TY - JOUR

T1 - On the use of bayesian probability theory for analysis of exponential decay date

T2 - An example taken from intravoxel incoherent motion experiments

AU - Neil, Jeffrey J.

AU - Bretthorst, G. Larry

PY - 1993/5

Y1 - 1993/5

N2 - Traditionally, the method of nonlinear least squares (NLLS) analysis has been used to estimate the parameters obtained from exponential decay data. In this study, we evaluated the use of Bayesian probability theory to analyze such data; specifically, that resulting from intravoxel incoherent motion NMR experiments. Analysis was done both on simulated data to which different amounts of Gaussian noise had been added and on actual data derived from rat brain. On simulated data, Bayesian analysis performed substantially better than NLLS under conditions of relatively low signal‐to‐noise ratio. Bayesian probability theory also offers the advantages of: a) not requiring initial parameter estimates and hence not being susceptible to errors due to incorrect starting values and b) providing a much better representation of the uncertainty in the parameter estimates in the form of the probability density function. Bayesian analysis of rat brain data was used to demonstrate the shape of the probability density function from data sets of different quality.

AB - Traditionally, the method of nonlinear least squares (NLLS) analysis has been used to estimate the parameters obtained from exponential decay data. In this study, we evaluated the use of Bayesian probability theory to analyze such data; specifically, that resulting from intravoxel incoherent motion NMR experiments. Analysis was done both on simulated data to which different amounts of Gaussian noise had been added and on actual data derived from rat brain. On simulated data, Bayesian analysis performed substantially better than NLLS under conditions of relatively low signal‐to‐noise ratio. Bayesian probability theory also offers the advantages of: a) not requiring initial parameter estimates and hence not being susceptible to errors due to incorrect starting values and b) providing a much better representation of the uncertainty in the parameter estimates in the form of the probability density function. Bayesian analysis of rat brain data was used to demonstrate the shape of the probability density function from data sets of different quality.

KW - Bayesian probability theory

KW - intravoxel incoherent motion

KW - nonlinear least squares

UR - http://www.scopus.com/inward/record.url?scp=0027158141&partnerID=8YFLogxK

U2 - 10.1002/mrm.1910290510

DO - 10.1002/mrm.1910290510

M3 - Article

C2 - 8505900

AN - SCOPUS:0027158141

VL - 29

SP - 642

EP - 647

JO - Magnetic Resonance in Medicine

JF - Magnetic Resonance in Medicine

SN - 0740-3194

IS - 5

ER -