rstream: Streams of Random Numbers for Stochastic Simulation

The package rstream provides a unified interface to streams of random numbers for the R statistical computing language. Features are: * independent streams of random numbers * substreams * easy handling of streams (initialize, reset) * antithetic random variates The paper describes this packages and demonstrates an simple example the usefulness of this approach.Series: Preprint Series / Department of Applied Statistics and Data Processin

Computing the Two-Sided Kolmogorov-Smirnov Distribution

We propose an algorithm to compute the cumulative distribution function of the two-sided Kolmogorov-Smirnov test statistic D_n and its complementary distribution in a fast and reliable way. Different approximations are used in different regions of n, x. Java and C programs are available.

On the existence and scaling of structure functions in turbulence according to the data

We sample a velocity field that has an inertial spectrum and a skewness that matches experimental data. In particular, we compute a self-consistent correction to the Kolmogorov exponent and find that for our model it is zero. We find that the higher order structure functions diverge for orders larger than a certain threshold, as theorized in some recent work. The significance of the results for the statistical theory of homogeneous turbulence is reviewed.Comment: 15 pages, 5 figures, to appear in PNA

Random number generation with multiple streams for sequential and parallel computing

International audienceWe provide a review of the state of the art on the design and implementation of random number generators (RNGs) for simulation, on both sequential and parallel computing environments. We focus on the need for multiple streams and substreams of random numbers, explain how they can be constructed and managed, review software libraries that offer them, and illustrate their usefulness via examples. We also review the basic quality criteria for good random number generators and their theoretical and empirical testing

Estimating the Probability of a Rare Event Over a Finite Time Horizon

We study an approximation for the zero-variance change of measure to estimate the probability of a rare event in a continuous-time Markov chain. The rare event occurs when the chain reaches a given set of states before some fixed time limit. The jump rates of the chain are expressed as functions of a rarity parameter in a way that the probability of the rare event goes to zero when the rarity parameter goes to zero, and the behavior of our estimators is studied in this asymptotic regime. After giving a general expression for the zero-variance change of measure in this situation, we develop an approximation of it via a power series and show that this approximation provides a bounded relative error when the rarity parameter goes to zero. We illustrate the performance of our approximation on small numerical examples of highly reliableMarkovian systems. We compare it to a previously proposed heuristic that combines forcing with balanced failure biaising. We also exhibit the exact zero-variance change of measure for these examples and compare it with these two approximations

The Rampart, Manley Hot Springs, And Fort Gibbon Mining Districts Of Alaska.

Thesis (M.A.) University of Alaska Fairbanks, 1995This thesis on the Rampart, Manley Hot Springs, and Fort Gibbon mining districts of Alaska provides the first comprehensive public history of prospecting and mining activity in these three districts within the gold belt of Interior Alaska. Spanning almost one hundred years, the history begins in 1894 and extracts material from early recorders' books, old newspapers, correspondence of miners whose dreams drew them to the gold fields, and U.S. Geological Survey reports which analyzed Alaska's natural resources and mining economy. It surveys mining development from stampedes during the boom years of the turn-into-the-twentieth-century through periods of decline and on into the modern, mechanized, open-pit operations near the beginning of the twenty-first century. It concludes with an extensive annotated bibliography designed to assist other researchers in finding specialized, in-depth information about the three districts. <p

Density Estimation by Monte Carlo and Quasi-Monte Carlo

Estimating the density of a continuous random variable $X$ has been studied extensively in statistics, in the setting where $n$ independent observations of $X$ are given a priori and one wishes to estimate the density from that. Popular methods include histograms and kernel density estimators. In this review paper, we are interested instead in the situation where the observations are generated by Monte Carlo simulation from a model. Then, one can take advantage of variance reduction methods such as stratification, conditional Monte Carlo, and randomized quasi-Monte Carlo (RQMC), and obtain a more accurate density estimator than with standard Monte Carlo for a given computing budget. We discuss several ways of doing this, proposed in recent papers, with a focus on methods that exploit RQMC. A first idea is to directly combine RQMC with a standard kernel density estimator. Another one is to adapt a simulation-based derivative estimation method such as smoothed perturbation analysis or the likelihood ratio method to obtain a continuous estimator of the cumulative density function (CDF), whose derivative is an unbiased estimator of the density. This can then be combined with RQMC. We summarize recent theoretical results with these approaches and give numerical illustrations of how they improve the convergence of the mean square integrated error.NSERC Discovery Grant, IVADO Grant, ERDF, ESF, EXP. 2019/0043

Computing the Two-Sided Kolmogorov-Smirnov Distribution

We propose an algorithm to compute the cumulative distribution function of the two-sided Kolmogorov-Smirnov test statistic Dn and its complementary distribution in a fast and reliable way. Different approximations are used in different regions of n, x. Java and C programs are available