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bogus comments on Learning Mathematics in Context - Less Wrong Discussion
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Comments (35)
Statistical tools rely on such proofs.
Statistics is an applied science, similar to engineering. It has to deal with the messy world where you might need to draw conclusions from a small data set of uncertain provenance where some outliers might be data entry mistakes (or maybe not), you are uncertain of the shape of the distributions you are dealing with, have a sneaking suspicion that the underlying process is not stable in time, etc. etc. None of the nice assumptions underlying nice proofs of optimality apply. You still need to analyse this data set.
Well, this is a matter of degree. There is a reason we use these tools in the first place. A good statistician must be quite aware of the underlying assumptions of each tool, if only so that they can switch to something else when warranted. (For instance, use "robust" methods which try to identify and appropriately discount outliers.)
Well, of course.
Heh. The word "appropriately" is a tricky one. There is a large variety of robust methods which use different ways of discounting outliers, naturally with different results. The statistician will need to figure out what's "appropriate" in this particular case and proofs don't help here.