Use of Bayesian inference in crystallographic structure refinement via full diffraction profile analysis

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

doi:10.1038/srep31625

Use of Bayesian inference in crystallographic structure refinement via full diffraction profile analysis

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

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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.

Original language	English
Article number	31625
Journal	Scientific Reports
Volume	6
DOIs	https://doi.org/10.1038/srep31625
State	Published - Aug 23 2016
Externally published	Yes

Funding

The authors acknowledge the support of the Kenan Institute for Engineering, Technology and Science at NC State and the Eastman Chemical Company - University Engagement Fund at NC State. JLJ acknowledges support from the National Science Foundation under DMR-1445926. This research used resources of the Advanced Photon Source, a US. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.

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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.",

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AU - Fancher, Chris M.

AU - Han, Zhen

AU - Levin, Igor

AU - Page, Katharine

AU - Reich, Brian J.

AU - Smith, Ralph C.

AU - Wilson, Alyson G.

AU - Jones, Jacob L.

PY - 2016/8/23

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84983527047

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SN - 2045-2322

VL - 6

JO - Scientific Reports

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M1 - 31625

ER -

Use of Bayesian inference in crystallographic structure refinement via full diffraction profile analysis

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