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We apply Markov Chain Monte Carlo (MCMC) to the problem of parametric galaxy modeling, estimating posterior distributions of galaxy properties such as ellipticity and brightness for more than 100,000 images of galaxies taken from DC2, a simulated telescope survey resembling the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST). We use a physically informed prior and apply selection corrections to the likelihood. The resulting posterior samples enable rigorous probabilistic inference of galaxy model parameters and their uncertainties. These posteriors are one key ingredient in a fully probabilistic description of galaxy catalogs, which can ultimately enable a refined Bayesian estimate of cosmological parameters. We systematically examine the reliability of the posterior mean as a point estimator of galaxy parameters, and of the posterior width as a measure of uncertainty, under some common modeling approximations. We implement the probabilistic modeling and MCMC inference using the JIF (Joint Image Framework) tool, which we make freely available online., Comment: 34 pages, 16 figures

We describe an algorithm to solve Bellman optimization that replaces a sum over paths determining the optimal cost-to-go by an analytic method localized in state space. Our approach follows from the established relation between stochastic control problems in the class of linear Markov decision processes and quantum inverse scattering. We introduce a practical online computational method to solve for a potential function that informs optimal agent actions. This approach suggests that optimal control problems, including those with many degrees of freedom, can be solved with parallel computations., Comment: 6 pages, 2 figures

We present a Cross-Entropy based population Monte Carlo algorithm. This methods stands apart from previous work in that we are not optimizing a mixture distribution. Instead, we leverage deterministic mixture weights and optimize the distributions individually through a reinterpretation of the typical derivation of the cross-entropy method. Demonstrations on numerical examples show that the algorithm can outperform existing resampling population Monte Carlo methods, especially for higher-dimensional problems.

A significant fraction of observed galaxies in the Rubin Observatory Legacy Survey of Space and Time (LSST) will overlap at least one other galaxy along the same line of sight, in a so-called "blend." The current standard method of assessing blend likelihood in LSST images relies on counting up the number of intensity peaks in the smoothed image of a blend candidate, but the reliability of this procedure has not yet been comprehensively studied. Here we construct a realistic distribution of blended and unblended galaxies through high-fidelity simulations of LSST-like images, and from this we examine the blend classification accuracy of the standard peak-finding method. Furthermore, we develop a novel Gaussian process blend classifier model, and show that this classifier is competitive with both the peak-finding method as well as with a convolutional neural network model. Finally, whereas the peak-finding method does not naturally assign probabilities to its classification estimates, the Gaussian process model does, and we show that the Gaussian process classification probabilities are generally reliable., Comment: 20 pages, 6 figures, version accepted by ApJ

We introduce a novel method for discerning optical telescope images of stars from those of galaxies using Gaussian processes (GPs). Although applications of GPs often struggle in high-dimensional data modalities such as optical image classification, we show that a low-dimensional embedding of images into a metric space defined by the principal components of the data suffices to produce high-quality predictions from real large-scale survey data. We develop a novel method of GP classification hyperparameter training that scales approximately linearly in the number of image observations, which allows for application of GP models to large-size Hyper Suprime-Cam (HSC) Subaru Strategic Program data. In our experiments we evaluate the performance of a principal component analysis (PCA) embedded GP predictive model against other machine learning algorithms including a convolutional neural network and an image photometric morphology discriminator. Our analysis shows that our methods compare favorably with current methods in optical image classification while producing posterior distributions from the GP regression that can be used to quantify object classification uncertainty. We further describe how classification uncertainty can be used to efficiently parse large-scale survey imaging data to produce high-confidence object catalogs., Comment: 18 pages, 8 figures

As astronomical photometric surveys continue to tile the sky repeatedly, the potential to pushdetection thresholds to fainter limits increases; however, traditional digital-tracking methods cannotachieve this efficiently beyond time scales where motion is approximately linear. In this paper weprototype an optimal detection scheme that samples under a user defined prior on a parameterizationof the motion space, maps these sampled trajectories to the data space, and computes an optimalsignal-matched filter for computing the signal to noise ratio of trial trajectories. We demonstrate thecapability of this method on a small test data set from the Dark Energy Camera. We recover themajority of asteroids expected to appear and also discover hundreds of new asteroids with only a fewhours of observations. We conclude by exploring the potential for extending this scheme to larger datasets that cover larger areas of the sky over longer time baselines., Comment: 28 pages, 12 figures

