Comments on: Probability and information

By: Probability that a number is prime — The Endeavour

Probability that a number is prime — The Endeavour — Wed, 06 Oct 2010 11:19:36 +0000

[...] Probability and information What a probability means Connecting probability and number theory ? X [...]

By: John

John — Tue, 21 Apr 2009 20:53:41 +0000

Loss functions are contentious and easily lead to bike shed arguments. And when people can't agree on a loss function, the mathematicians win by default: everyone uses classical methods that implicitly assume a squared-error loss function that makes the mathematics most convenient.

By: ekzept

ekzept — Tue, 21 Apr 2009 20:25:50 +0000

Although I found Berger’s book on Bayesian statistics tough going, he does do a lot with Loss functions and utility. As an undergraduate physics major and later engineer I was taught a lot of probability in the classic guise. However, this idea that errors have costs, and you can’t really make the right choice unless and until you decide where your risks are was revealing and interesting. Not everyone has such a good understanding of the decision they are about to make, so I guess they go with the Loss function equivalent of the uninformed Prior. Yet, often, as in ROC curves and elsewhere, there’s a natural place for costs of being wrong to be introduced, and I wonder why courses don’t use them more.

By: John

John — Thu, 13 Mar 2008 14:21:29 +0000

Agreed. “Optimal” is a loaded term: optimal by what criteria? Does the labor required to compute the solution fit in? A lot of sub-optimal things begin to look closer to optimal when you take more factors — especially human limitations — into account.

By: Andrew Gelman

Andrew Gelman — Thu, 13 Mar 2008 14:17:27 +0000

Sure, but “optimal” seems a bit strong!