We study the dynamical behavior of disordered many-particle systems with long-range Coulomb interactions by means of damage-spreading simulations. In this type of Monte-Carlo simulations one investigates the time evolution of the damage, i.e. the difference of the o ccupation numbers of two systems, subjected to the same thermal noise. We analyze the dependence of the damage on temperature and disorder strength. For zero disorder the spreading transition coincides with the equilibrium phase transition, whereas for finite disorder, we find an evidence for a dynamical phase transition well below the transition temperature of the pure system.

To evaluate the expectation of a simple function with respect to a complicated multivariate density Monte Carlo integration has become the main technique. Gibbs sampling and importance sampling are the most popular methods for this task. In this contribution we propose a new simple general purpose importance sampling procedure. In a simulation study we compare the performance of this method with the performance of Gibbs sampling and of importance sampling using a vector of independent variates. It turns out that the new procedure is much better than independent importance sampling; up to dimension five it is also better than Gibbs sampling. The simulation results indicate that for higher dimensions Gibbs sampling is superior. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

We demonstrate that for the fast numerical inversion of the (generalized) inverse Gaussian distribution two algorithms based on polynomial interpolation are well-suited. Their precision is close to machine precision and they are much faster than the bisection method recently proposed by Y. Lai. / Series: Research Report Series / Department of Statistics and Mathematics

The acceptance-rejection algorithm is often used to sample from non-standard distributions. For this algorithm to be efficient, however, the user has to create a hat function that majorizes and closely matches the density of the distribution to be sampled from. There are many methods for automatically creating such hat functions, but these methods require that the user transforms the density so that she knows the exact location of the transformed density's inflection points. In this paper, we propose an acceptancerejection algorithm which obviates this need and can thus be used to sample from a larger class of distributions. / Series: Research Report Series / Department of Statistics and Mathematics

We study the dynamical behavior of disordered many-particle systems with long-range Coulomb interactions by means of damage-spreading simulations. In this type of Monte-Carlo simulations one investigates the time evolution of the damage, i.e. the difference of the o ccupation numbers of two systems, subjected to the same thermal noise. We analyze the dependence of the damage on temperature and disorder strength. For zero disorder the spreading transition coincides with the equilibrium phase transition, whereas for finite disorder, we find an evidence for a dynamical phase transition well below the transition temperature of the pure system.

There arise two problems when the expectation of some function with respect to a nonuniform multivariate distribution has to be computed by (quasi-) Monte Carlo integration: the integrand can have singularities when the domain of the distribution is unbounded and it can be very expensive or even impossible to sample points from a general multivariate distribution. We show that importance sampling is a simple method to overcome both problems. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

The paper is dedicated to the modeling and the simulation of random processes and fields. Using the concept and the theory of weakly correlated functions a consistent representation of sufficiently smooth random processes will be derived. Special applications will be given with respect to the simulation of road surfaces in vehicle dynamics and to the confirmation of theoretical results with respect to the zeros of random polynomials.

Generating samples from multivariate distributions efficiently is an important task in Monte Carlo integration and many other stochastic simulation problems. Markov chain Monte Carlo has been shown to be very efficient compared to "conventional methods", especially when many dimensions are involved. In this article we propose a Hit-and-Run sampler in combination with the Ratio-of-Uniforms method. We show that it is well suited for an algorithm to generate points from quite arbitrary distributions, which include all log-concave distributions. The algorithm works automatically in the sense that only the mode (or an approximation of it) and an oracle is required, i.e., a subroutine that returns the value of the density function at any point x. We show that the number of evaluations of the density increases slowly with dimension. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Perfect slice sampling is a method to turn Markov Chain Monte Carlo (MCMC) samplers into exact generators for independent random variates. The originally proposed method is rather slow and thus several improvements have been suggested. However, two of them are erroneous. In this article we give a short introduction to perfect slice sampling, point out incorrect methods, and give a new improved version of the original algorithm. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

There are situations in the framework of quasi-Monte Carlo integration where nonuniform low-discrepancy sequences are required. Using the inversion method for this task usually results in the best performance in terms of the integration errors. However, this method requires a fast algorithm for evaluating the inverse of the cumulative distribution function which is often not available. Then a smoothed version of transformed density rejection is a good alternative as it is a fast method and its speed hardly depends on the distribution. It can easily be adjusted such that it is almost as good as the inversion method. For importance sampling it is even better to use the hat distribution as importance distribution directly. Then the resulting algorithm is as good as using the inversion method for the original importance distribution but its generation time is much shorter. / Series: Preprint Series / Department of Applied Statistics and Data Processing