1,131 research outputs found
Constructing A Flexible Likelihood Function For Spectroscopic Inference
We present a modular, extensible likelihood framework for spectroscopic
inference based on synthetic model spectra. The subtraction of an imperfect
model from a continuously sampled spectrum introduces covariance between
adjacent datapoints (pixels) into the residual spectrum. For the high
signal-to-noise data with large spectral range that is commonly employed in
stellar astrophysics, that covariant structure can lead to dramatically
underestimated parameter uncertainties (and, in some cases, biases). We
construct a likelihood function that accounts for the structure of the
covariance matrix, utilizing the machinery of Gaussian process kernels. This
framework specifically address the common problem of mismatches in model
spectral line strengths (with respect to data) due to intrinsic model
imperfections (e.g., in the atomic/molecular databases or opacity
prescriptions) by developing a novel local covariance kernel formalism that
identifies and self-consistently downweights pathological spectral line
"outliers." By fitting many spectra in a hierarchical manner, these local
kernels provide a mechanism to learn about and build data-driven corrections to
synthetic spectral libraries. An open-source software implementation of this
approach is available at http://iancze.github.io/Starfish, including a
sophisticated probabilistic scheme for spectral interpolation when using model
libraries that are sparsely sampled in the stellar parameters. We demonstrate
some salient features of the framework by fitting the high resolution -band
spectrum of WASP-14, an F5 dwarf with a transiting exoplanet, and the moderate
resolution -band spectrum of Gliese 51, an M5 field dwarf.Comment: Accepted to ApJ. Incorporated referees' comments. New figures 1, 8,
10, 12, and 14. Supplemental website: http://iancze.github.io/Starfish
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
Evidence for the accelerated expansion of the Universe from weak lensing tomography with COSMOS
We present a tomographic cosmological weak lensing analysis of the HST COSMOS
Survey. Applying our lensing-optimized data reduction, principal component
interpolation for the ACS PSF, and improved modelling of charge-transfer
inefficiency, we measure a lensing signal which is consistent with pure
gravitational modes and no significant shape systematics. We carefully estimate
the statistical uncertainty from simulated COSMOS-like fields obtained from
ray-tracing through the Millennium Simulation. We test our pipeline on
simulated space-based data, recalibrate non-linear power spectrum corrections
using the ray-tracing, employ photometric redshifts to reduce potential
contamination by intrinsic galaxy alignments, and marginalize over systematic
uncertainties. We find that the lensing signal scales with redshift as expected
from General Relativity for a concordance LCDM cosmology, including the full
cross-correlations between different redshift bins. For a flat LCDM cosmology,
we measure sigma_8(Omega_m/0.3)^0.51=0.75+-0.08 from lensing, in perfect
agreement with WMAP-5, yielding joint constraints Omega_m=0.266+0.025-0.023,
sigma_8=0.802+0.028-0.029 (all 68% conf.). Dropping the assumption of flatness
and using HST Key Project and BBN priors only, we find a negative deceleration
parameter q_0 at 94.3% conf. from the tomographic lensing analysis, providing
independent evidence for the accelerated expansion of the Universe. For a flat
wCDM cosmology and prior w in [-2,0], we obtain w<-0.41 (90% conf.). Our dark
energy constraints are still relatively weak solely due to the limited area of
COSMOS. However, they provide an important demonstration for the usefulness of
tomographic weak lensing measurements from space. (abridged)Comment: 26 pages, 25 figures, matches version accepted for publication by
Astronomy and Astrophysic
Cosmological Parameters from Observations of Galaxy Clusters
Studies of galaxy clusters have proved crucial in helping to establish the
standard model of cosmology, with a universe dominated by dark matter and dark
energy. A theoretical basis that describes clusters as massive,
multi-component, quasi-equilibrium systems is growing in its capability to
interpret multi-wavelength observations of expanding scope and sensitivity. We
review current cosmological results, including contributions to fundamental
physics, obtained from observations of galaxy clusters. These results are
consistent with and complementary to those from other methods. We highlight
several areas of opportunity for the next few years, and emphasize the need for
accurate modeling of survey selection and sources of systematic error.
Capitalizing on these opportunities will require a multi-wavelength approach
and the application of rigorous statistical frameworks, utilizing the combined
strengths of observers, simulators and theorists.Comment: 53 pages, 21 figures. To appear in Annual Review of Astronomy &
Astrophysic
- …