Abstract
Abstract A direct Monte Carlo method for volume estimation of star-shaped or convex domains is presented, and is generalized to a Markov Chain Monte Carlo method for high-dimensional problems. The direct approach itself, which is closely related to a method proposed by Fok and Crevier, is already applicable to some moderately high-dimensional problems. The combination with a Markov Chain Monte Carlo method and nested sampling or thermodynamic integration extends its scope considerably. Applications to the volume estimation for high-dimensional polytopes are presented, and the method is tested using exact results for the first 10 Birkho_ polytopes.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
