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This study shows that hyperparameters can be estimated without a separate exploratory phase in sequential computer experiments. This eliminates the need for an initial exploration phase, making methods faster and easier to use.

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Area of Science:

  • Computer Science
  • Statistics
  • Applied Mathematics

Background:

  • Sequential design of computer experiments often uses a two-phase approach: an exploratory phase for initial hyperparameter estimation and global exploration, followed by a sequential phase for problem-solving.
  • Gaussian Process Emulators (GPEs) are commonly used, requiring hyperparameter estimation, often necessitating a dedicated exploratory phase.

Purpose of the Study:

  • To investigate the feasibility of estimating hyperparameters without a distinct exploratory phase in sequential computer experiment design.
  • To adapt acquisition functions and GPE estimators for handling uncertain hyperparameters in early iterations, using non-Gaussian random fields.

Main Methods:

  • Developing and testing a sequential design method that integrates hyperparameter estimation within the main problem-solving phase.
  • Adapting acquisition functions and Gaussian Process Emulator estimators to account for hyperparameter uncertainty.
  • Performing numerical experiments on a sequential method for solving Bayesian inverse problems.

Main Results:

  • Hyperparameters can be effectively estimated without a separate exploratory phase.
  • The proposed method achieves nearly the same efficiency as methods where hyperparameters are known beforehand.
  • The sequential design method becomes faster and simpler to use by eliminating the exploratory phase.

Conclusions:

  • The estimation of hyperparameters is not a sufficient reason to mandate a separate exploratory phase in sequential experimental design.
  • Removing the exploratory phase leads to significant improvements in both computational speed and user convenience.
  • This research streamlines sequential design methodologies for computer experiments, particularly for applications like Bayesian inverse problems.