Using parallel computation to improve Independent Metropolis--Hastings based estimation

In this paper, we consider the implications of the fact that parallel raw-power can be exploited by a generic Metropolis--Hastings algorithm if the proposed values are independent. In particular, we present improvements to the independent Metropolis--Hastings algorithm that significantly decrease the variance of any estimator derived from the MCMC output, for a null computing cost since those improvements are based on a fixed number of target density evaluations. Furthermore, the techniques developed in this paper do not jeopardize the Markovian convergence properties of the algorithm, since they are based on the Rao--Blackwell principles of Gelfand and Smith (1990), already exploited in Casella and Robert (1996), Atchade and Perron (2005) and Douc and Robert (2010). We illustrate those improvements both on a toy normal example and on a classical probit regression model, but stress the fact that they are applicable in any case where the independent Metropolis-Hastings is applicable.Comment: 19 pages, 8 figures, to appear in Journal of Computational and Graphical Statistic

The H-test probability distribution revisited: Improved sensitivity

Aims: To provide a significantly improved probability distribution for the H-test for periodicity in X-ray and $\gamma$-ray arrival times, which is already extensively used by the $\gamma$-ray pulsar community. Also, to obtain an analytical probability distribution for stacked test statistics in the case of a search for pulsed emission from an ensemble of pulsars where the significance per pulsar is relatively low, making individual detections insignificant on their own. This information is timely given the recent rapid discovery of new pulsars with the Fermi-LAT t $\gamma$-ray telescope. Methods: Approximately $10^{14}$ realisations of the H-statistic ($H$) for random (white) noise is calculated from a random number generator for which the repitition cycle is $\gg 10^{14}$. From these numbers the probability distribution $P(>H)$ is calculated. Results: The distribution of $H$ is is found to be exponential with parameter $\lambda=0.4$ so that the cumulative probability distribution $P(>H)=\exp{(-\lambda H)}$. If we stack independent values for $H$, the sum of $K$ such values would follow the Erlang-K distribution with parameter $\lambda$ for which the cumulative probability distribution is also a simple analytical expression. Conclusion: Searches for weak pulsars with unknown pulse profile shapes in the Fermi-LAT, Agile or other X-ray data bases should benefit from the {\it H-test} since it is known to be powerful against a broad range of pulse profiles, which introduces only a single statistical trial if only the {\it H-test} is used. The new probability distribution presented here favours the detection of weaker pulsars in terms of an improved sensitivity relative to the previously known distribution.Comment: 4 pages, two figures, to appear in Astronomy and Astrophysics, Letter

The Scythe Statistical Library: An Open Source C++ Library for Statistical Computation

The Scythe Statistical Library is an open source C++ library for statistical computation. It includes a suite of matrix manipulation functions, a suite of pseudo-random number generators, and a suite of numerical optimization routines. Programs written using Scythe are generally much faster than those written in commonly used interpreted languages, such as R and \proglang{MATLAB}; and can be compiled on any system with the GNU GCC compiler (and perhaps with other C++ compilers). One of the primary design goals of the Scythe developers has been ease of use for non-expert C++ programmers. Ease of use is provided through three primary mechanisms: (1) operator and function over-loading, (2) numerous pre-fabricated utility functions, and (3) clear documentation and example programs. Additionally, Scythe is quite flexible and entirely extensible because the source code is available to all users under the GNU General Public License.

JAPARA - A Java parallel random number generator library for high-performance computing

Copyright © 2004 IEEERandom number generators are one of the most common numerical library functions used in scientific applications. The standard random number generator provided within Java is fine for most purposes, however it does not adequately meet the needs of large-scale scientific applications, such as Monte Carlo simulations. Previous work has addressed some of these problems by extending the standard Random API in Java and providing an implementation that includes a choice of several different generator algorithms. One issue that was not addressed in this work was concurrency. Implementations of the standard Java random number generator use synchronized methods to support the use of the generator across multiple Java threads, however this is a sequential bottleneck for parallel applications. Here we present a proposal for further extending the standard API to support parallel generation of random number streams, which we have implemented in JAPARA, a Java Parallel Random Number Generator Library for high-performance computing.P. D. Coddington, A. J. Newel

Capacity Planning of a Commodity Cluster in an Academic Environment: A Case Study

In this paper, the design of a simulation model for evaluating two alternative supercomputer configurations in an academic environment is presented. The workload is analyzed and modeled, and its effect on the relative performance of both systems is studied. The Integrated Capacity Planning Environment (ICPE) toolkit, developed for commodity cluster capacity planning, is successfully applied to the target environment. The ICPE is a tool for workload modeling, simulation modeling, and what-if analysis. A new characterization strategy is applied to the workload to more accurately model commodity cluster work- loads. Through what-if analysis, the sensitivity of the baseline system performance to workload change, and also the relative performance of the two proposed alternative systems are compared and evaluated. This case study demonstrates the usefulness of the methodology and the applicability of the tools in gauging system capacity and making design decisions

How to Correctly Deal With Pseudorandom Numbers in Manycore Environments - Application to GPU programming with Shoverand

International audienceStochastic simulations are often sensitive to the source of randomness that character-izes the statistical quality of their results. Consequently, we need highly reliable Random Number Generators (RNGs) to feed such applications. Recent developments try to shrink the computa-tion time by relying more and more General Purpose Graphics Processing Units (GP-GPUs) to speed-up stochastic simulations. Such devices bring new parallelization possibilities, but they also introduce new programming difficulties. Since RNGs are at the base of any stochastic simulation, they also need to be ported to GP-GPU. There is still a lack of well-designed implementations of quality-proven RNGs on GP-GPU platforms. In this paper, we introduce ShoveRand, a frame-work defining common rules to generate random numbers uniformly on GP-GPU. Our framework is designed to cope with any GPU-enabled development platform and to expose a straightfor-ward interface to users. We also provide an existing RNG implementation with this framework to demonstrate its efficiency in both development and ease of use