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Why theoretically Bayesian-based model calibration can be better than regression-based model calibration?

Bayesian and nonlinear least-squares methods of calibration were evaluated and compared for gray-box modeling of a retail building.

Bayesian techniques is necessary to provide robustness to sensor noise within an embedded thermal zone identification, specifically with regard to lower dimensional problems, where model calibration is preferred over uncertainty quantification. That is, there is a distinction between identifying a calibrated model and quantifying uncertainties associated with variables and parameters. Bayesian inference will reveal the presence and level of interactions between model parameters, illuminating trade-offs that a least-squares minimization will not; however, any simplified model (calibrated or not) inherently averages over dynamics and diminishes the power of uncertainty quantification as physical variables are marginalized.

One characteristic of Bayesian-based procedures is that they allow both prior information (including expert judgment) and sampling information to be combined in the weighting scheme inherent in Bayes' formula. The second characteristic of Bayesian-based methods is they can be formulated in a recursive form. This means Bayesian methods allow successive updating of battery interpretation as additional tests results are obtained, which is particularly useful if sequential testing procedures are being considered.

The calibration problem in regression model is the use of known data on the observed relationship between a dependent variable and an independent variable to make estimates of other values of the independent variable from new observations of the dependent variable.

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