30,486 research outputs found
Interpolating point spread function anisotropy
Planned wide-field weak lensing surveys are expected to reduce the
statistical errors on the shear field to unprecedented levels. In contrast,
systematic errors like those induced by the convolution with the point spread
function (PSF) will not benefit from that scaling effect and will require very
accurate modeling and correction. While numerous methods have been devised to
carry out the PSF correction itself, modeling of the PSF shape and its spatial
variations across the instrument field of view has, so far, attracted much less
attention. This step is nevertheless crucial because the PSF is only known at
star positions while the correction has to be performed at any position on the
sky. A reliable interpolation scheme is therefore mandatory and a popular
approach has been to use low-order bivariate polynomials. In the present paper,
we evaluate four other classical spatial interpolation methods based on splines
(B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and
ordinary Kriging (OK). These methods are tested on the Star-challenge part of
the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and
are compared with the classical polynomial fitting (Polyfit). We also test all
our interpolation methods independently of the way the PSF is modeled, by
interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are
known exactly at star positions). We find in that case RBF to be the clear
winner, closely followed by the other local methods, IDW and OK. The global
methods, Polyfit and B-splines, are largely behind, especially in fields with
(ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all
interpolators reach a variance on PSF systematics better than
the upper bound expected by future space-based surveys, with
the local interpolators performing better than the global ones
Multiperiodicity, modulations and flip-flops in variable star light curves I. Carrier fit method
The light curves of variable stars are commonly described using simple
trigonometric models, that make use of the assumption that the model parameters
are constant in time. This assumption, however, is often violated, and
consequently, time series models with components that vary slowly in time are
of great interest. In this paper we introduce a class of data analysis and
visualization methods which can be applied in many different contexts of
variable star research, for example spotted stars, variables showing the
Blazhko effect, and the spin-down of rapid rotators. The methods proposed are
of explorative type, and can be of significant aid when performing a more
thorough data analysis and interpretation with a more conventional method.Our
methods are based on a straightforward decomposition of the input time series
into a fast "clocking" periodicity and smooth modulating curves. The fast
frequency, referred to as the carrier frequency, can be obtained from earlier
observations (for instance in the case of photometric data the period can be
obtained from independently measured radial velocities), postulated using some
simple physical principles (Keplerian rotation laws in accretion disks), or
estimated from the data as a certain mean frequency. The smooth modulating
curves are described by trigonometric polynomials or splines. The data
approximation procedures are based on standard computational packages
implementing simple or constrained least-squares fit-type algorithms.Comment: 14 pages, 23 figures, submitted to Astronomy and Astrophysic
Parametrization and penalties in spline models with an application to survival analysis
In this paper we show how a simple parametrization, built from the definition of cubic
splines, can aid in the implementation and interpretation of penalized spline models, whatever
configuration of knots we choose to use. We call this parametrization value-first derivative
parametrization. We perform Bayesian inference by exploring the natural link between quadratic
penalties and Gaussian priors. However, a full Bayesian analysis seems feasible only for some
penalty functionals. Alternatives include empirical Bayes methods involving model selection
type criteria. The proposed methodology is illustrated by an application to survival analysis
where the usual Cox model is extended to allow for time-varying regression coefficients
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