Uncertainty Aware Equation of State for Tantalum

We develop an approach for construction of uncertainty aware equations of state and demostrate this for an illustrative case of Tantalum. In this work Bayesian inference is implemented through Markov Chain Monte Carlo to generate equation of state model parameter probability distributions based on the available experimental data and uncertainties. This yields in the end an ensemble of equations of state which are then deemed together an uncertainty aware equation of state. Additionally, while not used in the generation of the equation of state we provide further comparison with density functional theory calculations which can access regions of thermodynamic space not available in the experimental results.