Sampling From A Manifold
  We develop algorithms for sampling from a probability distribution on a submanifold embedded in Rn. Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of fit tests in exponential families and to Neyman's smooth test. This article is partially expository, giving an introduction to the tools of geometric measure theory. 
Persi Diaconis, Susan Holmes and Mehrdad Shahshahani
math.ST stat.TH