Discretization-based direct random sample generation

An efficient Monte Carlo method for random sample generation from high dimensional distributions of complex structures is developed. The method is based on random discretization of the sample space and direct inversion of the discretized cumulative distribution function. It requires only the knowledge of the target density function up to a multiplicative constant and applies to standard distributions as well as high-dimensional distributions arising from real data applications. Numerical examples and real data applications are used for illustration. The algorithms are implemented in statistical software R and a package dsample has been developed and is available online.