We present a novel Bayesian framework to relate changes in data to changes in model parameters even in models that cannot be directly inverted. We do so by training probabilistic models that characterise how the measurements change as a result of a change in the parameters. While the approach is general, in this work we used the framework to study microstructural parameter changes that are associated with the appearance of areas of white matter hyperintensities. We found a dichotomy between periventricular and deep white matter hyperintensities, where the latter are associated with increased extracellular signal.
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