Extreme Value Theory (2009) [pdf] | Hacker News Reader

Extreme Value Theory (2009) [pdf]

rls.sites.oasis.unc.edu

38 pointsjruohonen10 comments

A lady at work was talking about this years ago, and I had a look. It's pretty interesting, because it focuses on the opposite of what we're normally introduced to in stats classes, that being measures of central tendency.

Somehow it isn't often talked about. For instance, if you have some gaussian and you sample from it a small number of times, what is the distribution of the largest value?

You would use one of the Generalized Extreme Value distributions. One of those, the Gumbel distribution, is actually commonly used in machine learning to sample from a softmax in a differentiable manner (by reparametrization), and should work for the maximum of normals (it's definitely one of the three).

You may be interested in this theorem : https://en.m.wikipedia.org/wiki/Fisher%E2%80%93Tippett%E2%80...

Very interesting second question! I wonder what distribution it follows as a function of sample quantity

In some formats, the question is easy. If the CDF is F(x), then the CDF of the maximum of n independent draws is G(x) = F(x)^n. This is because the probability that the max is less than x is the product of the probabilities that each is less than x.

Thanks for sharing! I was always wondering how climate scientists were able to identify if an event was due to climate change. Now I have a good reference!

The first slide makes the disclaimer that one is not "able to identify if an event was due to climate change", only likelihoods of certain events occurring under various conditions. People might treat those two things the same due to our mental heuristics, but they are not.

It's true that this method can't say event X was or was not due to condition Y.

But it is fair to say that a pattern of such events that matches (or doesn't) the probabilities given by condition Y is evidence that Y is (or isn't) accurate.

A single heatwave, however anomalous, isn't evidence of anything. Several heatwaves may be ample evidence that one model is more accurate than another.

If you think a continuous unbounded distribution is more fat-tailed than the normal distribution, you can fit a Student's t distribution with the degrees of freedom (as well as location and scale) a free parameter. What insights does EVT give you that fitting fitting a fat-tailed distribution does not?

That covers a very narrow subset of use cases where you have something that’s normal-ish and you want hand-wavy fatter tails. EVT theory extends to more general cases

I have used EVT quite a lot in my work as SRE.

It's a pity it is not well known among SRE or production engineers, unless you have a personal interest or math background.

Reply on news.ycombinator.com