Isn't noise in the data going to dominate output size of lossless compression? Wouldn't linguistics and vision be better off with direct measurements of predictive strength?
Noise certainly affects the compression rate. But you are not concerned with the absolute compression rate, you are only concerned with the relative rate achieved by two theories A and B. Both theories will be negatively impacted to the same degree by the noise, so the comparison still works to select which theory is better.