Earl Lawrence

The Coyote Universe Extended: Precision Emulation of the Matter Power Spectrum

Modern sky surveys are returning precision measurements of cosmological statistics such as weak lensing shear correlations, the distribution of galaxies, and cluster abundance. To fully exploit these observations, theorists must provide predictions that are at least as accurate as the measurements, as well as robust estimates of systematic errors that are inherent to the modeling process. In the nonlinear regime of structure formation, this challenge can only be overcome by developing a large-scale, multi-physics simulation capability covering a range of cosmological models and astrophysical processes. As a first step to achieving this goal, we have recently developed a prediction scheme for the matter power spectrum (a so-called emulator), accurate at the 1% level out to k ~ 1 Mpc–1 and z = 1 for wCDM cosmologies based on a set of high-accuracy N-body simulations. It is highly desirable to increase the range in both redshift and wavenumber and to extend the reach in cosmological parameter space. To make progress in this direction, while minimizing computational cost, we present a strategy that maximally reuses the original simulations. We demonstrate improvement over the original spatial dynamic range by an order of magnitude, reaching k ~ 10 h Mpc–1, a four-fold increase in redshift coverage, to z = 4, and now include the Hubble parameter as a new independent variable. To further the range in k and z, a new set of nested simulations run at modest cost is added to the original set. The extension in h is performed by including perturbation theory results within a multi-scale procedure for building the emulator. This economical methodology still gives excellent error control, ~5% near the edges of the domain of applicability of the emulator. A public domain code for the new emulator is released as part of the work presented in this paper.

Network tomography: A review and recent developments

The modeling and analysis of computer communications networks give rise to a variety of interesting statistical problems. This paper focuses on network tomography, a term used to characterize two classes of large-scale inverse problems. The first deals with passive tomography where aggregate data are collected at the individual router/node level and the goal is to recover path-level information. The main problem of interest here is the estimation of the origin-destination traffic matrix. The second, referred to as active tomography, deals with reconstructing link-level information from end-to-end path-level measurements obtained by actively probing the network. The primary application in this case is estimation of quality-of-service parameters such as loss rates and delay distributions. The paper provides a review of the statistical issues and developments in network tomography with an emphasis on active tomography. An application to Internet telephony is used to illustrate the results.

A MILLISECOND INTERFEROMETRIC SEARCH FOR FAST RADIO BURSTS WITH THE VERY LARGE ARRAY

We report on the first millisecond timescale radio interferometric search for the new class of transient known as fast radio bursts (FRBs). We used the Very Large Array (VLA) for a 166-hour, millisecond imaging campaign to detect and precisely localize an FRB. We observed at 1.4 GHz and produced visibilities with 5 ms time resolution over 256 MHz of bandwidth. Dedispersed images were searched for transients with dispersion measures from 0 to 3000 pc/cm3. No transients were detected in observations of high Galactic latitude fields taken from September 2013 though October 2014. Observations of a known pulsar show that images typically had a thermal-noise limited sensitivity of 120 mJy/beam (8 sigma; Stokes I) in 5 ms and could detect and localize transients over a wide field of view. Our nondetection limits the FRB rate to less than 7e4/sky/day (95% confidence) above a fluence limit of 1.2 Jy-ms. Assuming a Euclidean flux distribution, the VLA rate limit is inconsistent with the published rate of Thornton et al. We recalculate previously published rates with a homogeneous consideration of the effects of primary beam attenuation, dispersion, pulse width, and sky brightness. This revises the FRB rate downward and shows that the VLA observations had a roughly 60% chance of detecting a typical FRB and that a 95% confidence constraint would require roughly 500 hours of similar VLA observing. Our survey also limits the repetition rate of an FRB to 2 times less than any known repeating millisecond radio transient.

Bayesian Inference for Multivariate Ordinal Data Using Parameter Expansion

Multivariate ordinal data arise in many applications. This article proposes a new, efficient method for Bayesian inference for multivariate probit models using Markov chain Monte Carlo techniques. The key idea is the novel use of parameter expansion to sample correlation matrices. A nice feature of the approach is that inference is performed using straightforward Gibbs sampling. Bayesian methods for model selection are also discussed. Our approach is motivated by a study of how women make decisions on taking medication to reduce the risk of breast cancer. Furthermore, we compare and contrast the performance of our approach with other methods.

Statistical inverse problems in active network tomography

The analysis of computer and communication networks gives rise to some interesting inverse problems. This paper is concerned with active network tomography where the goal is to recover information about quality-of-service (QoS) parameters at the link level from aggregate data measured on end-to- end network paths. The estimation and monitoring of QoS parameters, such as loss rates and delays, are of considerable interest to network engineers and Internet service providers. The paper provides a review of the inverse problems and recent research on inference for loss rates and delay distributions. Some new results on parametric inference for delay distributions are also developed. In addition, a real application on Internet telephony is discussed.

