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In numerical analysis and computational statistics, rejection sampling is a basic technique used to generate observations from a distribution.It is also commonly called the acceptance-rejection method or "accept-reject algorithm" and is a type of exact simulation method.
Rare event sampling is an umbrella term for a group of computer simulation methods intended to selectively sample 'special' regions ... by John von Neumann and ...
Non-uniform random variate generation or pseudo-random number sampling is the numerical practice of generating pseudo-random numbers (PRN) that follow a given probability distribution. Methods are typically based on the availability of a uniformly distributed PRN generator .
Von Neumann's method used a pivoting algorithm between simplices, with the pivoting decision determined by a nonnegative least squares subproblem with a convexity constraint (projecting the zero-vector onto the convex hull of the active simplex). Von Neumann's algorithm was the first interior point method of linear programming. [274]
In the 1949 talk, Von Neumann quipped that "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." What he meant, he elaborated, was that there were no true "random numbers", just means to produce them, and "a strict arithmetic procedure", like the middle-square method, "is not such a method".
A simple pen-and-paper method for generating random numbers is the so-called middle-square method suggested by John von Neumann. While simple to implement, its output is of poor quality. It has a very short period and severe weaknesses, such as the output sequence almost always converging to zero.
The von Neumann method is based on the decomposition of the errors into Fourier series.To illustrate the procedure, consider the one-dimensional heat equation = defined on the spatial interval , with the notation = (,) where are the specific x values, and are the sequence of t values.
John von Neumann (1903–1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath.He had perhaps the widest coverage of any mathematician of his time, integrating pure and applied sciences and making major contributions to many fields, including mathematics, physics, economics, computing, and statistics.