Systematic errors in the galaxy redshift distribution $n(z)$ can propagate to systematic errors in the derived cosmology. We characterize how the degenerate effects in tomographic bin widths and galaxy bias impart systematic errors on cosmology inference using observational data from the Deep Lens Survey. For this we use a combination of galaxy clustering and galaxy-galaxy lensing. We present two end-to-end analyses from the catalogue level to parameter estimation. We produce an initial cosmological inference using fiducial tomographic redshift bins derived from photometric redshifts, then compare this with a result where the redshift bins are empirically corrected using a set of spectroscopic redshifts. We find that the derived parameter $S_8 \equiv \sigma_8 (\Omega_m/.3)^{1/2}$ goes from $.841^{+0.062}_{-.061}$ to $.739^{+.054}_{-.050}$ upon correcting the n(z) errors in the second method., Comment: 13 pages, 9 figures

We present a Bayesian data fusion method to approximate a posterior distribution from an ensemble of particle estimates that only have access to subsets of the data. Our approach relies on approximate probabilistic inference of model parameters through Monte Carlo methods, followed by an update and resample scheme related to multiple importance sampling to combine information from the initial estimates. We show the method is convergent in the particle limit and directly suited to application on multi-sensor data fusion problems by demonstrating efficacy on a multi-sensor Keplerian orbit determination problem and a bearings-only tracking problem.

Modern cosmological surveys such as the Hyper Suprime-Cam (HSC) survey produce a huge volume of low-resolution images of both distant galaxies and dim stars in our own galaxy. Being able to automatically classify these images is a long-standing problem in astronomy and critical to a number of different scientific analyses. Recently, the challenge of "star-galaxy" classification has been approached with Deep Neural Networks (DNNs), which are good at learning complex nonlinear embeddings. However, DNNs are known to overconfidently extrapolate on unseen data and require a large volume of training images that accurately capture the data distribution to be considered reliable. Gaussian Processes (GPs), which infer posterior distributions over functions and naturally quantify uncertainty, haven't been a tool of choice for this task mainly because popular kernels exhibit limited expressivity on complex and high-dimensional data. In this paper, we present a novel approach to the star-galaxy separation problem that uses GPs and reap their benefits while solving many of the issues traditionally affecting them for classification of high-dimensional celestial image data. After an initial filtering of the raw data of star and galaxy image cutouts, we first reduce the dimensionality of the input images by using a Principal Components Analysis (PCA) before applying GPs using a simple Radial Basis Function (RBF) kernel on the reduced data. Using this method, we greatly improve the accuracy of the classification over a basic application of GPs while improving the computational efficiency and scalability of the method.

Modern surveys of gravitational microlensing events have progressed to detecting thousands per year. Surveys are capable of probing Galactic structure, stellar evolution, lens populations, black hole physics, and the nature of dark matter. One of the key avenues for doing this is studying the microlensing Einstein radius crossing time distribution ($t_E$). However, systematics in individual light curves as well as over-simplistic modeling can lead to biased results. To address this, we developed a model to simultaneously handle the microlensing parallax due to Earth's motion, systematic instrumental effects, and unlensed stellar variability with a Gaussian Process model. We used light curves for nearly 10,000 OGLE-III and IV Milky Way bulge microlensing events and fit each with our model. We also developed a forward model approach to infer the timescale distribution by forward modeling from the data rather than using point estimates from individual events. We find that modeling the variability in the baseline removes a source of significant bias in individual events, and previous analyses over-estimated the number of long timescale ($t_E>100$ days) events due to their over simplistic models ignoring parallax effects and stellar variability. We use our fits to identify hundreds of events that are likely black holes., Comment: Submitted version, in review, 33 pages, 18 figures, MCMC posterior samples available by publisher after acceptance

Quantum computers have the opportunity to be transformative for a variety of computational tasks. Recently, there have been proposals to use the unsimulatably of large quantum devices to perform regression, classification, and other machine learning tasks with quantum advantage by using kernel methods. While unsimulatably is a necessary condition for quantum advantage in machine learning, it is not sufficient, as not all kernels are equally effective. Here, we study the use of quantum computers to perform the machine learning tasks of one- and multi-dimensional regression, as well as reinforcement learning, using Gaussian Processes. By using approximations of performant classical kernels enhanced with extra quantum resources, we demonstrate that quantum devices, both in simulation and on hardware, can perform machine learning tasks at least as well as, and many times better than, the classical inspiration. Our informed kernel design demonstrates a path towards effectively utilizing quantum devices for machine learning tasks.

