An iterative algorithm for sampling from manifolds

We develop an algorithm that generates samples from a given probability distribution on a manifold embedded in a Euclidean space based only on the ability to evaluate the mapping defined by the parametrization of the manifold. In particular, we do not assume the ability to evaluate the derivatives of the mapping and the ability to tell whether a given point in the ambient space belongs to the manifold or not. The new approach is useful when the manifold is analytically intractable and highly nonlinear-for example, in studying complex regulatory networks in systems biology where the mapping is typically defined by the solution of a system of ordinary differential equations.