Bayesian Analysis

Error analysis for small angle neutron scattering datasets using Bayesian inference

Charles R. Hogg, Joseph B. Kadane, Jong Soo Lee, and Sara A. Majetich

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Abstract

We present a Bayesian methodology for extracting correlation lengths from small-angle neutron scattering (SANS) experiments. For demonstration, we apply the technique to data from a previous paper, which investigated the presence of dipolar ferromagnetism in assemblies of ferromagnetic Co nanoparticles. Bayesian analysis confirms the presence of multiparticle dipolar domains even at zero magnetic field, but higher-field correlation lengths were found to be much smaller than previously believed, yielding new information on the maximum lengthscale which the instrument can reliably probe. We use two complementary types of graph to visualize the results. Plots of standardized residual distributions show quality of fit, and guide model refinement. These principles can be applied to other types of sample, and even to other small-angle scattering techniques.

Article information

Source
Bayesian Anal., Volume 5, Number 1 (2010), 1-33.

Dates
First available in Project Euclid: 22 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1340369788

Digital Object Identifier
doi:10.1214/10-BA501

Mathematical Reviews number (MathSciNet)
MR2596431

Zentralblatt MATH identifier
1330.62134

Citation

Hogg, Charles R.; Kadane, Joseph B.; Lee, Jong Soo; Majetich, Sara A. Error analysis for small angle neutron scattering datasets using Bayesian inference. Bayesian Anal. 5 (2010), no. 1, 1--33. doi:10.1214/10-BA501. https://projecteuclid.org/euclid.ba/1340369788


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See also

  • Related item: Nick Hengartner. Comment on article by Hogg et al. Bayesian Anal., Vol. 5, Iss. 1(2010), 35-37.
  • Related item: Devinder Sivia, John Skilling. Comment on article by Hogg et al. Bayesian Anal., Vol. 5, Iss. 1(2010), 39-40.
  • Related item: Charles R. Hogg, Joseph B. Kadane, Jong Soo Lee, Sara A. Majetich. Rejoinder. Bayesian Anal., Vol. 5, Iss. 1(2010), 41-43.