Bayesian sequential I-optimal designs for split-plot experiments under model uncertainty

Yao Xiao

doi:10.1080/00224065.2025.2534385

2025-08-15

PRE

Yao Xiao *

Po Yang *

Na Zou *

DOI：10.1080/00224065.2025.2534385

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摘要

En 中文

Split-plot designs have enjoyed great popularity since their inception. The I-optimality criterion is frequently employed to select split-plot designs that exhibit good predictive performance under a specified model. However, in situations where the true model is highly uncertain and/or the assumed model is misspecified, I-optimal split-plot designs may lack efficiency in fitting the true model. To address this issue, we propose the Bayesian version of the I-optimality criterion for split-plot experiments, encompassing both primary and potential terms in the full model. Subsequently, we extend the Bayesian I-optimal split-plot design into a two-stage sequential framework, in which the first-stage design is constructed based on this Bayesian criterion, and experimental data are analyzed to rearrange potential terms according to their activeness, then the second-stage design is selectedviaan augmented I-optimality criterion under the rearranged primary model. Through comparison with counterparts using several numerical examples and a practical experiment, the proposed Bayesian I-I optimal split-plot designs demonstrate superior performance. In addition, further numerical results are discussed in theSupplementary Materials.

Keyword:

Bayesian I-optimality criterion

optimal designs

sequential designs

split-plot designs