title: Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis.
abstract: A Bayesian inference method for refining crystallographic structures is presented. The distribution of model parameters is stochastically sampled using Markov chain Monte Carlo. Posterior probability distributions are constructed for all model parameters to properly quantify uncertainty by appropriately modeling the heteroskedasticity and correlation of the error structure. The proposed method is demonstrated by analyzing a National Institute of Standards and Technology silicon standard reference material. The results obtained by Bayesian inference are compared with those determined by Rietveld refinement. Posterior probability distributions of model parameters provide both estimates and uncertainties. The new method better estimates the true uncertainties in the model as compared to the Rietveld method.
authors.affiliation: Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA.
authors.forename: Chris M
authors.initials: CM
authors.lastname: Fancher
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, USA.
authors.forename: Zhen
authors.initials: Z
authors.lastname: Han
authors.affiliation: Materials Measurement Science Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
authors.forename: Igor
authors.initials: I
authors.lastname: Levin
authors.affiliation: Neutron Scattering Science Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA.
authors.forename: Katharine
authors.initials: K
authors.lastname: Page
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, USA.
authors.forename: Brian J
authors.initials: BJ
authors.lastname: Reich
authors.affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695, USA.
authors.forename: Ralph C
authors.initials: RC
authors.lastname: Smith
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, USA.
authors.forename: Alyson G
authors.initials: AG
authors.lastname: Wilson
authors.affiliation: Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA.
authors.forename: Jacob L
authors.initials: JL
authors.lastname: Jones