While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex nonlinear embeddings, but do not naturally quantify uncertainty and are often data-inefficient to train. GPs infer posterior distributions over functions, but popular kernels exhibit limited expressivity on complex and high-dimensional data. Fortunately, recently discovered conjugate and neural tangent kernel functions encode the behavior of overparameterized neural networks in the kernel domain. We demonstrate that these kernels can be efficiently applied to regression and reinforcement learning problems by analyzing a baseline case study. We apply GPs with neural network dual kernels to solve reinforcement learning tasks for the first time. We demonstrate, using the well-understood mountain-car problem, that GPs empowered with dual kernels perform at least as well as those using the conventional radial basis function kernel. We conjecture that by inheriting the probabilistic rigor of GPs and the powerful embedding properties of DNNs, GPs using NN dual kernels will empower future reinforcement learning models on difficult domains., Comment: 22 pages, 5 figures

We infer gravitational lensing shear and convergence fields from galaxy ellipticity catalogs under a spatial process prior for the lensing potential. We demonstrate the performance of our algorithm with simulated Gaussian-distributed cosmological lensing shear maps and a reconstruction of the mass distribution of the merging galaxy cluster Abell 781 using galaxy ellipticities measured with the Deep Lens Survey. Given interim posterior samples of lensing shear or convergence fields on the sky, we describe an algorithm to infer cosmological parameters via lens field marginalization. In the most general formulation of our algorithm we make no assumptions about weak shear or Gaussian distributed shape noise or shears. Because we require solutions and matrix determinants of a linear system of dimension that scales with the number of galaxies, we expect our algorithm to require parallel high-performance computing resources for application to ongoing wide field lensing surveys., Comment: 22 pages, 17 figures, submitted, comments welcome

We present a Bayesian algorithm to combine optical imaging of unresolved objects from distinct epochs and observation platforms for orbit determination and tracking. By propagating the non-Gaussian uncertainties we are able to optimally combine imaging of arbitrary signal-to-noise ratios, allowing the integration of data from low-cost sensors. Our Bayesian approach to image characterization also allows large compression of imaging data without loss of statistical information. With a computationally efficient algorithm to combine multiple observation epochs and multiple telescopes, we show statistically optimal orbit inferences., Comment: 8 pages, 6 figures, contribution to Advanced Maui Optical and Space Surveillance Technologies Conference 2016

We have developed a maximum likelihood source detection method capable of detecting ultra-faint streaks with surface brightnesses approximately an order of magnitude fainter than the pixel level noise. Our maximum likelihood detection method is a model based approach that requires no a priori knowledge about the streak location, orientation, length, or surface brightness. This method enables discovery of typically undiscovered objects, and enables the utilization of low-cost sensors (i.e., higher-noise data). The method also easily facilitates multi-epoch co-addition. We will present the results from the application of this method to simulations, as well as real low earth orbit observations., Comment: 11 pages, 7 figures, contribution to the Advanced Maui Optical and Space Surveillance Technologies Conference 2016

We present a tomographic cosmic shear study from the Deep Lens Survey (DLS), which, providing a limiting magnitude r_{lim}~27 (5 sigma), is designed as a pre-cursor Large Synoptic Survey Telescope (LSST) survey with an emphasis on depth. Using five tomographic redshift bins, we study their auto- and cross-correlations to constrain cosmological parameters. We use a luminosity-dependent nonlinear model to account for the astrophysical systematics originating from intrinsic alignments of galaxy shapes. We find that the cosmological leverage of the DLS is among the highest among existing >10 sq. deg cosmic shear surveys. Combining the DLS tomography with the 9-year results of the Wilkinson Microwave Anisotropy Probe (WMAP9) gives Omega_m=0.293_{-0.014}^{+0.012}, sigma_8=0.833_{-0.018}^{+0.011}, H_0=68.6_{-1.2}^{+1.4} km/s/Mpc, and Omega_b=0.0475+-0.0012 for LCDM, reducing the uncertainties of the WMAP9-only constraints by ~50%. When we do not assume flatness for LCDM, we obtain the curvature constraint Omega_k=-0.010_{-0.015}^{+0.013} from the DLS+WMAP9 combination, which however is not well constrained when WMAP9 is used alone. The dark energy equation of state parameter w is tightly constrained when Baryonic Acoustic Oscillation (BAO) data are added, yielding w=-1.02_{-0.09}^{+0.10} with the DLS+WMAP9+BAO joint probe. The addition of supernova constraints further tightens the parameter to w=-1.03+-0.03. Our joint constraints are fully consistent with the final Planck results and also the predictions of a LCDM universe., Comment: Accepted for publication in ApJ

