To Bayes or not to Bayes?

The goal of geophysical inversion is to make quantitative inferences about the Earth from noisy, finite data. The limitations of noise and the inadequacy of the data mean that geophysical inversion problems are fundamentally problems of statistical inference. We do not invert data to find “models.” as much as we might like to; we invert data to make inferences about models. There will usually be an infinity of models that fit the data. Thus we must look to probability theory for help.