Bayesian calibration of electrical conductivity relaxation and isotope exchange-secondary ion mass spectrometry experiments

Abstract

Bayesian calibration is a powerful tool for measurement techniques that involve the estimation of physical parameters via calibrating (or “fitting”) a model to an experimental dataset. In contrast to optimization techniques, which produce a ’point estimate’ of the parameters devoid of uncertainty quantification, Bayesian calibration returns a distribution on the parameter space, revealing the extent to which each parameter can be considered well-estimated as well as any confounding uncertainty in multi-parameter calibration. This article covers the basic theory along with the practicalities of implementation for Bayesian calibration, linking these principles to a new open source software package for Bayesian calibration of electrical conductivity relaxation and isotope-exchange / secondary ion mass spectrometry measurements.