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Many experiments require modeling a non-Normal response. In particular, count responses and binary responses are quite common. The relationship between predictors and the responses are typically modeled via a Generalized Linear Model (GLM). Finding D-optimal designs for GLMs, which reduce the generalized variance of the model coefficients, is desired. A common approach to finding optimal designs for GLMs is to use a local design, but local designs are vulnerableto parameter misspecification. The focus of this paper is to provide designs for GLMs that are robust to parameter misspecification. This is done by applying a bagging procedure to pilot data, where the results of many locally optimal designsare aggregated to produce an approximate design that reflects the uncertainty in the model coefficients. Results show that the proposed bagging procedure is robust to changes in the underlying model parameters. Furthermore, the proposed designs are shown to be preferable to traditional methods, which may be over-conservative.
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Bayesian D-Optimal Design of Experiments with Quantitative and Qualitative Responses
Systems with both quantitative and qualitative responses are widely encountered in many applications. Design of experiment methods are needed when experiments are conducted to study such systems. Classic experimental design methods are unsuitable here because they often focus on one type of response. In this paper, we develop a Bayesian D-optimal design method for experiments with one continuous and one binary response. Both noninformative and conjugate informative prior distributions on the unknown parameters are considered. The proposed design criterion has meaningful interpretations regarding the D-optimality for the models for both types of responses. An efficient point-exchange search algorithm is developed to construct the local D-optimal designs for given parameter values. Global D-optimal designs are obtained by accumulating the frequencies of the design points in local D-optimal designs, where the parameters are sampled from the prior distributions. The performances of the proposed methods are evaluated through two examples.
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- PAR ID:
- 10427647
- Date Published:
- Journal Name:
- The New England Journal of Statistics in Data Science
- ISSN:
- 2693-7166
- Page Range / eLocation ID:
- 1 to 15
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.51387/23-NEJSDS30
