Publications
128 results found
Shariff H, Dhawan S, Jiao X, et al., 2016, Standardizing type Ia supernovae optical brightness using near infrared rebrightening time, Monthly Notices of the Royal Astronomical Society, Vol: 463, Pages: 4311-4316, ISSN: 1365-2966
Accurate standardization of Type Ia supernovae (SNIa) is instrumental to theusage of SNIa as distance indicators. We analyse a homogeneous sample of 22 lowzSNIa, observed by the Carnegie Supernova Project (CSP) in the optical and nearinfra-red (NIR). We study the time of the second peak in the J-band, t2, as an alternativestandardization parameter of SNIa peak optical brightness, as measured by thestandard SALT2 parameter mB. We use BAHAMAS, a Bayesian hierarchical modelfor SNIa cosmology, to estimate the residual scatter in the Hubble diagram.We find that in the absence of a colour correction, t2 is a better standardizationparameter compared to stretch: t2 has a 1σ posterior interval for the Hubble residualscatter of σ∆µ = {0.250, 0.257} mag, compared to σ∆µ = {0.280, 0.287} mag whenstretch (x1) alone is used. We demonstrate that when employed together with a colourcorrection, t2 and stretch lead to similar residual scatter. Using colour, stretch andt2 jointly as standardization parameters does not result in any further reduction inscatter, suggesting that t2 carries redundant information with respect to stretch andcolour. With a much larger SNIa NIR sample at higher redshift in the future, t2 couldbe a useful quantity to perform robustness checks of the standardization procedure.
Wagner-Kaiser R, Stenning D, Sarajedini A, et al., 2016, Bayesian analysis of two stellar populations in Galactic globular clusters III: Analysis of 30 clusters, Monthly Notices of the Royal Astronomical Society, Vol: 463, Pages: 3768-3782, ISSN: 1365-2966
We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival ACSTreasury observations of 30 Galactic Globular Clusters to characterize two distinctstellar populations. A sophisticated Bayesian technique is employed to simultaneouslysample the joint posterior distribution of age, distance, and extinction for each cluster,as well as unique helium values for two populations within each cluster and therelative proportion of those populations. We find the helium differences among thetwo populations in the clusters fall in the range of ∼0.04 to 0.11. Because adequatemodels varying in CNO are not presently available, we view these spreads as upperlimits and present them with statistical rather than observational uncertainties. Evidencesupports previous studies suggesting an increase in helium content concurrentwith increasing mass of the cluster and also find that the proportion of the first populationof stars increases with mass as well. Our results are examined in the context ofproposed globular cluster formation scenarios. Additionally, we leverage our Bayesiantechnique to shed light on inconsistencies between the theoretical models and theobserved data.
Jeffery EJ, von Hippel T, van Dyk D, et al., 2016, A BAYESIAN ANALYSIS OF THE AGES OF FOUR OPEN CLUSTERS, Astrophysical Journal, Vol: 828, ISSN: 1538-4357
In this paper we apply a Bayesian technique to determine the best fit of stellar evolution modelsto find the main sequence turn off age and other cluster parameters of four intermediate-age openclusters: NGC 2360, NGC 2477, NGC 2660, and NGC 3960. Our algorithm utilizes a Markov chainMonte Carlo technique to fit these various parameters, objectively finding the best fit isochrone foreach cluster. The result is a high precision isochrone fit. We compare these results with the those oftraditional “by eye” isochrone fitting methods. By applying this Bayesian technique to NGC 2360,NGC 2477, NGC 2660, and NGC 3960 we determine the ages of these clusters to be 1.35 ± 0.05,1.02 ± 0.02, 1.64 ± 0.04, and 0.860 ± 0.04 Gyr, respectively. The results of this paper continue oureffort to determine cluster ages to higher precision than that offered by these traditional methods ofisochrone fitting.
