TY - JOUR

T1 - How accurately can parameters from exponential models be estimated? A Bayesian view

AU - Bretthorst, G. Larry

PY - 2005/11/1

Y1 - 2005/11/1

N2 - Estimating the amplitudes and decay rate constants of exponentially decaying signals is an important problem in NMR. Understanding how the uncertainty in the parameter estimates depends on the data acquisition parameters and on the "true" but unknown values of the exponential signal parameters is an important step in designing experiments and determining the amount and quality of the data that must be gathered to make good parameter estimates. In this article, Bayesian probability theory is applied to this problem. Explicit relationships between the data acquisition parameters and the "true" but unknown exponential signal parameters are derived for the cases of data containing one and two exponential signal components. Because uniform prior probabilities are purposely employed, the results are broadly applicable to experimental parameter estimation.

AB - Estimating the amplitudes and decay rate constants of exponentially decaying signals is an important problem in NMR. Understanding how the uncertainty in the parameter estimates depends on the data acquisition parameters and on the "true" but unknown values of the exponential signal parameters is an important step in designing experiments and determining the amount and quality of the data that must be gathered to make good parameter estimates. In this article, Bayesian probability theory is applied to this problem. Explicit relationships between the data acquisition parameters and the "true" but unknown exponential signal parameters are derived for the cases of data containing one and two exponential signal components. Because uniform prior probabilities are purposely employed, the results are broadly applicable to experimental parameter estimation.

KW - Bayesian probability theory

KW - Exponential parameter estimation

UR - http://www.scopus.com/inward/record.url?scp=30744433867&partnerID=8YFLogxK

U2 - 10.1002/cmr.a.20044

DO - 10.1002/cmr.a.20044

M3 - Article

AN - SCOPUS:30744433867

VL - 27

SP - 73

EP - 83

JO - Concepts in Magnetic Resonance Part A: Bridging Education and Research

JF - Concepts in Magnetic Resonance Part A: Bridging Education and Research

SN - 1546-6086

IS - 2

ER -