We present first results from the third GRavitational lEnsing Accuracy Testing (GREAT3) challenge, the third in a sequence of challenges for testing methods of inferring weak gravitational lensing shear distortions from simulated galaxy images. GREAT3 was divided into experiments to test three specific questions, and included simulated space- and ground-based data with constant or cosmologically-varying shear fields. The simplest (control) experiment included parametric galaxies with a realistic distribution of signal-to-noise, size, and ellipticity, and a complex point spread function (PSF). The other experiments tested the additional impact of realistic galaxy morphology, multiple exposure imaging, and the uncertainty about a spatially-varying PSF; the last two questions will be explored in Paper II. The 24 participating teams competed to estimate lensing shears to within systematic error tolerances for upcoming Stage-IV dark energy surveys, making 1525 submissions overall. GREAT3 saw considerable variety and innovation in the types of methods applied. Several teams now meet or exceed the targets in many of the tests conducted (to within the statistical errors). We conclude that the presence of realistic galaxy morphology in simulations changes shear calibration biases by $\sim 1$ per cent for a wide range of methods. Other effects such as truncation biases due to finite galaxy postage stamps, and the impact of galaxy type as measured by the S\'{e}rsic index, are quantified for the first time. Our results generalize previous studies regarding sensitivities to galaxy size and signal-to-noise, and to PSF properties such as seeing and defocus. Almost all methods' results support the simple model in which additive shear biases depend linearly on PSF ellipticity., Comment: 32 pages + 15 pages of technical appendices; 28 figures; published in MNRAS; all data and other information may be found at https://github.com/barnabytprowe/great3-public as the GREAT3 website and leaderboard are no longer live. v3 has updates to this comment only

Point estimators for the shearing of galaxy images induced by gravitational lensing involve a complex inverse problem in the presence of noise, pixelization, and model uncertainties. We present a probabilistic forward modeling approach to gravitational lensing inference that has the potential to mitigate the biased inferences in most common point estimators and is practical for upcoming lensing surveys. The first part of our statistical framework requires specification of a likelihood function for the pixel data in an imaging survey given parameterized models for the galaxies in the images. We derive the lensing shear posterior by marginalizing over all intrinsic galaxy properties that contribute to the pixel data (i.e., not limited to galaxy ellipticities) and learn the distributions for the intrinsic galaxy properties via hierarchical inference with a suitably flexible conditional probabilitiy distribution specification. We use importance sampling to separate the modeling of small imaging areas from the global shear inference, thereby rendering our algorithm computationally tractable for large surveys. With simple numerical examples we demonstrate the improvements in accuracy from our importance sampling approach, as well as the significance of the conditional distribution specification for the intrinsic galaxy properties when the data are generated from an unknown number of distinct galaxy populations with different morphological characteristics., Comment: 23 pages, 9 figures, submitted, related to the 'MBI' team submissions to the GREAT3 gravitational lensing community challenge

Using overlapping fields with space-based Hubble Space Telescope (HST) and ground-based Subaru Telescope imaging we identify a population of blended galaxies that are blended to such a large degree that they are detected as single objects in the ground-based monochromatic imaging, which we label as 'ambiguous blends'. For deep imaging data, such as the depth targeted with the Large Synoptic Survey Telescope (LSST), the ambiguous blend population is both large ($\sim 14$%) and has a distribution of ellipticities that is different from that of unblended objects in a way that will likely be important for the weak lensing measurements. Most notably, for a limiting magnitude of $i \sim 27$ we find that ambiguous blending results in a ~14% increase in shear noise (or ~12% decrease in the effective projected number density of lensed galaxies; neff) due to 1) larger intrinsic ellipticity dispersion, 2) a scaling with the galaxy number density $N_{gal}$ that is shallower than 1/$\sqrt{N_{gal}}$. For the LSST Gold Sample ($i < 25.3$) there is a ~7% increase in shear noise (or ~7% decrease in $n_{eff}$). More importantly than these increases in the shear noise, we find that the ellipticity distribution of ambiguous blends has an RMS 13% larger than that of non-blended galaxies. Given the need of future weak lensing surveys to constrain the ellipticity distribution of galaxies to better than a percent in order to mitigate cosmic shear multiplicative biases, the different ellipticity distribution of ambiguous blends could be a dominant systematic if unaccounted for., Comment: Accepted ApJ, 11 pages, 6 figures

