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Entropy 2016, 18(2), 57; doi:10.3390/e18020057

Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra

1
Brookhaven National Lab, 2 Center Street, Upton, NY 11973, USA
2
Department of Physics, University at Albany, 1400 Washington Ave, Albany, NY 12222, USA
*
Author to whom correspondence should be addressed.
Received: 31 October 2015 / Accepted: 25 January 2016 / Published: 6 February 2016
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Abstract

In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the optimum parameter set and to estimate parameter uncertainties. The posterior distribution allows us to define a metric on parameter space that induces a geometry with negative curvature that affects the parameter uncertainty estimates, particularly for spectra with low signal to noise. View Full-Text
Keywords: parameter optimization; spin resonance spectroscopy; bayes; information geometry parameter optimization; spin resonance spectroscopy; bayes; information geometry
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Hock, K.; Earle, K. Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra. Entropy 2016, 18, 57.

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