Take the 2-minute tour ×  An answer to another question derived
a formula for the volume of a delta-ball in $O(n)$. I am
wondering if there is a (constructive) way to draw samples
uniformly at random from such a region.  For my purposes, an
acceptance-rejection scheme is not viable. I am trying to study
the behavior of an integral over $O(n)$ of a function that is
very small outside of certain regions, so accepting samples that
lie within the ball is no different (from a computational
perspective) from sampling from $O(n)$ in its entirety.
Alternatively, any other non-uniform sampling scheme on $O(n)$
might be of interest, especially if it concentrates more samples
around diagonal matrices $\text{diag}(\pm1,\dots,\pm1)$.
share|improve this question For small $\delta$, sampling
uniformly from a $\delta$-ball in the (linear) space of
antisymmetric matrices and exponentiating ought to give an
approximately uniform sample. –  Mark Meckes Dec 19 '11 at 23:45
If you tell what your function is, somebody may come u