Bayesian ANALYSIS. IV. Noise and computing time considerations

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Abstract

Probability theory, when interpreted as logic, enables one to ask many questions not possible with the frequency interpretation of probability theory. Often, answering these questions can be computationally intensive. If these techniques are to find their way into general use in NMR, a way that allows one to calculate the probability for the frequencies, amplitudes, and decay rate constants quickly and easily must be found. In this paper, a procedure that allows one to compute the posterior probability for the frequencies, amplitudes, and decay rate constants from a series of zero-padded discrete Fourier transforms of the complex FID data when the data have been multiplied by a decaying exponential is described. Additionally, the calculation is modified to include prior information about the noise, and it is shown that obtaining a sample of the noise is almost as important as obtaining a signal sample, because it allows one to investigate complicated spectra using simple models. Three examples are given to illustrate the calculations.

Original languageEnglish
Pages (from-to)369-394
Number of pages26
JournalJournal of Magnetic Resonance (1969)
Volume93
Issue number2
DOIs
StatePublished - Jun 15 1991

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