  The problem of sampling constrained continuous distributions has frequently
appeared in many machine/statistical learning models. Many Monte Carlo Markov
Chain (MCMC) sampling methods have been adapted to handle different types of
constraints on the random variables. Among these methods, Hamilton Monte Carlo
(HMC) and the related approaches have shown significant advantages in terms of
computational efficiency compared to other counterparts. In this article, we
first review HMC and some extended sampling methods, and then we concretely
explain three constrained HMC-based sampling methods, reflection,
reformulation, and spherical HMC. For illustration, we apply these methods to
solve three well-known constrained sampling problems, truncated multivariate
normal distributions, Bayesian regularized regression, and nonparametric
density estimation. In this review, we also connect constrained sampling with
another similar problem in the statistical design of experiments of constrained
design space.