We present a maximum-likelihood weak lensing analysis of the mass distribution in optically selected spectroscopic Galaxy Groups (G$^3$Cv5) in the Galaxy And Mass Assembly (GAMA) survey, using background Sloan Digital Sky Survey (SDSS) photometric galaxies. The scaling of halo mass, $M_h$, with various group observables is investigated. Our main results are: 1) the measured relations of halo mass with group luminosity, virial volume and central galaxy stellar mass, $M_\star$, agree very well with predictions from mock group catalogues constructed from a GALFORM semi-analytical galaxy formation model implemented in the Millennium $\Lambda$CDM N-body simulation; 2) the measured relations of halo mass with velocity dispersion and projected half-abundance radius show weak tension with mock predictions, hinting at problems in the mock galaxy dynamics and their small scale distribution; 3) the median $M_h|M_\star$ measured from weak lensing depends more sensitively on the lognormal dispersion in $M_\star$ at fixed $M_h$ than it does on the median $M_\star|M_h$. Our measurements suggest an intrinsic dispersion of $\sigma_{\log(M_\star)}\sim 0.15$; 4) Comparing our mass estimates with those in the catalogue, we find that the G$^3$Cv5 mass can give biased results when used to select subsets of the group sample. Of the various new halo mass estimators that we calibrate using our weak lensing measurements, group luminosity is the best single-proxy estimator of group mass., Comment: MNRAS accepted

I present an estimator for the angular cross-correlation of two tracers of the cosmological large-scale structure that utilizes redshift information to isolate separate physical contributions. The estimator is derived by solving the Limber equation for a re-weighting of the foreground tracer that nulls either clustering or lensing contributions to the cross-correlation function. Applied to future photometric surveys, the estimator can enhance the measurement of gravitational lensing magnification effects to provide a competitive independent constraint on the dark energy equation of state., Comment: 5 pages, 3 figures, accepted for publication in PRL

We constrain the distributions of projected radial alignment angles of satellite galaxy shapes within the Galaxy And Mass Assembly survey group catalogue. We identify the galaxy groups using spectroscopic redshifts and measure galaxy projected ellipticities from Sloan Digital Sky Survey imaging. With a sample of 3,850 groups with 13,655 satellite galaxies with high quality shape measurements, we find a less than 2-sigma signal of radial alignments in the mean projected ellipticity components and the projected position angle when using galaxy shape estimates optimized for weak lensing measurements. Our radial alignment measurement increases to greater than 3-sigma significance relative to the expectation for no alignments if we use 2-D S\'ersic model fits to define galaxy orientations. Our weak measurement of radial alignments is in conflict with predictions from dark matter N-body simulations, which we interpret as evidence for large mis-alignments of baryons and dark matter in group and cluster satellites. Within our uncertainties, that are dominated by our small sample size, we find only weak and marginally significant trends of the radial alignment angle distributions on projected distance from the group centre, host halo mass, and redshift that could be consistent with a tidal torquing mechanism for radial alignments. Using our lensing optimized shape estimators, we estimate that intrinsic alignments of galaxy group members may contribute a systematic error to the mean differential projected surface mass density of groups inferred from weak lensing observations by -1 +/- 20% at scales around 300 kpc/h from the group centre assuming a photometric redshift r.m.s. error of 10%, and given our group sample with median redshift of 0.17 and median virial masses ~10^{13} h^{-1}M_{sun}., Comment: 14 pages, 11 figures, accepted for publication in MNRAS

We describe a statistical model to estimate the covariance matrix of matter tracer two-point correlation functions with cosmological simulations. Assuming a fixed number of cosmological simulation runs, we describe how to build a `statistical emulator' of the two-point function covariance over a specified range of input cosmological parameters. Because the simulation runs with different cosmological models help to constrain the form of the covariance, we predict that the cosmology-dependent covariance may be estimated with a comparable number of simulations as would be needed to estimate the covariance for fixed cosmology. Our framework is a necessary first step in planning a simulations campaign for analyzing the next generation of cosmological surveys., Comment: 17 pages, 7 Figures, Submitted to JCAP

