TY - JOUR

T1 - Bayesian analysis. I. Parameter estimation using quadrature NMR models

AU - Bretthorst, G. Larry

N1 - Funding Information:
This work was supported by NIH Grant GM-30331, J. J. H. Ackerman principal encouragement of Professor J. J. H. Ackerman is greatly appreciated as are the editorial C. Ray Smith and extensive conversations with Professor E. T. Jaynes.

PY - 1990/7

Y1 - 1990/7

N2 - In the analysis of magnetic resonance data, a great deal of prior information is available which is ordinarily not used. For example, considering high-resolution NMR spectroscopy, one knows in general terms what functional form the signal will take (e.g., sum of exponentially decaying sinusoids) and that, for quadrature measurements, it will be the same in both channels except for a 90° phase shift. When prior information is incorporated into the analysis of time-domain data, the frequencies, decay rate constants, and amplitudes may be estimated much more precisely than by direct use of discrete Fourier transforms. Here, Bayesian probability theory is used to estimate parameters using quadrature models of NMR data. The calculation results in an interpretation of the quadrature model fitting that allows one to understand on an intuitive level what frequencies and decay rates will be estimated and why.

AB - In the analysis of magnetic resonance data, a great deal of prior information is available which is ordinarily not used. For example, considering high-resolution NMR spectroscopy, one knows in general terms what functional form the signal will take (e.g., sum of exponentially decaying sinusoids) and that, for quadrature measurements, it will be the same in both channels except for a 90° phase shift. When prior information is incorporated into the analysis of time-domain data, the frequencies, decay rate constants, and amplitudes may be estimated much more precisely than by direct use of discrete Fourier transforms. Here, Bayesian probability theory is used to estimate parameters using quadrature models of NMR data. The calculation results in an interpretation of the quadrature model fitting that allows one to understand on an intuitive level what frequencies and decay rates will be estimated and why.

UR - http://www.scopus.com/inward/record.url?scp=44949286565&partnerID=8YFLogxK

U2 - 10.1016/0022-2364(90)90287-J

DO - 10.1016/0022-2364(90)90287-J

M3 - Article

AN - SCOPUS:44949286565

VL - 88

SP - 533

EP - 551

JO - Journal of Magnetic Resonance (1969)

JF - Journal of Magnetic Resonance (1969)

SN - 0022-2364

IS - 3

ER -