Related papers: Biased Moments of Undersampled Sources
Consider a Gaussian memoryless multiple source with $m$ components with joint probability distribution known only to lie in a given class of distributions. A subset of $k \leq m$ components are sampled and compressed with the objective of…
Recent high-resolution interferometric images of submillimetre galaxies (SMGs) reveal fascinatingly complex morphologies. This raises a number of questions: how does the relative orientation of a galaxy affect its observed submillimetre…
Wide-field survey instruments are used to efficiently observe large regions of the sky. To achieve the necessary field of view, and to provide a higher signal-to-noise ratio for faint sources, many modern instruments are undersampled.…
Class imbalance and distributional differences in large datasets present significant challenges for classification tasks machine learning, often leading to biased models and poor predictive performance for minority classes. This work…
Noise is an unavoidable part of most measurements which can hinder a correct interpretation of the data. Uncertainties propagate in the data analysis and can lead to biased results even in basic descriptive statistics such as the central…
Digital camera pixels measure image intensities by converting incident light energy into an analog electrical current, and then digitizing it into a fixed-width binary representation. This direct measurement method, while conceptually…
We present a Bayesian inference approach to estimating the cumulative mass profile and mean squared velocity profile of a globular cluster given the spatial and kinematic information of its stars. Mock globular clusters with a range of…
Weak gravitational lensing, or weak lensing, is one of the most powerful probes for dark matter and dark energy science, although it faces increasing challenges in controlling systematic uncertainties as \edit{the statistical errors become…
An energy efficient use of large scale sensor networks necessitates activating a subset of possible sensors for estimation at a fusion center. The problem is inherently combinatorial; to this end, a set of iterative, randomized algorithms…
We use cosmological N-body simulations to investigate whether measurements of the moments of large-scale structure can yield constraints on primordial non-Gaussianity. We measure the variance, skewness, and kurtosis of the evolved density…
In this talk, I will show how to determine the biasing factor $b$ from the high-order moments of galaxies. The determination is based on the analytical modeling of primordial peaks and virialized halos and is independent of the currently…
Future cosmological galaxy surveys such as the Large Synoptic Survey Telescope (LSST) will photometrically observe very large numbers of galaxies. Without spectroscopy, the redshifts required for the analysis of these data will need to be…
The moment method is an image analysis technique for sub-pixel estimation of particle positions. The total error in the calculated particle position includes effects of pixel locking and random noise in each pixel. Pixel locking, also known…
Weak lensing surveys are expected to provide direct measurements of the statistics of the projected dark matter distribution. Most analytical studies of weak lensing statistics have been limited to quasilinear scales as they relied on…
The intensity statistics of signals in the presence of Gaussian noise is obtained by studying the model of a random signal plus a random phasor sum. The additive Gaussian noise is shown to result in a Bessel transform of the probability…
Geometric details of a nuclear reaction zone, at the time of particle emission, can be restored from low relative-velocity particle-correlations, following imaging. Some of the source details get erased and are a potential cause of problems…
A persistent challenge in astronomical machine learning is a systematic bias where predictions compress the dynamic range of true values-high values are consistently predicted too low while low values are predicted too high. Understanding…
Random field and random cluster theory are used to describe certain mathematical results concerning the probability distribution of image pixel intensities characterized as generic $2D$ integer arrays. The size of the smallest bounded…
Gaussian Boson Sampling is a promising method for experimental demonstrations of quantum advantage because it is easier to implement than other comparable schemes. While most of the properties of Gaussian Boson Sampling are understood to…
An accurate method for warping images is presented. Differently from most commonly used techniques, this method guarantees the conservation of the intensity of the transformed image, evaluated as the sum of its pixel values over the whole…