Extracting parameter constraints from cosmological observations requires accurate determination of the covariance matrix for use in the likelihood function. We show here that uncertainties in the elements of the covariance matrix propagate directly to increased uncertainties in cosmological parameters. When the covariance matrix is determined by simulations, the resulting variance of the each parameter increases by a factor of order $1+N_b/N_s$ where $N_b$ is the number of bands in the measurement and $N_s$ is the number of simulations., Comment: 5 pages, 1 figure. Matches version accepted for publication in PRD

We present a cosmic shear study from the Deep Lens Survey (DLS), a deep BVRz multi-band imaging survey of five 4 sq. degree fields with two National Optical Astronomy Observatory (NOAO) 4-meter telescopes at Kitt Peak and Cerro Tololo. For both telescopes, the change of the point-spread-function (PSF) shape across the focal plane is complicated, and the exposure-to-exposure variation of this position-dependent PSF change is significant. We overcome this challenge by modeling the PSF separately for individual exposures and CCDs with principal component analysis (PCA). We find that stacking these PSFs reproduces the final PSF pattern on the mosaic image with high fidelity, and the method successfully separates PSF-induced systematics from gravitational lensing effects. We calibrate our shears and estimate the errors, utilizing an image simulator, which generates sheared ground-based galaxy images from deep Hubble Space Telescope archival data with a realistic atmospheric turbulence model. For cosmological parameter constraints, we marginalize over shear calibration error, photometric redshift uncertainty, and the Hubble constant. We use cosmology-dependent covariances for the Markov Chain Monte Carlo analysis and find that the role of this varying covariance is critical in our parameter estimation. Our current non-tomographic analysis alone constrains the Omega_M-sigma_8 likelihood contour tightly, providing a joint constraint of Omega_M=0.262+-0.051 and sigma_8=0.868+-0.071. We expect that a future DLS weak-lensing tomographic study will further tighten these constraints because explicit treatment of the redshift dependence of cosmic shear more efficiently breaks the Omega_M-sigma_8 degeneracy. Combining the current results with the Wilkinson Microwave Anisotropy Probe 7-year (WMAP7) likelihood data, we obtain Omega_M=0.278+-0.018 and sigma_8=0.815+-0.020., Comment: Accepted to ApJ. Replaced with the accepted version

We present measurements of a population of matched radio sources at 1.4 and 5 GHz down to a flux limit of 1.5 mJy in 7 sq. degs. of the NOAO Deep Field South. We find a significant fraction of sources with inverted spectral indices that all have 1.4 GHz fluxes less than 10 mJy, and are therefore too faint to have been detected and included in previous radio source count models that are matched at multiple frequencies. Combined with the matched source population at 1.4 and 5 GHz in 1 sq. deg. in the ATESP survey, we update models for the 5 GHz differential number counts and distributions of spectral indices in 5 GHz flux bins that can be used to estimate the unresolved point source contribution to the cosmic microwave background temperature anisotropies. We find a shallower logarithmic slope in the 5 GHz differential counts than in previously published models for fluxes < 100 mJy as well as larger fractions of inverted spectral indices at these fluxes. Because the Planck flux limit for resolved sources is larger than 100 mJy in all channels, our modified number counts yield at most a 10% change in the predicted Poisson contribution to the Planck temperature power spectrum. For a flux cut of 5 mJy with the South Pole Telescope and a flux cut of 20 mJy with the Atacama Cosmology Telescope we predict a ~30% and ~10% increase, respectively, in the radio source Poisson power in the lowest frequency channels of each experiment relative to that predicted by previous models., Comment: 14 pages, 9 figures, includes ApJ proof corrections

We present measurements of the triaxial dark matter halo shapes and alignment correlation functions in the Millennium and Millennium-2 dark matter N-body simulations. These two simulations allow us to measure the distributions of halo shapes down to 10% of the virial radius over a halo mass range of 6E9 - 2E14 M_sun/h. We largely confirm previous results on the distributions of halo axis ratios as a function of halo mass, but we find that the median angle between halo major axes at different halo radii can vary by a factor of 2 between the Millennium-1 and 2 simulations because of the different mass resolution. Thus, error in the shape determinations from limited resolution is potentially degenerate with the misalignment of halo inner and outer shapes used to constrain Brightest Cluster Galaxy alignments in previous works. We also present simplifying parameterizations for the 3-D halo-mass alignment correlation functions that are necessary ingredients for triaxial halo models of large-scale structure and models of galaxy intrinsic alignments as contaminants for cosmic shear surveys. We measure strong alignments between halos of all masses and the surrounding dark matter overdensities out to several tens of Mpc/h, in agreement with observed shear-galaxy and cluster shape correlations. We use these measurements to forecast the contribution to the weak lensing signal around galaxy clusters from correlated mass along the line-of-sight. For prolate clusters with major axes aligned with the line-of-sight the fraction of the weak lensing signal from mass external to the cluster can be twice that predicted if the excess halo alignment correlation is assumed to be zero., Comment: 44 pages, 21 figures, submitted to JCAP, includes referee revisions

