constraint geometry research project

[bob-carpenter]

Stan makes some particular constraint choices to map between constrained and unconstrained parameterizations, such as covariance matrices being Cholesky factors on the unconstrained scale and simplexes being defined by stick-breaking and so on.

There are other choices, and it'd be a great research project to explore how they compare in terms of sampling.

The obvious people to supervise such an effort would be Michael or Ben or Marcus.

[betanalpha]

My intuition is that the well-posed transformations will all end up being
equivalent (as we’ve seen with the simplex transformations) but it’s
definitely worth exploring and writing up. The whole “map to R^{n}” is
an important principle that is rarely discussed in the statistical literature
but is crucial for efficient algorithms.

On May 9, 2014, at 11:29 AM, Bob Carpenter notifications@github.com wrote:

Stan makes some particular constraint choices to map between constrained and unconstrained parameterizations, such as covariance matrices being Cholesky factors on the unconstrained scale and simplexes being defined by stick-breaking and so on.

There are other choices, and it'd be a great research project to explore how they compare in terms of sampling.

The obvious people to supervise such an effort would be Michael or Ben or Marcus.

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[mbrubake]

I'd be happy to help supervise this if there is an interested student. I've actually started doing some work along these lines for parameterizing S^n which I really need to get around to finishing up and publishing...

[syclik]

Closing this cause it's not really an issue. We should pick this up on a wiki or in a longer todo.