THE MIRA–TITAN UNIVERSE: PRECISION PREDICTIONS FOR DARK ENERGY SURVEYS

Ground and space-based sky surveys enable powerful cosmological probes based on measurements of galaxy properties and the distribution of galaxies in the Universe. These probes include weak lensing, baryon acoustic oscillations, abundance of galaxy clusters, and redshift space distortions; they are essential to improving our knowledge of the nature of dark energy. On the theory and modeling front, large-scale simulations of cosmic structure formation play an important role in interpreting the observations and in the challenging task of extracting cosmological physics at the needed precision. These simulations must cover a parameter range beyond the standard six cosmological parameters and need to be run at high mass and force resolution. One key simulation-based task is the generation of accurate theoretical predictions for observables, via the method of emulation. Using a new sampling technique, we explore an 8-dimensional parameter space including massive neutrinos and a variable dark energy equation of state. We construct trial emulators using two surrogate models (the linear power spectrum and an approximate halo mass function). The new sampling method allows us to build precision emulators from just 26 cosmological models and to increase the emulator accuracy by adding new sets of simulations in a prescribed way. This allows emulator fidelity to be systematically improved as new observational data becomes available and higher accuracy is required. Finally, using one LCDM cosmology as an example, we study the demands imposed on a simulation campaign to achieve the required statistics and accuracy when building emulators for dark energy investigations.

Cosmic Emulation: Fast Predictions for the Galaxy Power Spectrum

The halo occupation distribution (HOD) approach has proven to be an effective method for modeling galaxy clustering and bias. In this approach, galaxies of a given type are probabilistically assigned to individual halos in N-body simulations. In this paper, we present a fast emulator for predicting the fully nonlinear galaxy–galaxy auto and galaxy–dark matter cross power spectrum and correlation function over a range of freely specifiable HOD modeling parameters. The emulator is constructed using results from 100 HOD models run on a large ΛCDM N-body simulation, with Gaussian Process interpolation applied to a PCA-based representation of the galaxy power spectrum. The total error is currently ∼1% in the auto correlations and ∼2% in the cross correlations from z = 1 to z = 0, over the considered parameter range. We use the emulator to investigate the accuracy of various analytic prescriptions for the galaxy power spectrum, parametric dependencies in the HOD model, and the behavior of galaxy bias as a function of HOD parameters. Additionally, we obtain fully nonlinear predictions for tangential shear correlations induced by galaxy–galaxy lensing from our galaxy–dark matter cross power spectrum emulator. All emulation products are publicly available at http://www.hep.anl.gov/cosmology/CosmicEmu/emu.html.

Line Outage Localization Using Phasor Measurement Data in Transient State

This paper introduces a statistical classifier that quickly locates line outages in a power system utilizing only time series phasor measurement data sampled during the systems transient response to the outage. The presented classifier is a linear multinomial regression model that is trained by solving a maximum likelihood optimization problem using synthetic data. The synthetic data is produced through dynamic simulations which are initialized by random samples of a forecast load/generation distribution. Real time computation of the proposed classifier is minimal and therefore the classifier is capable of locating a line outage before steady state is reached, allowing for quick corrective action in response to an outage. In addition, the output of the classifier fits into a statistical framework that is easily accessible. Specific line outages are identified as being difficult to localize and future improvements to the classifier are proposed.

The Nonhomogeneous Poisson Process for Fast Radio Burst Rates

This paper presents the nonhomogeneous Poisson process (NHPP) for modeling the rate of fast radio bursts (FRBs) and other infrequently observed astronomical events. The NHPP, well-known in statistics, can model the dependence of the rate on both astronomical features and the details of an observing campaign. This is particularly helpful for rare events like FRBs because the NHPP can combine information across surveys, making the most of all available information. The goal of the paper is two-fold. First, it is intended to be a tutorial on the use of the NHPP. Second, we build an NHPP model that incorporates beam patterns and a power-law flux distribution for the rate of FRBs. Using information from 12 surveys including 15 detections, we find an all-sky FRB rate of 587 events per sky per day above a flux of 1 Jy (95% CI: 272, 924) and a flux power-law index of (95% CI: 0.57, 1.25). Our rate is lower than other published rates, but consistent with the rate given in Champion et al.

The Mira-Titan Universe. II. Matter Power Spectrum Emulation

We introduce a new cosmic emulator for the matter power spectrum covering eight cosmological parameters. Targeted at optical surveys, the emulator provides accurate predictions out to a wavenumber k~5/Mpc and redshift z<=2. Besides covering the standard set of LCDM parameters, massive neutrinos and a dynamical dark energy of state are included. The emulator is built on a sample set of 36 cosmological models, carefully chosen to provide accurate predictions over the wide and large parameter space. For each model, we have performed a high-resolution simulation, augmented with sixteen medium-resolution simulations and TimeRG perturbation theory results to provide accurate coverage of a wide k-range; the dataset generated as part of this project is more than 1.2Pbyte. With the current set of simulated models, we achieve an accuracy of approximately 4%. Because the sampling approach used here has established convergence and error-control properties, follow-on results with more than a hundred cosmological models will soon achieve ~1% accuracy. We compare our approach with other prediction schemes that are based on halo model ideas and remapping approaches. The new emulator code is publicly available.