Matthew R Marler, I can’t help but notice your latest response doesn’t even attempt to address my recent comments as a whole. You apparently misunderstood my intended meaning, which is fine, but that we’ve now had this many comments go by without you acknowledging it is a shame. My meaning was quite simple, and there is no reason we should be unable to agree what it was. I suspect the problem is you continue to say things like:
With those, the discussion is unambiguous. You can make the discussion unambiguous by specifying other measures of accuracy and precision. For whatever measures you choose, achievement of a sufficient level of accuracy requires achievement of a sufficient level of precision.
Which are nothing more than hand-waving. There is no inherent reason a “sufficient level of accuracy” as measured by MSE would require “a sufficient level of precision.” You’ve done nothing to support the claim there is save to falsely claim improving accuracy requires improving both accuracy and variance.
There are times when significant variance is acceptable but bias is not. In these cases, a large degree of imprecision might be tolerated. In other cases, bias may be acceptable while only a little variance could be tolerated. In these cases, only a small degree of imprecision might be tolerated. Despite having very different requirements, both of these cases could be represented by the same MSE value. So when you say:
Given two models of equal accuracy, you have a choice between the one with the smaller bias and the one with the greater precision. I think that accuracy is the first consideration, and precision is the second, when evaluating both in the choice of model.
You’re merely stating an opinion which does not match all real-life requirements. It may match many, and perhaps it even matches the GCMs used in climate science, but it is not some inherent truth everyone must accept simply because you tell them to.
I honestly don’t know why you take issue with my position. I’ve scarcely ever had someone suggest looking at more measures of a model’s skill is inappropriate.
