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In certain cases of astronomical data analysis, the meaningful physical quantity to extract is the ratio $R$ between two data sets. Examples include the lensing ratio, the interloper rate in spectroscopic redshift samples, the decay rate of…
Evidence shows properties of dark matter haloes may vary with large-scale environment. By studying the halo occupation distribution in cosmic voids it is possible to obtain useful information that can shed light on the subject. The history…
By utilizing large-scale graph analytic tools implemented in the modern Big Data platform, Apache Spark, we investigate the topological structure of gravitational clustering in five different universes produced by cosmological $N$-body…
Astronomical data is full of holes. While there are many reasons for this missing data, the data can be randomly missing, caused by things like data corruptions or unfavourable observing conditions. We test some simple data imputation…
Metrics for rigorously defining a distance between two events have been used to study the properties of the dataspace manifold of particle collider physics. The probability distribution of pairwise distances on this dataspace is unique with…
We discuss non-parametric density estimation and regression for astrophysics problems. In particular, we show how to compute non-parametric confidence intervals for the location and size of peaks of a function. We illustrate these ideas…
Our recent estimates of galaxy counts and the luminosity density in the near-infrared (Keenan et al. 2010, 2012) indicated that the local universe may be under-dense on radial scales of several hundred megaparsecs (Mpc). Such a large-scale…
We develop a statistical method to measure the interaction cross-section of Dark Matter, exploiting the continuous minor merger events in which small substructures fall into galaxy clusters. We find that by taking the ratio of the distances…
The bulge is a region of the Galaxy of tremendous interest for understanding galaxy formation. However measuring photometry and kinematics in it raises several inherent issues, such as severe crowding and high extinction in the visible.…
Cosmic voids are the major volume component in the matter distribution of the Universe. They posses great potential for constraining dark energy as well as for testing theories of gravity. Nevertheless, in spite of their growing popularity…
This review article considers some of the most common methods used in astronomy for regressing one quantity against another in order to estimate the model parameters or to predict an observationally expensive quantity using trends between…
In weak-lensing cosmological studies, peak statistics is sensitive to nonlinear structures and thus complementary to cosmic shear two-point correlations. In this paper, we explore a new approach, namely, the peak steepness statistics, with…
Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…
We derived a geometric goodness-of-fit index, similar to $R^2$ using topological data analysis techniques. We build the Vietoris-Rips complex from the data-cloud projected onto each variable. Estimating the area of the complex and their…
Data which lie in the space $\mathcal{P}_{m\,}$, of $m \times m$ symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications including medical imaging, computer vision, and radar signal…
We present an analytic model for the sizes of voids in the galaxy distribution. Peebles and others have recently emphasized the possibility that the observed characteristics of voids may point to a problem in galaxy formation models, but…
We investigate the properties of voids and void galaxies in the \texttt{TNG300} simulation. Using a luminous galaxy catalog and a spherical void finding algorithm, we identify 5,078 voids at redshift $z = 0$. Within the voids, mass does not…
We consider the effects of large structures in the Universe on the Hubble diagram. This problem is treated non-linearly by considering a Swiss Cheese model of the Universe in which under-dense voids are represented as negatively curved…
We present radial density profiles, as traced by luminous galaxies and dark matter particles, for voids in eleven snapshots of the \texttt{TNG300} simulation. The snapshots span 11.65~Gyr of cosmic time, corresponding to the redshift range…
We present a method for finding high density, low-dimensional structures in noisy point clouds. These structures are sets with zero Lebesgue measure with respect to the $D$-dimensional ambient space and belong to a $d<D$ dimensional space.…