Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling

Ray Bing Chen, Weichung Wang, C. F.Jeff Wu

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

A numerical method, called overcomplete basis surrogate method (OBSM), was recently proposed, which employs overcomplete basis functions to achieve sparse representations. While the method can handle nonstationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach that first imposes a normal prior on the large space of linear coefficients, then applies the Markov chain Monte Carlo (MCMC) algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction of sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. Numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.

Original languageEnglish
Pages (from-to)139-152
Number of pages14
JournalTechnometrics
Volume59
Issue number2
DOIs
Publication statusPublished - 2017 Apr 3

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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