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Lumifer comments on Learning Mathematics in Context - Less Wrong Discussion
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Interesting. One of my recurring themes is that mathematics and statistics are very different things and require different kind of brains/thinking -- people good at one will rarely be good at the other, too.
If you define mathematics as being about proofs (and not so much about computation), the distinction becomes more pronounced: statistics isn't about proofs at all, it's about dealing with uncertainty. There are certainly areas where they touch (e.g. proving that certain estimators have certain properties), but at their core, mathematics and statistics are not similar at all.
I'm skeptical that there is any such distinction. "Computational" math is near-worthless in the absence of a proof of correctness for what you're computing. Even statistics relies on such proofs, though sometimes these can only provide approximate results. (For instance, maximum-likelihood methods are precisely optimal under the simplifying assumption of uniform priors and a 0-1 loss function.)
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.
Except for all that pesky theoretical statistics.
Math people can have that :-) It is, basically, applied math, anyway.
Except it's not math. Disciplines are socially constructed, statistics is what statisticians do. Applied math is what applied math people do. There are lots of very theoretical stats departments. I think you are having a similar confusion people have sometimes about computer science and programming.
I think if you say stuff like "well, all those people who publish in Annals of Statistics are applied math people" I am not sure what you are really saying. There is some intersection w/ applied math, ML, etc., but theoretical stats has their own set of big ideas that define the field and give it character.
I don't think I do? I am well aware of the famous Dijkstra's quote.
As you mentioned, statistics is what statisticians do. Most statisticians don't work in academia. I don't doubt there are a lot of theory-heavy stats deparments, just like there are a lot of physics-heavy engineering departments.
Going up one meta-level, I'm less interested in what discipline boundaries have the social reality constructed, and more interested in feeling for the joint in the underlying territory.
Not sure why we are having this discussion. Statistics is a discipline with certain themes, like "intelligently using data for conclusions we want." These themes are sufficient to give it its own character, and make it both an applied and theoretical discipline. I don't think you are a statistician, right? Why are you talking about this?
Statistics is as much an applied discipline as physics.
Because I'm interested in the subject. Do you have objections?
You can post about whatever you want. I have objections if you start mischaracterizing what statistics is about for fun on the internet. Fun on the internet is great, being snarky on the internet is ok, misleading people is not.
edit: In fact, you can view this whole recent "data science" thing that statisticians are so worried about as a reaction to the statistics discipline becoming too theoretical and divorced from actual data analysis problems. [This is a controversial opinion, I don't think I share it, quite.]