Shariff H, Jiao X, Trotta R, et al., 2016, Bahamas: new analysis of type Ia supernovae reveals inconsistencies with standard cosmology, The Astrophysical Journal, Vol: 827, ISSN: 1538-4357
We present results obtained by applying our BAyesian HierArchical Modeling for the Analysis of Supernova cosmology (BAHAMAS) software package to the 740 spectroscopically confirmed supernovae of type Ia (SNe Ia) from the "Joint Light-curve Analysis" (JLA) data set. We simultaneously determine cosmological parameters and standardization parameters, including corrections for host galaxy mass, residual scatter, and object-by-object intrinsic magnitudes. Combining JLA and Planck data on the cosmic microwave background, we find significant discrepancies in cosmological parameter constraints with respect to the standard analysis: we find ${{\rm{\Omega }}}_{{\rm{m}}}=0.399\pm 0.027$, $2.8\sigma $ higher than previously reported, and $w=-0.910\pm 0.045$, $1.6\sigma $ higher than the standard analysis. We determine the residual scatter to be ${\sigma }_{{\rm{res}}}=0.104\pm 0.005$. We confirm (at the 95% probability level) the existence of two subpopulations segregated by host galaxy mass, separated at ${\mathrm{log}}_{10}(M/{M}_{\odot })=10$, differing in mean intrinsic magnitude by 0.055 ± 0.022 mag, lower than previously reported. Cosmological parameter constraints, however, are unaffected by the inclusion of corrections for host galaxy mass. We find $\sim 4\sigma $ evidence for a sharp drop in the value of the color correction parameter, $\beta (z)$, at a redshift ${z}_{t}=0.662\pm 0.055$. We rule out some possible explanations for this behavior, which remains unexplained.
Wong RKW, Kashyap VL, Lee TCM, et al., 2016, Detecting abrupt changes in the spectra of high-energy astrophysical sources, Annals of Applied Statistics, Vol: 10, Pages: 1107-1134, ISSN: 1941-7330
Variable-intensity astronomical sources are the result of complex and often extreme physical processes. Abrupt changes in source intensity are typically accompanied by equally sudden spectral shifts, that is, sudden changes in the wavelength distribution of the emission. This article develops a method for modeling photon counts collected from observation of such sources. We embed change points into a marked Poisson process, where photon wavelengths are regarded as marks and both the Poisson intensity parameter and the distribution of the marks are allowed to change. To the best of our knowledge, this is the first effort to embed change points into a marked Poisson process. Between the change points, the spectrum is modeled nonparametrically using a mixture of a smooth radial basis expansion and a number of local deviations from the smooth term representing spectral emission lines. Because the model is over-parameterized, we employ an ℓ1ℓ1 penalty. The tuning parameter in the penalty and the number of change points are determined via the minimum description length principle. Our method is validated via a series of simulation studies and its practical utility is illustrated in the analysis of the ultra-fast rotating yellow giant star known as FK Com.
Stenning D, Wagner-Kaiser R, Robinson E, et al., 2016, BAYESIAN ANALYSIS OF TWO STELLAR POPULATIONS IN GALACTIC GLOBULAR CLUSTERS I: STATISTICAL AND COMPUTATIONAL METHODS, Astrophysical Journal, Vol: 826, ISSN: 1538-4357
We develop a Bayesian model for globular clusters composed of multiple stellar populations, extendingearlier statistical models for open clusters composed of simple (single) stellar populations (e.g., vanDyk et al. 2009; Stein et al. 2013). Specifically, we model globular clusters with two populations thatdiffer in helium abundance. Our model assumes a hierarchical structuring of the parameters in whichphysical properties—age, metallicity, helium abundance, distance, absorption, and initial mass—arecommon to (i) the cluster as a whole or to (ii) individual populations within a cluster, or are unique to(iii) individual stars. An adaptive Markov chain Monte Carlo (MCMC) algorithm is devised for modelfitting that greatly improves convergence relative to its precursor non-adaptive MCMC algorithm. Ourmodel and computational tools are incorporated into an open-source software suite known as BASE-9.We use numerical studies to demonstrate that our method can recover parameters of two-populationclusters, and also show model misspecification can potentially be identified. As a proof of concept,we analyze the two stellar populations of globular cluster NGC 5272 using our model and methods.(BASE-9 is available from GitHub: https://github.com/argiopetech/base/releases).
