Bayesian analysis. I. Parameter estimation using quadrature NMR models

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.