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Keywords:

  • Bayesian statistics;
  • latent variable;
  • regression;
  • partial least squares;
  • principal components analysis;
  • Gibbs sampling;
  • noninformative prior

Abstract

Advanced empirical process modeling methods such as those used for process monitoring and data reconciliation rely on information about the nature of noise in the measured variables. Because this likelihood information is often unavailable for many practical problems, approaches based on repeated measurements or process constraints have been developed for their estimation. Such approaches are limited by data availability and often lack theoretical rigor. In this article, a novel Bayesian approach is proposed to tackle this problem. Uncertainty about the error variances is incorporated in the Bayesian framework by setting noninformative priors for the noise variances. This general strategy is used to modify the Sampling-based Bayesian Latent Variable Regression (Chen et al., J Chemom., 2007) approach, to make it more robust to inaccurate information about the likelihood functions. Different noninformative priors for the noise variables are discussed and unified in this work. The benefits of this new approach are illustrated via several case studies. © 2009 American Institute of Chemical Engineers AIChE J, 2009