Wagner-Kaiser R, Stenning D, Robinson E, et al., 2016, Bayesian Analysis of Two Stellar Populations in Galactic Globular Clusters. II. NGC 5024, NGC 5272, and NGC 6352, Astrophysical Journal, Vol: 826, ISSN: 1538-4357
We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival Advanced Camera for Surveys Treasury observations of Galactic Globular Clusters to find and characterize two stellar populations in NGC 5024 (M53), NGC 5272 (M3), and NGC 6352. For these three clusters, both single and double-population analyses are used to determine a best fit isochrone(s). We employ a sophisticated Bayesian analysis technique to simultaneously fit the cluster parameters (age, distance, absorption, and metallicity) that characterize each cluster. For the two-population analysis, unique population level helium values are also fit to each distinct population of the cluster and the relative proportions of the populations are determined. We find differences in helium ranging from ~0.05 to 0.11 for these three clusters. Model grids with solar α-element abundances ([α/Fe] = 0.0) and enhanced α-elements ([α/Fe] = 0.4) are adopted.
Algeri S, Conrad J, van Dyk D, 2016, A method for comparing non-nested models with application to astrophysical searches for new physics, Monthly Notices of the Royal Astronomical Society: Letters, Vol: 458, Pages: L84-L88, ISSN: 1745-3933
Searches for unknown physics and decisions between competing astrophysical models to explain data both rely on statistical hypothesis testing. The usual approach in searches for new physical phenomena is based on the statistical likelihood ratio test and its asymptotic properties. In the common situation, when neither of the two models under comparison is a special case of the other i.e. when the hypotheses are non-nested, this test is not applicable. In astrophysics, this problem occurs when two models that reside in different parameter spaces are to be compared. An important example is the recently reported excess emission in astrophysical γ-rays and the question whether its origin is known astrophysics or dark matter. We develop and study a new, simple, generally applicable, frequentist method and validate its statistical properties using a suite of simulations studies. We exemplify it on realistic simulated data of the Fermi-Large Area Telescope γ-ray satellite, where non-nested hypotheses testing appears in the search for particle dark matter.
Stein NM, van Dyk D, Kashyap VL, 2016, Preprocessing solar images while preserving their latent structure, Statistics and its Interface, Vol: 9, Pages: 535-551, ISSN: 1938-7997
Telescopes such as the Atmospheric Imaging Assembly aboard the Solar DynamicsObservatory, a NASA satellite, collect massive streams of high resolution imagesof the Sun through multiple wavelength filters. Reconstructing pixel-by-pixel thermalproperties based on these images can be framed as an ill-posed inverse problem withPoisson noise, but this reconstruction is computationally expensive and there is disagreementamong researchers about what regularization or prior assumptions are mostappropriate. This article presents an image segmentation framework for preprocessingsuch images in order to reduce the data volume while preserving as much thermal informationas possible for later downstream analyses. The resulting segmented imagesreflect thermal properties but do not depend on solving the ill-posed inverse problem.This allows users to avoid the Poisson inverse problem altogether or to tackle it on eachof ∼10 segments rather than on each of ∼107 pixels, reducing computing time by afactor of ∼106. We employ a parametric class of dissimilarities that can be expressed ascosine dissimilarity functions or Hellinger distances between nonlinearly transformedvectors of multi-passband observations in each pixel. We develop a decision theoreticframework for choosing the dissimilarity that minimizes the expected loss that ariseswhen estimating identifiable thermal properties based on segmented images rather thanon a pixel-by-pixel basis. We also examine the efficacy of different dissimilarities forrecovering clusters in the underlying thermal properties. The expected losses are computedunder scientifically motivated prior distributions. Two simulation studies guideour choices of dissimilarity function. We illustrate our method by segmenting imagesof a coronal hole observed on 26 February 2015.
Stein NM, van Dyk DA, Kashyap VL, et al., 2015, Detecting Unspecified Structure in Low-Count Images, Astrophysical Journal, Vol: 813, ISSN: 1538-4357
Unexpected structure in images of astronomical sources often presents itself uponvisual inspection of the image, but such apparent structure may either correspond totrue features in the source or be due to noise in the data. This paper presents amethod for testing whether inferred structure in an image with Poisson noise represents asignificant departure from a baseline (null) model of the image. To infer image structure,we conduct a Bayesian analysis of a full model that uses a multiscale component toallow flexible departures from the posited null model. As a test statistic, we use atail probability of the posterior distribution under the full model. This choice of teststatistic allows us to estimate a computationally efficient upper bound on a p-valuethat enables us to draw strong conclusions even when there are limited computationalresources that can be devoted to simulations under the null model. We demonstratethe statistical performance of our method on simulated images. Applying our methodto an X-ray image of the quasar 0730+257, we find significant evidence against the nullmodel of a single point source and uniform background, lending support to the claim ofan X-ray jet.
