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Optimal design of dynamic experiments for scalar-on-function linear models with application to a biopharmaceutical

Damianos Michaelides1, Maria Adamou2, David C Woods2

  • 1Biostatistics Unit, The Cyprus Institute of Neurology and Genetics, 1683 Nicosia, Cyprus.

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|January 9, 2026
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Summary

This study introduces a Bayesian optimal experimental design for experiments with functional profile variables. The method uses basis expansions for efficient design and complexity control, demonstrated in bioreactor optimization.

Keywords:
basis functionsdesign of experimentsdynamic experimentsfunctional linear modelprofile variables

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Area of Science:

  • Statistics
  • Experimental Design
  • Biotechnology

Background:

  • Traditional experimental designs often assume fixed variable settings.
  • Functional data, where variables are functions over a domain, present unique design challenges.
  • Optimizing complex biological systems like bioreactors requires advanced experimental design methods.

Purpose of the Study:

  • To develop a Bayesian optimal experimental design framework for experiments with functional profile variables.
  • To enable efficient identification of optimal experimental designs for scalar-on-function models.
  • To provide a method for controlling the complexity of functional variables and the statistical model.

Main Methods:

  • A Bayesian optimal experimental design framework was developed.
  • Profile variables were represented using basis expansions within a scalar-on-function linear model.
  • The approach allowed for finite-dimensional representation and optimization of functional variables.

Main Results:

  • The proposed method successfully finds optimal experimental designs for functional data.
  • The framework allows for effective control over the complexity of profile variables and the model.
  • The approach was illustrated using dynamic feeding strategies in a bioreactor system.

Conclusions:

  • The developed Bayesian framework offers a robust approach for designing experiments with functional variables.
  • This method enhances the efficiency and control in optimizing complex systems.
  • The application in bioreactor optimization highlights the practical utility of the proposed design strategy.