TY - JOUR

T1 - Bayesian ANALYSIS. IV. Noise and computing time considerations

AU - Bretthorst, G. Larry

PY - 1991/6/15

Y1 - 1991/6/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0042841583&partnerID=8YFLogxK

U2 - 10.1016/0022-2364(91)90013-J

DO - 10.1016/0022-2364(91)90013-J

M3 - Article

AN - SCOPUS:0042841583

VL - 93

SP - 369

EP - 394

JO - Journal of Magnetic Resonance (1969)

JF - Journal of Magnetic Resonance (1969)

SN - 0022-2364

IS - 2

ER -