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We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…
We explore the mass distribution of material associated with galaxies from the observation of gravitational weak lensing for the galaxy mass correlation function with the aid of $N$-body simulations of dark matter. The latter is employed to…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
We give independent proof of the deficit of stars in the in-plane central disc with respect to the predictions of a pure exponential density distribution. We use three different methods: 1) the inversion of the red clump giant distribution…
In the last few years there has been an enormous effort in parameter estimation studies for different sources with the space based gravitational wave detector, LISA. While these studies have investigated sources of differing complexity, the…
Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…
The use of rapidity gaps is proposed as a measure of the spatial pattern of an event. When the event multiplicity is low, the gaps between neighboring particles carry far more information about an event than multiplicity spikes, which may…
Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…
We present density split statistics, a framework that studies lensing and counts-in-cells as a function of foreground galaxy density, thereby providing a large-scale measurement of both 2-point and 3-point statistics. Our method extends our…
Unsustained matter distributions unescapely collapse unless fragmentation and centrifugal or pressure support take place. Starting from the above evidence, supermassive compact objects at the centre of large-mass galaxies are conceived as…
Observational cosmology is entering an era in which high precision will be required in both measurement and data analysis. Accuracy, however, can only be achieved with a thorough understanding of potential sources of contamination from…
Large deviation statistics is implemented to predict the statistics of cosmic densities in cylinders applicable to photometric surveys. It yields few percent accurate analytical predictions for the one-point probability distribution…
We present a method to calculate gravitational potential gradients within regions containing few tens of thousands stars with known phase space coordinates. The central idea of the method is to calculate orbital arcs for each star within a…
We propose a new family of depth measures called the elastic depths that can be used to greatly improve shape anomaly detection in functional data. Shape anomalies are functions that have considerably different geometric forms or features…
The sizes and shapes of voids in a galaxy survey depend not only on the physics of structure formation, but also on the sampling density of the survey and on the algorithm used to define voids. Using an N-body simulation with a CDM power…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
For a set of $n$ points in $\Re^d$, and parameters $k$ and $\eps$, we present a data structure that answers $(1+\eps,k)$-\ANN queries in logarithmic time. Surprisingly, the space used by the data-structure is $\Otilde (n /k)$; that is, the…
Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical {\em ansatz}, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small…
Teramoto et al. defined a new measure called the gap ratio that measures the uniformity of a finite point set sampled from $\cal S$, a bounded subset of $\mathbb{R}^2$. We generalize this definition of measure over all metric spaces by…
Dark matter comprises the bulk of the matter in the universe but its particle nature and cosmological origin remain mysterious. Knowledge of the dark matter density distribution in the Milky Way Galaxy is crucial to both our understanding…