The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution. In many cases, this bound may be given in terms of first and second moments alone. We present a background of the method and state some fundamental Poisson approximation theorems. The body of this paper is an illustration, through varied...

We analyze the expected time penonnance of two versions of the thinning algorithm of Lewis and Shedler for generating random variates with a given hazard rate on [0,00). For thinning with fixed dominating hazard rate g(x) = c for example, it is shown that the expected number of iterations is cE(X) where X is the random variate tQat is produced. For DHR distributions, we can use dynamic thinning...

Real-time adaptive sampling is a new technique recently proposed for efficient importance in realtime Monte Carlo subsurface scattering. It adaptively places samples based on variance tracking to help escape the uncanny valley of rendering. However, occasional performance drop due temporal lighting dynamics (e.g., guns or lights turning and off) could hinder adoption games other applications wh...

We describe three tests of randomness—tests that many random number generators fail. In particular, all congruential generators—even those based on a prime modulus—fail at least one of the tests, as do many simple generators, such as shift register and lagged Fibonacci. On the other hand, generators that pass the three tests seem to pass all the tests in the Diehard Battery of Tests. Note that ...

This paper presents a method for meshing multi-material domains with additional features curves. This requirement arises for instance in situations where smooth objects (e.g. anatomical structures) are combined with technical objects (e.g. implants, surgical screws). Our approach avoids the tedious process of generating a single consistent input surface by means of an implicit representation, c...

Contributions to the generation and testing of random number sequences intended for cryptographic applications

Research on the mental representation of numbers has focused on a horizontally aligned mental number line, but more and more findings have begun to implicate a vertical orientation as well. We investigate the relationship between these two orientations when people generate random numbers. In the horizontal condition, people generated larger numbers when they looked right as opposed to left. In ...

A general methodology is presented for the construction and effective use of control variates for reversible MCMC samplers. The values of the coefficients of the optimal linear combination of the control variates are computed, and adaptive, consistent MCMC estimators are derived for these optimal coefficients. All methodological and asymptotic arguments are rigorously justified. Numerous MCMC s...