ON THE USE OF BAYESIAN PROBABILITY-THEORY FOR ANALYSIS OF EXPONENTIALDECAY DATA - AN EXAMPLE TAKEN FROM INTRAVOXEL INCOHERENT MOTION EXPERIMENTS

Traditionally, the method of nonlinear least squares (NLLS) analysis h as been used to estimate the parameters obtained from exponential deca y data. In this study, we evaluated the use of Bayesian probability th eory to analyze such data; specifically, that resulting from intravoxe l incoherent motion NMR experiments. Analysis was done both on simulat ed data to which different amounts of Gaussian noise had been added an d on actual data derived from rat brain. On simulated data, Bayesian a nalysis performed substantially better than NLLS under conditions of r elatively 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 v alues and b) providing a much better representation of the uncertainty in the parameter estimates in the form of the probability density fun ction. Bayesian analysis of rat brain data was used to demonstrate the shape of the probability density function from data sets of different quality.