Jones DE, Kashyap VL, van Dyk DA, 2015, DISENTANGLING OVERLAPPING ASTRONOMICAL SOURCES USING SPATIAL AND SPECTRAL INFORMATION, Astrophysical Journal, Vol: 808, ISSN: 1538-4357
We present a powerful new algorithm that combines both spatial information (event locations and the point-spread function) and spectral information (photon energies) to separate photons from overlapping sources. We use Bayesian statistical methods to simultaneously infer the number of overlapping sources, to probabilistically separate the photons among the sources, and to fit the parameters describing the individual sources. Using the Bayesian joint posterior distribution, we are able to coherently quantify the uncertainties associated with all these parameters. The advantages of combining spatial and spectral information are demonstrated through a simulation study. The utility of the approach is then illustrated by analysis of observations of FK Aqr and FL Aqr with the XMM-Newton Observatory and the central region of the Orion Nebula Cluster with the Chandra X-ray Observatory.
van Dyk DA, Jiao X, 2015, Metropolis-Hastings Within Partially Collapsed Gibbs Samplers, Journal of Computational and Graphical Statistics, Vol: 24, Pages: 301-327, ISSN: 1061-8600
The partially collapsed Gibbs (PCG) sampler offers a new strategy for improving the convergence of a Gibbs sampler. PCG achieves faster convergence by reducing the conditioning in some of the draws of its parent Gibbs sampler. Although this can significantly improve convergence, care must be taken to ensure that the stationary distribution is preserved. The conditional distributions sampled in a PCG sampler may be incompatible and permuting their order may upset the stationary distribution of the chain. Extra care must be taken when Metropolis-Hastings (MH) updates are used in some or all of the updates. Reducing the conditioning in an MH within Gibbs sampler can change the stationary distribution, even when the PCG sampler would work perfectly if MH were not used. In fact, a number of samplers of this sort that have been advocated in the literature do not actually have the target stationary distributions. In this article, we illustrate the challenges that may arise when using MH within a PCG sampler and develop a general strategy for using such updates while maintaining the desired stationary distribution. Theoretical arguments provide guidance when choosing between different MH within PCG sampling schemes. Finally, we illustrate the MH within PCG sampler and its computational advantage using several examples from our applied work.
Liao K, Treu T, Marshall P, et al., 2015, STRONG LENS TIME DELAY CHALLENGE. II. RESULTS OF TDC1, ASTROPHYSICAL JOURNAL, Vol: 800, ISSN: 0004-637X
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- Citations: 106
Stenning DC, van Dyk DA, Yu Y, et al., 2015, A Bayesian Analysis of the Solar Cycle Using Multiple Proxy Variables, Current Trends in Bayesian Methodology with Applications, Pages: 585-608, ISBN: 9781482235111
Highly energetic solar eruptions involving bursts of radiation and discharges of plasma can eject charged particles into space and damage technological infrastructure (e.g. radio communications, electric power transmission, and the performance of low-Earth orbit satellites). Such 'space weather' events are in Bayesian of high solar activity-a loose term that is de?ned only by observable proxy variables. Variations in the level of solar activity follow a roughly 11-year cyclic pattern, which is known as the solar cycle. Since energetic space weather events are more common near the solar maximum-the peak in solar activity during the 11-year cycle-there is considerable interest in predicting the timing and amplitude of future solar maxima, which has practical value in the planning of space missions. Nevertheless, predicting solar maxima remains a di?cult task, with di?erent methods yielding substantially di?erent predictions (see [24] for an analysis of the various predictions made for the current solar cycle).
