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

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.
Authors:
ORCiD logo [1] ;  [2]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
  2. University at Albany, Albany, NY (United States). Department of Physics
Publication Date:
Report Number(s):
BNL-111849-2016-JA
Journal ID: ISSN 1099-4300; R&D Project: KBCH139; 18032; KB0202011
Grant/Contract Number:
SC0012704
Type:
Accepted Manuscript
Journal Name:
Entropy
Additional Journal Information:
Journal Volume: 18; Journal Issue: 2; Journal ID: ISSN 1099-4300
Publisher:
MDPI
Research Org:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; parameter optimization; spin resonance spectroscopy; bayes; information geometry
OSTI Identifier:
1335405