Bayesian Approaches to Uncertainty Quantification and Structure Refinement from X-Ray Diffraction

This chapter introduces classical frequentist and Bayesian inference applied to analyzing diffraction profiles, and the methods are compared and contrasted. The methods are applied to both the modelling of single diffraction profiles and the full profile refinement of crystallographic structures. In the Bayesian method, Markov chain Monte Carlo algorithms are used to sample the distribution of model parameters, allowing for the construction of posterior probability distributions, which provide both parameter estimates and quantifiable uncertainties. We present the application of this method to single peak fitting in lead zirconate titanate, and the crystal structure refinement of a National Institute of Standards and Technology silicon standard reference material.

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