Model selection for parameter identifiability problem in Bayesian inference of building energy model

Abstract

Recently, the issue of parameter identifiability has been highlighted in Bayesian inference of building energy models. Parameter identifiability addresses the correspondence between the observed data and the model parameters, and this analysis verifies whether the model parameters can be estimated using observed data. The authors propose a model selection process for Bayesian inference involving the unidentifiable parameters based on the model evidence. The model evidence is a component of the Bayes theorem, which corresponds to the observation probability (i.e., the goodness of fit) of the observed data for a given model. In this study, nested sampling was used to estimate the model evidence. A case study with the reference office building developed by the US Department of Energy shows the model selection process that uses the model evidence as the evaluation index for the unidentifiable parameter. For comparison with the existing approach of model evaluation, the authors present the results of a comparative analysis between the proposed process and that based on model prediction error (CV(RMSE)). As a result, it was observed that the higher the model evidence in the hypothesis for the unidentifiable parameters, the more the posteriors tend to be similar to the true values. In addition, no significant relationship was observed between the model prediction error and the accuracy of the posterior inference. This indicates that the model evidence can be used as an objective evaluation index for selecting the optimal hypothesis of unidentifiable parameters in the Bayesian inference of building energy models.