Stochastic simulation
Multivariate statistical simulation
Multivariate statistical simulation
New computer methods for global optimization
New computer methods for global optimization
Rigorous methods for global optimization
Recent advances in global optimization
Automatic sampling with the ratio-of-uniforms method
ACM Transactions on Mathematical Software (TOMS)
Computer Generation of Random Variables Using the Ratio of Uniform Deviates
ACM Transactions on Mathematical Software (TOMS)
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
Mathematical Programming: Series A and B
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Stochastic simulation is widely used to validate procedures and provide guidance for both theoretical and practical problems. Random variate generation is the basis of stochastic simulation. Applying the ratio-of-uniforms method to generate random vectors requires the ability to generate points uniformly in a suitable region of the space. Starting from the observation that, for many multivariate distributions, the multidimensional objective region can be covered by a hyper-ellipsoid more tightly than by a hyper-rectangle, a new algorithm to generate from multivariate distributions is proposed. Due to the computational saving it can produce, this method becomes an appealing statistical tool to generate random vectors from families of standard and nonstandard multivariate distributions. It is particularly interesting to generate from densities known up to a multiplicative constant, for example, from those arising in Bayesian computation. The proposed method is applied and its efficiency is shown for some classes of distributions.