Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary distribution, but most require O(n ln(n)) time, where n measures the size of the input. In this work a new protocol for creating perfect simulation algorithms that runs ...

The package copula (formerly nacopula) provides procedures for constructing nested Archimedean copulas in any dimensions and with any kind of nesting structure, generating vectors of random variates from the constructed objects, computing function values and probabilities of falling into hypercubes, as well as evaluation of characteristics such as Kendall’s tau and the tail-dependence coefficie...

We show how regional prediction of car insurance risks can be improved for finer subregions by combining explanatory modeling with phenomenological models from industrial practice. Motivated by the control-variates technique, we propose a suitable combined predictor when claims data are available for regions but not for subregions. We provide explicit conditions which imply that the mean square...

R is free software for statistical computing, providing a variety of statistical and graphical functionality. For use in simulation education, R’s capabilities help to develop student intuition. In this paper, we introduce the simEd package for R, written with a pedagogical focus. The package includes functions for generating discrete and continuous variates via inversion, with capabilities for...

The method of control variates is one of the most widely used variance reduction techniques associated with Monte Carlo simulation. This paper studies the method of control variates from several different viewpoints, and establishes new connections between the method of control variates and: conditional Monte Carlo, antithetics, rotation sampling, stratification, and nonparametric maximum likel...

Price's theorem is derived for complex valued variates. The derivation differs from the existing derivation in two respects. First, the normal variates are not assumed to be circularly complex. Thus the result is more general. Second, the characteristic function of the complex variates is not used.

Monte-Carlo Tree Search (MCTS) has proven to be a powerful, generic planning technique for decision-making in single-agent and adversarial environments. The stochastic nature of the Monte-Carlo simulations introduces errors in the value estimates, both in terms of bias and variance. Whilst reducing bias (typically through the addition of domain knowledge) has been studied in the MCTS literature...

A novel method is presented to compute the exit time for the stochastic simulation algorithm. The method is based on the addition of a series of random variables and is derived using the convolution theorem. The final distribution is derived and approximated in the frequency domain. The distribution for the final time is transformed back to the real domain and can be sampled from in a simulatio...

Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law distributions. The task is usually performed through standard methods that map uniform random variates into the desired probability space. Whereas all these algorit...