Dissertations Online Collection
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