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Fancher CM, Han Z, Levin I, et al. Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis. Sci Rep. 2016;6:31625doi: 10.1038/srep31625.
Fancher, C. M., Han, Z., Levin, I., Page, K., Reich, B. J., Smith, R. C., Wilson, A. G., & Jones, J. L. (2016). Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis. Scientific reports, 631625. https://doi.org/10.1038/srep31625
Fancher, Chris M, et al. "Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis." Scientific reports vol. 6 (2016): 31625. doi: https://doi.org/10.1038/srep31625
Fancher CM, Han Z, Levin I, Page K, Reich BJ, Smith RC, Wilson AG, Jones JL. Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis. Sci Rep. 2016 Aug 23;6:31625. doi: 10.1038/srep31625. PMID: 27550221; PMCID: PMC4994022.
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Sci Rep. 2016 Aug 23;6:31625. doi: 10.1038/srep31625.

Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis.

Scientific reports

Chris M Fancher, Zhen Han, Igor Levin, Katharine Page, Brian J Reich, Ralph C Smith, Alyson G Wilson, Jacob L Jones

Affiliations

  1. Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA.
  2. Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, USA.
  3. Materials Measurement Science Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
  4. Neutron Scattering Science Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA.
  5. Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695, USA.

PMID: 27550221 PMCID: PMC4994022 DOI: 10.1038/srep31625

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.

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