We select these non-overlapping regions of measurement for specific heat and enthalpy to demonstrate that the Bayesian framework can capture robust representations of both quantities when **data** does not cover the entire temperature range for each quantity. We generate synthetic **data** for the enthalpy, H and specific heat, C p , via Eq. (6a) and Eq. (6b), respectively,
H (T ) − H (298.15K) = 3Rθ e θ / T − 1 + a T 2 2 + b T 3 3 (6a) C p (T ) = d dT H (T ) = 3R θ / T 2 e θ / T e θ / T − 1 2 + aT + bT 2 ,(6b)
where R is the gas constant and the true model parameters are defined as follows: θ = 150K, a = 6 × 10 −3 J/mol.K, b = 7 × 10 −7 J/mol.K 2 and c = −5 × 10 3 J/mol. We add Gaussian noise with a standard error of 5000J/mol. to the enthalpy values. We add Gaussian noise to the specific heat values that scales linearly with the magnitude to a maximum of 3J/mol.K at 75K. Note that the model form of the specific heat in Eq. (6b) was proposed at the Ringberg workshop in 1995 to be effective across the entire temperature range [29]. In this case, the first term employs the Einstein model to account for low-temperature behavior, though the Debye or other models may be substituted [30].