  Finite-temperature effects can be included by calculating the vibrations
properties and this can greatly improve the fidelity of computational
screening. An important challenge for DFT-based screening is the sensitivity of
the predictions to the choice of the exchange correlation function. In this
work, we rigorously explore the sensitivity of finite temperature thermodynamic
properties to the choice of the exchange correlation functional using the
built-in error estimation capabilities within the Bayesian Error Estimation
Functional. The vibrational properties are estimated using the Debye model and
we quantify the uncertainty associated with finite-temperature properties for a
diverse collection of materials. We find good agreement with experiment and
small spread in predictions over different exchange correlation functionals for
Mg, Al$_2$O$_3$, Al, Ca, and GaAs. In the case of Li, Li$_2$O, and NiO,
however, we find a large spread in predictions as well as disagreement between
experiment and functionals due to complex bonding environments. While the
energetics generated by BEEF-vdW ensemble is typically normal, the complex
mapping through the Debye model leads to the derived finite temperature
properties having non-Gaussian behavior. We test a wide variety of probability
distributions that best represent the finite temperature distribution and find
that properties such as specific heat, Gibbs free energy, entropy, and the
thermal expansion coefficient are well described by normal or transformed
normal distributions, while the prediction spread of volume at a given
temperature does not appear to be drawn from a single distribution.
