Xi'an's Og

Attending the workshop “Computational methods for probability distributions on manifolds” (IHP, Paris, May 11-13, 2026) made me re-ponder the challenge of simulating a distribution conditional on the random variable X~p(x)  being constrained to the manifold M defined by q(x)=0. Fortunately, Claude helped a lot in downgrading the importance of the Hausdorff measure σ! The density writes p(x)/||∇q(x)||, with respect to the Hausdorff measure on M. Which accounts for the curvature of the manifold M. When resorting to an MCMC algorithm to simulate this density, there are two options: (a) simulate from a proposal on the manifold M whose density wrt the Hausdorff measure σ is known or (b) resort to a reparameterisation map φ of the manifold M whose input on an Euclidean space has density

wrt the Lebesgue measure.

This entry was posted on May 13, 2026 at 12:26 am and is filed under Books, Statistics, University life with tags Claude, Computational methods for probability distributions on manifolds, Hausdorff metric, IHP, Institut Henri Poincaré, LLMs, manifold exploration, MCMC, Paris, workshop. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.