[TobyTheCamel]

> However, the idea is that often a lot of the probability mass - an amount that is not small - will be concentrated around the maximum likelihood estimate, and so that's why it makes a good estimate, and worth using.

This may be true for low dimensions but doesn’t generalise to high dimensions. Consider a 100-dimensional standard normal distribution for example. The MLE will still be at the origin but most of the mass will live in a thin shell of distance roughly 7 units from the origin.

[blt]

I think the "mass" they are referring to might the mass of the Bayesian posterior in parameter space, not the mass of the data in event space.

[fergal_reid]

Yes, in parameter space.

However, TobyTheCamel's point is valid in that there are some parameter spaces where the MLE is going to be much less useful than others.

Even without having to go to high dimensions, if you've got a posterior that looks like a normal distribution, the MLE is going to the you a lot, whereas if it's a multimodal distribution with a lot of mass scattered around, knowing the MLE much less informative.

But this is a complex topic to address in general, so I'm trying to stick to what I see as the intuition behind the original question!

[lupire]

Concentration of mass is density. A shell is not dense.

If I am looking for a needle in a hyperhaystack, it's not important to know that it's more likely to be "somewhere on the huge hyperboundary" than "in the center hypercubic inch".

[zmgsabst]

Disagree:

A lot of why large corporations fail to make products that people enjoy is tied up in this behavior and that mass is not independently distributed along each distribution — you end up with “continents of taste” your centroid product sucks for equally.

[astrange]

This is similar to how they originally tried to build fighter jet seats for the average pilot, but it failed because it turned out there were no average pilots, so they had to make them adjustable.

[kgwgk]

And yet your parent comment was right in saying that it won't be true that "a lot of the probability mass - an amount that is not small - will be concentrated" in the center hypercubic inch.