Abstract
In NMR the response of a system of spins is described by a spectral density function G(ω). Typically, only the moments of this function can be computed from first principles. NMR data are typically sampled in the time domain. In the time domain, these moments are proportional to the derivatives of the Fourier transform of G(ω), evaluated at time t = 0. When comparing theory to experiment, good estimates of the moments are needed. Good estimates are difficult to obtain, because procedures like least-squares and maximum-likelihood do not tell what the data have to say about a particular moment; rather, they give information about all of the moments. In this paper, a Bayesian calculation of the probability for a given moment is presented, and an example of the calculation is given.
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© 1991 Springer Science+Business Media Dordrecht
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Bretthorst, G.L. (1991). Moment Estimation using Bayesian Probability Theory. In: Grandy, W.T., Schick, L.H. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 43. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3460-6_32
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DOI: https://doi.org/10.1007/978-94-011-3460-6_32
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