Exponential parameter estimation (in NMR) using Bayesian probability theory

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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.

Original languageEnglish
Pages (from-to)55-63
Number of pages9
JournalConcepts in Magnetic Resonance Part A: Bridging Education and Research
Issue number2
StatePublished - Nov 2005


  • Biexponential
  • Exponential data analysis
  • Rate constant
  • Time constant

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