Quantification of Uncertainty in Magnesium Oxide and Rhenium Pressure Standards Based on Bayesian Statistical Methods

Accurate pressure measurement in static high-pressure experiments relies on the equation of state (EOS) of standard materials, where uncertainties in EOS parameters can significantly affect the accuracy of pressure predictions. This study focuses on magnesium oxide (MgO, B1 phase) and rhenium (Re, hexagonal close packed phase), employing Bayesian statistical methods and Markov Chain Monte Carlo (MCMC) simulation techniques to systematically quantify the uncertainty in pressure prediction during diamond anvil cell (DAC) experiments. By constructing a Bayesian framework with uniform prior distributions and normal likelihood functions, and integrating multiple sets of experimental data for parameter calibration, the results demonstrate that the Bayesian statistical approach successfully quantifies the posterior distribution of EOS parameters, revealing strong correlations between them, e.g., a negative correlation between Grüneisen parameter and initial volume for MgO, and a positive correlation between bulk modulus and Grüneisen parameter for Re. The uncertainty in pressure predictions for both MgO and Re increases significantly at higher pressures; for Re, this uncertainty also rises markedly with increasing temperature, whereas no clear trend is observed for MgO. This study provides pressure benchmarks with quantified uncertainties, contributing to improved accuracy in high-pressure experimental measurements. It holds significant reference value for ensuring the reliability of experimental data in materials science and geophysical research.