Webster A, von Hippel T, Si S, et al., 2015, Deriving Precise Ages of Field White Dwarfs using Bayesian Techniques, 19th European Workshop on White Dwarfs, Publisher: ASTRONOMICAL SOC PACIFIC, Pages: 145-148
von Hippel T, van Dyk D, Si S, et al., 2015, Deriving the Ages of Field White Dwarfs, 19th European Workshop on White Dwarfs, Publisher: ASTRONOMICAL SOC PACIFIC, Pages: 107-112
Xu J, van Dyk DA, Kashyap VL, et al., 2014, A FULLY BAYESIAN METHOD FOR JOINTLY FITTING INSTRUMENTAL CALIBRATION AND X-RAY SPECTRAL MODELS, ASTROPHYSICAL JOURNAL, Vol: 794, ISSN: 0004-637X
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- Citations: 20
van Dyk DA, 2014, The Role of Statistics in the Discovery of a Higgs Boson, Annual Review of Statistics and Its Application, Vol: 1, Pages: 41-59, ISSN: 2326-831X
The 2012–2013 discovery of a Higgs boson appears to have filled the fi-nal missing gap in the Standard Model of particle physics and was greetedwith fanfare by the scientific community and by the public at large. Particlephysicists have developed and rigorously tested a specialized statistical toolkit that is designed for the search for new physics. This tool kit was putto the test in a 40-year search that culminated in the discovery of a Higgsboson. This article reviews these statistical methods, the controversies thatsurround them, and how they led to this historic discovery
von Hippel T, van Dyk DA, Stenning DC, et al., 2014, THE POWER OF PRINCIPLED BAYESIAN METHODS IN THE STUDY OF STELLAR EVOLUTION, 23rd Evry Schatzman School on Stellar Astrophysics (EES 2013), Publisher: E D P SCIENCES, Pages: 267-287, ISSN: 1633-4760
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- Citations: 4
Stenning D, Kashyap V, Lee TCM, et al., 2013, Morphological image analysis and sunspot classification, Pages: 329-342
The morphology of sunspot groups is predictive both of their future evolution and of explosive associated events higher in the solar atmosphere, such as solar flares and coronal mass ejections. To aid in this prediction, sunspot groups are manually classified according to one of a number of schemes. This process is both laborious and prone to inconsistencies stemming from the subjective nature of the classification. In this paper we describe how mathematical morphology can be used to extract numerical summaries of sunspot images that are relevant to their classification and can be used as features in an automated classification scheme. We include a general overview of basic morphological operations and describe our ongoing work on detecting and classifying sunspot groups using these techniques. © Springer Science+Business Media New York 2013.
Van Dyk DA, 2013, Commentary: Cosmological bayesian model selection, Pages: 141-146
Model selection methodology is an active field of discussion among statisticians, particularly for disjoint, non-nested models. Roberto Trotta has reviewed the issue in the context of model selection within the context of ΛCDM cosmological models. I briefly discuss the issue from both frequentist and Bayesian perspectives, expressing cautions about use of priors, Bayes factors, and p-values. There are no silver bullets, but Bayes factors seem most promising. © Springer Science+Business Media New York 2013.
Zhao S, Van Dyk D, Imai K, 2013, Propensity-Score Based Methods for Causal Inference in Observational Studies with Non-Binary Treatments, Publisher: SAGE Publications
Propensity score methods have become a part of the standard toolkit forapplied researchers who wish to ascertain causal effects from observationaldata. While they were originally developed for binary treatments, severalresearchers have proposed generalizations of the propensity score methodologyfor non-binary treatment regimes. Such extensions have widened theapplicability of propensity score methods and are indeed becoming increasinglypopular themselves. In this article, we closely examine the two maingeneralizations of propensity score methods, namely, the propensity function(P-FUNCTION) of Imai and van Dyk (2004) and the generalized propensity score(GPS) of Hirano and Imbens (2004), along with recent extensions of the GPS thataim to improve its robustness. We compare the assumptions, theoreticalproperties, and empirical performance of these alternative methodologies. On atheoretical level, the GPS and its extensions are advantageous in that they canbe used to estimate the full dose response function rather than the simpleaverage treatment effect that is typically estimated with the P-FUNCTION.Unfortunately, our analysis shows that in practice response models often usedwith the original GPS are less flexible than those typically used withpropensity score methods and are prone to misspecification. We compare new andexisting methods that improve the robustness of the GPS and propose methodsthat use the P-FUNCTION to estimate the dose response function. We illustrateour findings and proposals through simulation studies, including one based onan empirical application.
