Open AccessExponential parameter estimation (in NMR) using Bayesian probability theory
Author(s) -
Bretthorst G. Larry,
Hutton William C.,
Garbow Joel R.,
Ackerman Joseph J.H.
Publication year - 2005
Publication title -
concepts in magnetic resonance part a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.229
H-Index - 49
eISSN - 1552-5023
pISSN - 1546-6086
DOI - 10.1002/cmr.a.20043
Subject(s) - exponential function , markov chain monte carlo , monte carlo method , mathematics , statistical physics , bayesian probability , estimation theory , simulated annealing , posterior probability , markov chain , mathematical optimization , algorithm , statistics , physics , mathematical analysis
Data modeled as sums of exponentials arise in many areas of science and are common in NMR. However, exponential parameter estimation is fundamentally a difficult problem. In this article, Bayesian probability theory is used to obtain optimal exponential parameter estimates. The calculations are implemented using Markov chain Monte Carlo with simulated annealing to draw samples from the joint posterior probability for all of the parameters appearing in the exponential model. Monte Carlo integration is then used to approximate the marginal posterior probabilities for each of the parameters. We give numerical examples taken from simulated data and NMR relaxation experiments to illustrate the calculations and the effect of prior information on the parameter estimates. © 2005 Wiley Periodicals, Inc. Concepts Magn Reson Part A 27A: 55–63, 2005
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