Parameter identifiability in Bayesian inference for building energy models

Abstract

Parameter identifiability is the concept of whether uncertain parameters can be correctly estimated from the observed data. The main cause of parameter unidentifiability in Bayesian inference is known as ‘overparameterization’. In this study, the likelihood confidence interval (CI) and the likelihood confidence region (CR) were introduced for quantifying the parameter identifiability. The likelihood CI and CR can be regarded as the parameter range (one-dimensional) and parameter space (two-dimensional or higher) that can identify parameter values, respectively. For this purpose, an EnergyPlus reference office building provided by the US DOE was used in this study. Four estimation parameters in the EnergyPlus model were analyzed using the likelihood CI and CR. It was found that the closer the likelihood CI of a parameter is to the prior's parameter range, the more unidentifiable the parameter. In addition, a biplot analysis was conducted to examine a correlation between two parameters. The more correlated a parameter is with others, the more unidentifiable the parameter. It is suggested that the visual assessment of likelihood CIs and CRs can help in investigating whether Bayesian inference results can be accurately obtained.