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Lumifer comments on Why the tails come apart - Less Wrong

115 Post author: Thrasymachus 01 August 2014 10:41PM

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Comment author: Lumifer 28 July 2014 04:54:39PM *  4 points [-]

Another issue is that real-life processes are, generally speaking, not stationary (in the statistical sense) -- outside of physics, that is.

When you see an extreme event in reality it might be that the underlying process has heavier tails than you thought it does, or it might be that the whole underlying distribution switched and all your old estimates just went out of the window...

Comment author: othercriteria 28 July 2014 05:32:30PM 2 points [-]

Good point. When I introduced that toy example with Cauchy factors, it was the easiest way to get factors that, informally, don't fill in their observed support. Letting the distribution of the factors drift would be a more realistic way to achieve this.

the whole underlying distribution switched and all your old estimates just went out of the window...

I like to hope (and should probably endeavor to ensure) that I don' t find myself in situations like that. A system that generatively (what the joint distribution of factor X and outcome Y looks like) evolves over time, might be discriminatively (what the conditional distribution of Y looks like given X) stationary. Even if we have to throw out our information about what new X's will look like, we may be able to keep saying useful things about Y once we see the corresponding new X.

Comment author: Lumifer 28 July 2014 05:54:14PM 4 points [-]

I like to hope (and should probably endeavor to ensure) that I don' t find myself in situations like that.

It comes with certain territories. For example, any time you see the financial press talk about a six-sigma event you can be pretty sure the underlying distribution ain't what it used to be :-/