We describe a Bayesian sampling model for linking and constraining orbit models from angular observations of "streaks" in optical telescope images. Our algorithm is particularly suited to situations where the observation times are small fractions of the orbital periods of the observed objects or when there is significant confusion of objects in the observation field. We use Markov Chain Monte Carlo to sample from the joint posterior distribution of the parameters of multiple orbit models (up to the number of observed tracks) and parameters describing which tracks are linked with which orbit models. Using this algorithm, we forecast the constraints on geosynchronous (GEO) debris orbits achievable with the planned Large Synoptic Survey Telescope (LSST). Because of the short 15 second exposure times, preliminary orbit determinations of GEO objects from LSST will have large and degenerate errors on the orbital elements. Combined with the expected crowded fields of GEO debris it will be challenging to reliably link orbital tracks in LSST observations given the currently planned observing cadence., Comment: 12 pages, 6 figures. Accepted for publication in Advances in Space Research

We present an algorithm for quickly generating multiple realizations of N-body simulations to be used, for example, for cosmological parameter estimation from surveys of large-scale structure. Our algorithm uses a new method to resample the large-scale (Gaussian-distributed) Fourier modes in a periodic N-body simulation box in a manner that properly accounts for the nonlinear mode-coupling between large and small scales. We find that our method for adding new large-scale mode realizations recovers the nonlinear power spectrum to sub-percent accuracy on scales larger than about half the Nyquist frequency of the simulation box. Using 20 N-body simulations, we obtain a power spectrum covariance matrix estimate that matches the estimator in Takahashi et al. (2009) (from 5000 simulations) with < 20% errors in all matrix elements. Comparing the rates of convergence, we determine that our algorithm requires ~ 8 times fewer simulations to achieve a given error tolerance in estimates of the power spectrum covariance matrix. The degree of success of our algorithm indicates that we understand the main physical processes that give rise to the correlations in the matter power spectrum. Namely, the large-scale Fourier modes modulate both the degree of structure growth through the variation in the effective local matter density and also the spatial frequency of small-scale perturbations through large-scale displacements. We expect our algorithm to be useful for noise modeling when constraining cosmological parameters from weak lensing (cosmic shear) and galaxy surveys, rescaling summary statistics of N-body simulations for new cosmological parameter values, and any applications where the influence of Fourier modes larger than the simulation size must be accounted for., Comment: 13 pages, 11 figures. Matches version accepted for publication in ApJ. New panel in fig. 11 showing the covariance convergence rate with the number of mode resamplings

Aims: We outline the Bayesian approach to inferring f_NL, the level of non-Gaussianity of local type. Phrasing f_NL inference in a Bayesian framework takes advantage of existing techniques to account for instrumental effects and foreground contamination in CMB data and takes into account uncertainties in the cosmological parameters in an unambiguous way. Methods: We derive closed form expressions for the joint posterior of f_NL and the reconstructed underlying curvature perturbation, Phi, and deduce the conditional probability densities for f_NL and Phi. Completing the inference problem amounts to finding the marginal density for f_NL. For realistic data sets the necessary integrations are intractable. We propose an exact Hamiltonian sampling algorithm to generate correlated samples from the f_NL posterior. For sufficiently high signal-to-noise ratios, we can exploit the assumption of weak non-Gaussianity to find a direct Monte Carlo technique to generate independent samples from the posterior distribution for f_NL. We illustrate our approach using a simplified toy model of CMB data for the simple case of a 1-D sky. Results: When applied to our toy problem, we find that, in the limit of high signal-to-noise, the sampling efficiency of the approximate algorithm outperforms that of Hamiltonian sampling by two orders of magnitude. When f_NL is not significantly constrained by the data, the more efficient, approximate algorithm biases the posterior density towards f_NL = 0., Comment: 11 pages, 7 figures. Accepted for publication in Astronomy and Astrophysics

