Prior selection method using likelihood confidence region and Dirichlet process Gaussian mixture model for Bayesian inference of building energy models

It is widely acknowledged that Bayesian inference is only beneficial when prior information is properly defined. However, there is no clear rule for prior selection, and it is apparently a matter of subjective selection by the domain expert(s). In other words, because the posterior inference results can vary depending on how the prior is set, a proper definition of the prior is important in terms of objectivity and accuracy for Bayesian inference of building energy models. Hence, the authors suggest a new prior selection method using Dirichlet process Gaussian mixture model (DPGMM) and the likelihood confidence region (hereafter referred to as likelihood CR). The DPGMM is a Bayesian nonparametric clustering technique that optimizes both the cluster shape and the number of clusters. Using the DPGMM, the finite probability distributions that make up the likelihood CR can be estimated, where the distribution with the highest maximum likelihood is applied as the informative prior. In this study, a reference office building of the United States Department of Energy was selected, and a surrogate model was generated using an artificial neural network. Based on a comparison between the authors’ suggestion and traditional informative (and/or non-informative) priors by domain experts, the proposed method requires only minimum information about the parameters (min and max) and performs better than the traditional approach