Mateusz Baran

Oh, I see you need the Hessian of the cost function at the minimizer, this will be fun on manifolds.

Do you have a reference for the more general case? I only managed to find this: https://mathoverflow.net/questions/40329/how-to-define-the-quotient-of-a-measure-which-is-invariant-under-group-action and I have no idea what would the practical implications be. In particular,...

I'm not sure how much more work ManifoldMeasure actually needs but I was also thinking about moving random point and tangent vector generation out of Manifolds.jl too.

It's even more complex, as there are other ways to measure the volume than from the Riemannian metric (see the paper I've linked), and connection is not sufficient as far...

Isn't the Hausdorff measure only defined for submanifolds of R^n? It would make sense to me to have an interface for getting the volume of the manifold with respect to...

> > > > I believe it's defined for manifolds with an embedding in a metric space. So e.g. if one embedded the Sphere in R^n with varying radii, this...

I don't really like the two-argument variants of `mean`: a measure knows its manifold, and the manifold knows its embededing. So there is not much point to providing the manifold...

Yes, we could definitely encode the embedding in `Symmetric` as a constraint in `AbstractStatisticType`. It would also be possible to include some "empirical" estimation methods as `AbstractStatisticType` (drawing samples and...

One of the drawbacks of `EmbeddedManifold` is that for two given manifolds, it only lets us do one embedding, while `AbstractStatisticType` could describe the desired embedding.

Look at `SpecialEuclideanInGeneralLinear`: if I wanted to embed SE in GL as `-affine_matrix` instead of `affine_matrix`, I couldn't do it, because `EmbeddedManifold` couples them in one way. I could override...