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

Journal Article · Fri Feb 05 23:00:00 EST 2016 · Entropy

DOI:https://doi.org/10.3390/e18020057· OSTI ID:1335405

Hock, Kiel ^[1]; Earle, Keith ^[2]

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1. Brookhaven National Lab. (BNL), Upton, NY (United States)
2. University at Albany, Albany, NY (United States). Department of Physics

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. In conclusion, 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.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
• Grant/Contract Number: SC0012704
• OSTI ID: 1335405
• Report Number(s): BNL--111849-2016-JA; KB0202011
• Journal Information: Entropy, Journal Name: Entropy Journal Issue: 2 Vol. 18; ISSN 1099-4300
• Publisher: MDPI
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
bayes
information geometry
parameter optimization
spin resonance spectroscopy