ABSTRACT
This chapter first discusses the classical inversion technique for simulation introduced in 1947 by John Von Neumann, then other popular methods such as the change of variable and the rejection techniques, and several sampling techniques of probability measures over a finite set. These methodologies are used in Bayesian statistical machine learning, in physics and chemistry in the modeling of fragmentation (a.k.a aggregation) and coagulation processes, as well as in the modeling of dynamic population models using stochastic partial differential equations. Sampling conditional probabilities is one of the most important problems in Bayesian statistics and in applied probability. The conditioning principles are applied in formulating some basic properties of spatial Poisson point processes. Spatial Poisson processes are sometimes called complete spatial randomness (CSR). They arise in statistical inference in social sciences, biology, pharmacology, as well as in astronomy.
