There is a particular form of statistical inference which is not well-understood as problematic. I will use my “smart” scale as an example. It takes weight and several impedance measurements, which are taken from a large population along with body composition truth measurements from DEXA, and the coefficients of the algorithm are determined by regression. It should be no surprise that the weight measurement overpowers all other measurements in the regression, and the impedance covariance is ill-conditioned, so really it’s just a height and weight formula. My information gain from the impedance measurement is zero. The correct way to do the regression is in reverse, from more (relevant) information to less, so the parameters should be well-conditioned. This is assuming that DEXA contains all useful information to predict impedance. If not, forget about the whole thing. If that model works, then the reverse can be found through Bayesian optimization. You still have bias set by the covariance prior, but it is at least known, and you can give information about how it is affecting the result.