202 research outputs found
Detecting abrupt changes in the spectra of high-energy astrophysical sources
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 â1â1 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
STACCATO: a novel solution to supernova photometric classification with biased training sets
We present a new solution to the problem of classifying Type Ia supernovae from their light curves alone given a spectroscopically confirmed but biased training set, circumventing the need to obtain an observationally expensive unbiased training set. We use Gaussian processes (GPs) to model the supernovae's (SN's) light curves, and demonstrate that the choice of covariance function has only a small influence on the GPs ability to accurately classify SNe. We extend and improve the approach of Richards et al. â a diffusion map combined with a random forest classifier â to deal specifically with the case of biased training sets. We propose a novel method called Synthetically Augmented Light Curve Classification (STACCATO) that synthetically augments a biased training set by generating additional training data from the fitted GPs. Key to the success of the method is the partitioning of the observations into subgroups based on their propensity score of being included in the training set. Using simulated light curve data, we show that STACCATO increases performance, as measured by the area under the Receiver Operating Characteristic curve (AUC), from 0.93 to 0.96, close to the AUC of 0.977 obtained using the âgold standardâ of an unbiased training set and significantly improving on the previous best result of 0.88. STACCATO also increases the true positive rate for SNIa classification by up to a factor of 50 for high-redshift/low-brightness SNe
Analysis of energy spectra with low photon counts via Bayesian posterior simulation
Over the past 10 years Bayesian methods have rapidly grown more popular as several computationally intensive statistical algorithms have become feasible with increased computer power. In this paper, we begin with a general description of the Bayesian paradigm for statistical inference and the various state-of-the-art model fitting techniques that we employ (e.g., Gibbs sampler and Metropolis- Hastings). These algorithms are very flexible and can be used to fit models that account for the highly hierarchical structure inherent in the collection of high-quality spectra and thus can keep pace with the accelerating progress of new space telescope designs. The methods we develop, which will soon be available in the CIAO software package, explicitly model photon arrivals as a Poisson process and, thus, have no difficulty with high resolution low count X-ray and gamma-ray data. We expect these methods to be useful not only for the recently launched Chandra X-ray observatory and XMM but also new generation telescopes such as Constellation X, GLAST, etc. In the context of two examples (Quasar S5 0014+813 and Hybrid-Chromosphere Supergiant Star alpha TrA) we illustrate a new highly structured model and how Bayesian posterior sampling can be used to compute estimates, error bars, and credible intervals for the various model parameters
A BAYESIAN ANALYSIS OF THE AGES OF FOUR OPEN CLUSTERS
In this paper we apply a Bayesian technique to determine the best fit of stellar evolution models to find the main sequence turn off age and other cluster parameters of four intermediate-age open clusters: NGC 2360, NGC 2477, NGC 2660, and NGC 3960. Our algorithm utilizes a Markov chain Monte Carlo technique to fit these various parameters, objectively finding the best fit isochrone for each cluster. The result is a high precision isochrone fit. We compare these results with the those of traditional âby eyeâ 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 our effort to determine cluster ages to higher precision than that offered by these traditional methods of isochrone fitting
BAYESIAN ANALYSIS OF TWO STELLAR POPULATIONS IN GALACTIC GLOBULAR CLUSTERS I: STATISTICAL AND COMPUTATIONAL METHODS
We develop a Bayesian model for globular clusters composed of multiple stellar populations, extending earlier statistical models for open clusters composed of simple (single) stellar populations (e.g., van Dyk et al. 2009; Stein et al. 2013). Specifically, we model globular clusters with two populations that differ in helium abundance. Our model assumes a hierarchical structuring of the parameters in which physical propertiesâage, metallicity, helium abundance, distance, absorption, and initial massâare common 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 model fitting that greatly improves convergence relative to its precursor non-adaptive MCMC algorithm. Our model 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-population clusters, 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)
Bayesian estimates of astronomical time delays between gravitationally lensed stochastic light curves
The gravitational field of a galaxy can act as a lens and deflect the light emitted by a more distant object such as a quasar. Strong gravitational lensing causes multiple images of the same quasar to ap- pear in the sky. Since the light in each gravitationally lensed image traverses a different path length from the quasar to the Earth, fluc- tuations in the source brightness are observed in the several images at different times. The time delay between these fluctuations can be used to constrain cosmological parameters and can be inferred from the time series of brightness data or light curves of each image. To estimate the time delay, we construct a model based on a state- space representation for irregularly observed time series generated by a latent continuous-time Ornstein-Uhlenbeck process. We account for microlensing, an additional source of independent long-term ex- trinsic variability, via a polynomial regression. Our Bayesian strategy adopts a Metropolis-Hastings within Gibbs sampler. We improve the sampler by using an ancillarity-sufficiency interweaving strategy and adaptive Markov chain Monte Carlo. We introduce a profile likeli- hood of the time delay as an approximation of its marginal posterior distribution. The Bayesian and profile likelihood approaches comple- ment each other, producing almost identical results; the Bayesian method is more principled but the profile likelihood is simpler to implement. We demonstrate our estimation strategy using simulated data of doubly- and quadruply-lensed quasars, and observed data from quasars Q0957+561 and J1029+2623
