Quantified Maxent: An NMR Application
‘Classic MaxEnt’ is a Bayesian derivation of the MaxEnt treatment of inverse problems leading to a posterior probability ‘bubble’ over the solution. This probability bubble—which is maximised at the optimal regularised solution—provides the framework for quantitative inferences about the solution. In particular, the framework allows the computation of fluxes and associated error bars over the solution. This is an important advance in the general theory of inverse problems which has thus far lacked a quantitative reliability treatment of the computed solution. This paper discusses this quantification procedure and applies it to practical NMR spectroscopy.
KeywordsInverse Problem Maximum Entropy MaxEnt Spectrum Negative Line True Flux
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- Skilling J., (1989). Classic Maximum Entropy. Maximum Entropy and Bayesian Methods (ed. J. Skilling), 45–52, Kluwer.Google Scholar
- Gull S.F., (1989). Developments in Maximum Entropy Data Analysis. Maximum Entropy and Bayesian Methods (ed. J. Skilling), 53–71, Kluwer.Google Scholar
- Laue E.D., Skilling J., Staunton J., (1985). Maximum Entropy Reconstruction of Spectra Containing Antiphase Peaks. J. Mag. Res., 63, 418–424Google Scholar
- Bretthorst G.L., (1989) Bayesian Model Selection: Examples Relevant to NMR. Maximum Entropy and Bayesian Methods (ed. J. Skilling), 377–388, Kluwer.Google Scholar