99 research outputs found

### Spectral fit residuals as an indicator to increase model complexity

Spectral fitting of X-ray data usually involves minimizing statistics like
the chi-square and the Cash statistic. Here we discuss their limitations and
introduce two measures based on the cumulative sum (CuSum) of model residuals
to evaluate whether model complexity could be increased: the percentage of bins
exceeding a nominal threshold in a CuSum array (pct$_{CuSum}$), and the excess
area under the CuSum compared to the nominal (p$_\textit{area}$). We
demonstrate their use with an application to a $\textit{Chandra}$ ACIS spectral
fit.Comment: 3 pages, 1 figure, published in the Research Notes of the American
Astronomical Society (RNAAS

### Preprocessing Solar Images while Preserving their Latent Structure

Telescopes such as the Atmospheric Imaging Assembly aboard the Solar Dynamics
Observatory, a NASA satellite, collect massive streams of high resolution
images of the Sun through multiple wavelength filters. Reconstructing
pixel-by-pixel thermal properties based on these images can be framed as an
ill-posed inverse problem with Poisson noise, but this reconstruction is
computationally expensive and there is disagreement among researchers about
what regularization or prior assumptions are most appropriate. This article
presents an image segmentation framework for preprocessing such images in order
to reduce the data volume while preserving as much thermal information as
possible for later downstream analyses. The resulting segmented images reflect
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 each of $\sim$10 segments rather than on each of $\sim$10$^7$ pixels,
reducing computing time by a factor of $\sim$10$^6$. We employ a parametric
class of dissimilarities that can be expressed as cosine dissimilarity
functions or Hellinger distances between nonlinearly transformed vectors of
multi-passband observations in each pixel. We develop a decision theoretic
framework for choosing the dissimilarity that minimizes the expected loss that
arises when estimating identifiable thermal properties based on segmented
images rather than on a pixel-by-pixel basis. We also examine the efficacy of
different dissimilarities for recovering clusters in the underlying thermal
properties. The expected losses are computed under scientifically motivated
prior distributions. Two simulation studies guide our choices of dissimilarity
function. We illustrate our method by segmenting images of a coronal hole
observed on 26 February 2015

### Detecting Unspecified Structure in Low-Count Images

Unexpected structure in images of astronomical sources often presents itself
upon visual inspection of the image, but such apparent structure may either
correspond to true features in the source or be due to noise in the data. This
paper presents a method for testing whether inferred structure in an image with
Poisson noise represents a significant 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 to allow flexible departures from
the posited null model. As a test statistic, we use a tail probability of the
posterior distribution under the full model. This choice of test statistic
allows us to estimate a computationally efficient upper bound on a p-value that
enables us to draw strong conclusions even when there are limited computational
resources that can be devoted to simulations under the null model. We
demonstrate the statistical performance of our method on simulated images.
Applying our method to an X-ray image of the quasar 0730+257, we find
significant evidence against the null model of a single point source and
uniform background, lending support to the claim of an X-ray jet

### Automatic estimation of flux distributions of astrophysical source populations

In astrophysics a common goal is to infer the flux distribution of
populations of scientifically interesting objects such as pulsars or
supernovae. In practice, inference for the flux distribution is often conducted
using the cumulative distribution of the number of sources detected at a given
sensitivity. The resulting "$\log(N>S)$-$\log (S)$" relationship can be used to
compare and evaluate theoretical models for source populations and their
evolution. Under restrictive assumptions the relationship should be linear. In
practice, however, when simple theoretical models fail, it is common for
astrophysicists to use prespecified piecewise linear models. This paper
proposes a methodology for estimating both the number and locations of
"breakpoints" in astrophysical source populations that extends beyond existing
work in this field. An important component of the proposed methodology is a new
interwoven EM algorithm that computes parameter estimates. It is shown that in
simple settings such estimates are asymptotically consistent despite the
complex nature of the parameter space. Through simulation studies it is
demonstrated that the proposed methodology is capable of accurately detecting
structural breaks in a variety of parameter configurations. This paper
concludes with an application of our methodology to the Chandra Deep Field
North (CDFN) data set.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS750 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org

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