  Modeling buildings' heat dynamics is a complex process which depends on
various factors including weather, building thermal capacity, insulation
preservation, and residents' behavior. Gray-box models offer a causal inference
of those dynamics expressed in few parameters specific to built environments.
These parameters can provide compelling insights into the characteristics of
building artifacts and have various applications such as forecasting HVAC
usage, indoor temperature control monitoring of built environments, etc. In
this paper, we present a systematic study of modeling buildings' thermal
characteristics and thus derive the parameters of built conditions with a
Bayesian approach. We build a Bayesian state-space model that can adapt and
incorporate buildings' thermal equations and propose a generalized solution
that can easily adapt prior knowledge regarding the parameters. We show that a
faster approximate approach using variational inference for parameter
estimation can provide similar parameters as that of a more time-consuming
Markov Chain Monte Carlo (MCMC) approach. We perform extensive evaluations on
two datasets to understand the generative process and show that the Bayesian
approach is more interpretable. We further study the effects of prior selection
for the model parameters and transfer learning, where we learn parameters from
one season and use them to fit the model in the other. We perform extensive
evaluations on controlled and real data traces to enumerate buildings'
parameter within a 95% credible interval.
