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On the use of bayesian probability theory for analysis of exponential decay date: An example taken from intravoxel incoherent motion experiments
Author(s) -
Neil Jeffrey J.,
Bretthorst G. Larry
Publication year - 1993
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.1910290510
Subject(s) - bayesian probability , probability density function , exponential function , mathematics , statistics , intravoxel incoherent motion , bayes' theorem , statistical physics , bayesian statistics , noise (video) , gaussian , computer science , bayesian inference , artificial intelligence , physics , mathematical analysis , medicine , image (mathematics) , quantum mechanics , magnetic resonance imaging , radiology , effective diffusion coefficient
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.