Simulation design is the choice of locations in parameter space at which simulations are to be run and is the first step in building an emulator capable of quickly providing estimates of simulation results for arbitrary locations in the parameter space. We introduce an alteration to the "OALHS" design used by Heitmann et al. (2006) that reduces the number of simulation runs required to achieve a fixed accuracy in our case study by a factor of two. We also compare interpolation procedures for emulators and find that interpolation via Gaussian Process models and via the much-easier-to-implement polynomial interpolation have comparable accuracy. A very simple emulation-building procedure consisting of a design sampled from the parameter prior distribution, combined with interpolation via polynomials also performs well. Although our primary motivation is efficient emulators of non-linear cosmological N-body simulations, in an appendix we describe an emulator for the CMB temperature power spectrum publicly available as computer code., Comment: 13 pages, 13 figures, Matches version to be published in ApJ. Emulator code available at http://www.emucmb.info

Correlations between intrinsic ellipticities of galaxies are a potentially important systematic error when constraining dark energy properties from weak gravitational lensing (cosmic shear) surveys. In the absence of perfectly known galaxy redshifts some modeling of the galaxy intrinsic alignments is likely to be required to extract the lensing signal to sufficient accuracy. We present a new model based on the placement of galaxies into dark matter halos. The central galaxy ellipticity follows the large scale potential and, in the simplest case, the satellite galaxies point at the halo center. The two-halo term is then dominated by the linear alignment model and the one-halo term provides a motivated extension of intrinsic alignment models to small scales. We provide fitting formulae for the spatial projected source power spectra for both intrinsic-intrinsic (II) and shear-intrinsic (GI) correlations. We illustrate the potential impact of ignoring intrinsic alignments on cosmological parameter constraints from non-tomographic surveys, finding that sigma_8 could be underestimated by up to the size of the current 1-sigma error bar from cosmic shear if very small scales are included in the analysis. Finally, we highlight areas of interest for numerical simulations of dark matter clustering and galaxy formation that can further constrain the intrinsic alignment signal., Comment: 16 pages, 11 figures, submitted to PRD

We describe an approximate statistical model for the sample variance distribution of the non-linear matter power spectrum that can be calibrated from limited numbers of simulations. Our model retains the common assumption of a multivariate Normal distribution for the power spectrum band powers, but takes full account of the (parameter dependent) power spectrum covariance. The model is calibrated using an extension of the framework in Habib et al. (2007) to train Gaussian processes for the power spectrum mean and covariance given a set of simulation runs over a hypercube in parameter space. We demonstrate the performance of this machinery by estimating the parameters of a power-law model for the power spectrum. Within this framework, our calibrated sample variance distribution is robust to errors in the estimated covariance and shows rapid convergence of the posterior parameter constraints with the number of training simulations., Comment: 14 pages, 3 figures, matches final version published in PRD

(Abridged) We describe here the most ambitious survey currently planned in the optical, the Large Synoptic Survey Telescope (LSST). A vast array of science will be enabled by a single wide-deep-fast sky survey, and LSST will have unique survey capability in the faint time domain. The LSST design is driven by four main science themes: probing dark energy and dark matter, taking an inventory of the Solar System, exploring the transient optical sky, and mapping the Milky Way. LSST will be a wide-field ground-based system sited at Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m effective) primary mirror, a 9.6 deg$^2$ field of view, and a 3.2 Gigapixel camera. The standard observing sequence will consist of pairs of 15-second exposures in a given field, with two such visits in each pointing in a given night. With these repeats, the LSST system is capable of imaging about 10,000 square degrees of sky in a single filter in three nights. The typical 5$\sigma$ point-source depth in a single visit in $r$ will be $\sim 24.5$ (AB). The project is in the construction phase and will begin regular survey operations by 2022. The survey area will be contained within 30,000 deg$^2$ with $\delta<+34.5^\circ$, and will be imaged multiple times in six bands, $ugrizy$, covering the wavelength range 320--1050 nm. About 90\% of the observing time will be devoted to a deep-wide-fast survey mode which will uniformly observe a 18,000 deg$^2$ region about 800 times (summed over all six bands) during the anticipated 10 years of operations, and yield a coadded map to $r\sim27.5$. The remaining 10\% of the observing time will be allocated to projects such as a Very Deep and Fast time domain survey. The goal is to make LSST data products, including a relational database of about 32 trillion observations of 40 billion objects, available to the public and scientists around the world., Comment: 57 pages, 32 color figures, version with high-resolution figures available from https://www.lsst.org/overview