ON COMPUTING UPPER LIMITS TO SOURCE INTENSITIES
A common problem in astrophysics is determining how bright a source could be
and still not be detected. Despite the simplicity with which the problem can be
stated, the solution involves complex statistical issues that require careful
analysis. In contrast to the confidence bound, this concept has never been
formally analyzed, leading to a great variety of often ad hoc solutions. Here
we formulate and describe the problem in a self-consistent manner. Detection
significance is usually defined by the acceptable proportion of false positives
(the TypeI error), and we invoke the complementary concept of false negatives
(the TypeII error), based on the statistical power of a test, to compute an
upper limit to the detectable source intensity. To determine the minimum
intensity that a source must have for it to be detected, we first define a
detection threshold, and then compute the probabilities of detecting sources of
various intensities at the given threshold. The intensity that corresponds to
the specified TypeII error probability defines that minimum intensity, and is
identified as the upper limit. Thus, an upper limit is a characteristic of the
detection procedure rather than the strength of any particular source and
should not be confused with confidence intervals or other estimates of source
intensity. This is particularly important given the large number of catalogs
that are being generated from increasingly sensitive surveys. We discuss the
differences between these upper limits and confidence bounds. Both measures are
useful quantities that should be reported in order to extract the most science
from catalogs, though they answer different statistical questions: an upper
bound describes an inference range on the source intensity, while an upper
limit calibrates the detection process. We provide a recipe for computing upper
limits that applies to all detection algorithms.Comment: 30 pages, 12 figures, accepted in Ap
The Sagittarius dwarf irregular galaxy: metallicity and stellar populations
We present deep observations of the dwarf irregular galaxy UKS1927-177
in Sagittarius. Statistically cleaned , CMDs clearly display the key
evolutionary features in this galaxy. Previously detected C stars are located
in the CMDs and shown to be variable, thus confirming the presence of a
significant upper-AGB intermediate age population. A group of likely red
supergiants is also identified, whose magnitude and color is consistent with a
30 Myr old burst of star formation. The observed colors of both blue and red
stars in SagDIG are best explained by introducing a differential reddening
scenario in which internal dust extinction affects the star forming regions.
Adopting a low reddening for the red giants, , gives
[Fe/H]= for the mean stellar metallicity, a value consistent with
the [O/H] abundance measured in the HII regions. This revised metallicity,
which is in accord with the trend of metallicity against luminosity for dwarf
irregular galaxies, is indicative of a ``normal'', although metal-poor, dIrr
galaxy. A quantitative description is given of the spatial distribution of
stars in different age intervals, in comparison with the distribution of the
neutral hydrogen. We find that the youngest stars are located near the major
peaks of emission on the HI shell, whereas the red giants and intermediate-age
C stars define an extended halo or disk with scale length comparable to the
size of the hydrogen cloud. The relationship between the distribution of ISM
and star formation is briefly discussed.Comment: 10 pages, 7 figures, accepted A&
Bayesian astrostatistics: a backward look to the future
This perspective chapter briefly surveys: (1) past growth in the use of
Bayesian methods in astrophysics; (2) current misconceptions about both
frequentist and Bayesian statistical inference that hinder wider adoption of
Bayesian methods by astronomers; and (3) multilevel (hierarchical) Bayesian
modeling as a major future direction for research in Bayesian astrostatistics,
exemplified in part by presentations at the first ISI invited session on
astrostatistics, commemorated in this volume. It closes with an intentionally
provocative recommendation for astronomical survey data reporting, motivated by
the multilevel Bayesian perspective on modeling cosmic populations: that
astronomers cease producing catalogs of estimated fluxes and other source
properties from surveys. Instead, summaries of likelihood functions (or
marginal likelihood functions) for source properties should be reported (not
posterior probability density functions), including nontrivial summaries (not
simply upper limits) for candidate objects that do not pass traditional
detection thresholds.Comment: 27 pp, 4 figures. A lightly revised version of a chapter in
"Astrostatistical Challenges for the New Astronomy" (Joseph M. Hilbe, ed.,
Springer, New York, forthcoming in 2012), the inaugural volume for the
Springer Series in Astrostatistics. Version 2 has minor clarifications and an
additional referenc
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