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In a quadruply imaged lens system the angular distribution of images around the lens center is completely described by three relative angles. We show empirically that in the 3D space of these angles, spanning 180 x 180 x 90 degrees, quads…

We present a technique for constructing suitable posterior probability distributions in situations for which the sampling distribution of the data is not known. This is very useful for modern scientific data analysis in the era of "big…

Gravitational lensing is potentially able to observe mass-selected halos, and to measure the projected cluster mass function. An optimal mass-selection requires a quantitative understanding of the noise behavior in mass maps. This paper is…

Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…

The large-system performance of MAP estimation is studied considering a general distortion function when the observation vector is received through a linear system with additive white Gaussian noise. The analysis considers the system matrix…

With increasingly large data sets, weak lensing measurements are able to measure cosmological parameters with ever greater precision. However this increased accuracy also places greater demands on the statistical tools used to extract the…

We introduce a novel framework for upsampled Point Spread Function (PSF) modeling using pixel-level Bayesian inference. Accurate PSF characterization is critical for precision measurements in many fields including: weak lensing, astrometry,…

We explore in detail the physics potential of a measurement of the ttbar invariant mass distribution. First, we assess the accuracy of the best available predictions for this observable and find that in the low invariant mass region, the…

For a given spatial distribution of the lenses and distribution of the transverse velocity of the lens relative to the line-of-sight, a probability distribution for the lens mass for a single observed event is derived. In addition, similar…

We present a framework for analyzing weak gravitational lensing survey data, including lensing and source-density observables, plus spectroscopic redshift calibration data. All two-point observables are predicted in terms of parameters of a…

While the probability density function (PDF) of the cosmic microwave background (CMB) convergence field approximately follows a Gaussian distribution, primordial non-Gaussianities and small contributions from structures at low redshifts…

We investigate the problem of noise bias in maximum likelihood and maximum a posteriori estimators for cosmic shear. We derive the leading and next-to-leading order biases and compute them in the context of galaxy ellipticity measurements,…

Here we present a number of improvements to weak lensing 3D power spectrum analysis, 3D cosmic shear, that uses the shape and redshift information of every galaxy to constrain cosmological parameters. We show how photometric redshift…

CMB lensing maps probe the mass distribution in projection out to high redshifts, but significant sensitivity to low-redshift structure remains. In this paper we discuss a method to remove the low-redshift contributions from CMB lensing…

Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…

We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…

In Stage-IV imaging surveys, a significant amount of the cosmologically useful information is due to sources whose images overlap with those of other sources on the sky. The cosmic shear signal is primarily encoded in the estimated shapes…

The weak distortions produced by gravitational lensing in the images of background galaxies provide a method to measure directly the distribution of mass in the universe. However this technique requires high precision measurements of the…

We examine the errors on counts in cells extracted from galaxy surveys. The measurement error, related to the finite number of sampling cells, is disentangled from the ``cosmic error'', due to the finiteness of the survey. Using the…