Stenning DC, Lee TCM, van Dyk DA, et al., 2013, Morphological feature extraction for statistical learning with applications to solar image data, Statistical Analysis and Data Mining, Vol: 6, Pages: 329-345, ISSN: 1932-1872
Many areas of science are generating large volumes of digital image data. In order to take full advantage of the high-resolution and high-cadence images modern technology is producing, methods to automatically process and analyze large batches of such images are needed. This involves reducing complex images to simple representations such as binary sketches or numerical summaries that capture embedded scientific information. Using techniques derived from mathematical morphology, we demonstrate how to reduce solar images into simple ‘sketch’ representations and numerical summaries that can be used for statistical learning. We demonstrate our general techniques on two specific examples: classifying sunspot groups and recognizing coronal loop structures. Our methodology reproduces manual classifications at an overall rate of 90% on a set of 119 magnetogram and white light images of sunspot groups. We also show that our methodology is competitive with other automated algorithms at producing coronal loop tracings and demonstrate robustness through noise simulations.
Stenning D, Kahsyap V, Lee TCM, et al., 2013, Morphological Image Analysis and Its Application to Sunspot Classification, Statistical Challenges in Modern Astronomy V \rm (Editors: E. Feigelson and G. Babu), Publisher: Springer, New York, Pages: 329-342-329-342
O Malley EM, von Hippel T, van Dyk DA, 2013, A Bayesian Approach to Deriving Ages of Individual Field White Dwarfs, The Astrophysical Journal, Pages: under revision-under revision
van Dyk DA, 2013, Discussion of “Cosmological Bayesian Model Selection: Recent Advances and Open Challenges by R. Trotta”, Statistical Challenges in Modern Astronomy V \rm (Editors: E. Feigelson and G. Babu), Publisher: Springer Verlag, Pages: 141-146-141-146
Olson CB, Kim JS, Scarcella R, et al., 2012, Enhancing the Interpretive Reading and Analytical Writing of Mainstreamed English Learners in Secondary School: Results From a Randomized Field Trial Using a Cognitive Strategies Approach, AMERICAN EDUCATIONAL RESEARCH JOURNAL, Vol: 49, Pages: 323-355, ISSN: 0002-8312
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- Citations: 36
Stenning D, Kashyap V, Lee TCM, et al., 2012, Morphological image analysis and sunspot classification, Pages: 329-342, ISSN: 0930-0325
The morphology of sunspot groups is predictive both of their future evolution and of explosive associated events higher in the solar atmosphere, such as solar flares and coronal mass ejections. To aid in this prediction, sunspot groups are manually classified according to one of a number of schemes. This process is both laborious and prone to inconsistencies stemming from the subjective nature of the classification. In this paper we describe how mathematical morphology can be used to extract numerical summaries of sunspot images that are relevant to their classification and can be used as features in an automated classification scheme. We include a general overview of basic morphological operations and describe our ongoing work on detecting and classifying sunspot groups using these techniques. © Springer Science+Business Media New York 2013.
Van Dyk DA, 2012, Commentary: Cosmological bayesian model selection, Pages: 141-146, ISSN: 0930-0325
Model selection methodology is an active field of discussion among statisticians, particularly for disjoint, non-nested models. Roberto Trotta has reviewed the issue in the context of model selection within the context of ΛCDM cosmological models. I briefly discuss the issue from both frequentist and Bayesian perspectives, expressing cautions about use of priors, Bayes factors, and p-values. There are no silver bullets, but Bayes factors seem most promising. © Springer Science+Business Media New York 2013.
Stein N, Kashyap V, Meng X-L, et al., 2012, H-MEANS IMAGE SEGMENTATION TO IDENTIFY SOLAR THERMAL FEATURES, 19th IEEE International Conference on Image Processing (ICIP), Publisher: IEEE, Pages: 1597-1600, ISSN: 1522-4880
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- Citations: 1
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