Reliable Estimation of Prediction Uncertainty for Physicochemical Property Models

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Spectroscopy

Background:

• Accurate prediction of observables in computational science requires reliable uncertainty quantification.
• Parametric property models are often used due to the infeasibility of high-accuracy first-principles calculations.
• Model predictions are sensitive to systematic errors from data, model assumptions, and computational methods.

Purpose of the Study:

• To discuss and apply bootstrapping for calibrating property models and estimating prediction uncertainty.
• To identify systematic errors in theoretical Mössbauer spectroscopy predictions.
• To provide statistically rigorous uncertainty analysis for physicochemical property models.

Main Methods:

• Application of bootstrapping to assess a linear property model for 57Fe Mössbauer isomer shift.
• Calculation of contact electron density using 12 density functionals across Jacob's ladder.
• Systematic-error diagnostics and uncertainty estimation for isomer-shift predictions.

Main Results:

• Bootstrapping provides reliable, locally resolved uncertainties for isomer-shift predictions.
• Hybrid density functionals yield prediction uncertainties (0.04-0.05 mm s-1) close to experimental values (0.02 mm s-1).
• Model parameters and uncertainties are sensitive to the reference data set composition and size.

Conclusions:

• Bootstrapping is a statistically rigorous method for calibrating property models and quantifying prediction uncertainty.
• Rankings of density functionals should not rely on single data sets due to sensitivity.
• The study provides a statistically meaningful reference data set (MIS39) and a new isomer shift calibration.