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

by Kiel Hock 1 and Keith Earle 2,*
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.
Entropy 2016, 18(2), 57; https://doi.org/10.3390/e18020057
Received: 31 October 2015 / Accepted: 25 January 2016 / Published: 6 February 2016
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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Hock, K.; Earle, K. Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra. Entropy 2016, 18, 57.

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