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We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…
We use FIRE-2 zoom simulations of Milky Way size disk galaxies to derive easy-to-use relationships between the observed circular speed of the Galaxy at the Solar location, $v_\mathrm{c}$, and dark matter properties of relevance for direct…
A maximum-likelihood method, tested as an unbiased estimator from numerical simulations, is used to estimate cosmic bulk flow from peculiar velocity surveys. The likelihood function is applied to four observational catalogues (ENEAR, SFI++,…
Here we present an application of two maxentropic procedures to determine the probability density distribution of compound sums of random variables, using only a finite number of empirically determined fractional moments. The two methods…
Rue and Held (2005) proposed a method for efficiently computing the Gaussian likelihood for stationary Markov random field models, when the data locations fall on a complete regular grid, and the model has no additive error term. The…
Video processing solutions for motion analysis are key tasks in many computer vision applications, ranging from human activity recognition to object detection. In particular, speed estimation algorithms may be relevant in contexts such as…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a well-known challenging problem. Closed-form expression of the sum distribution is usually intractable and presents an open problem. A crude Monte…
We give the distribution of $M_n$, the maximum of a sequence of $n$ observations from a moving average of order 1. Solutions are first given in terms of repeated integrals and then for the case where the underlying independent random…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
Extreme-ultraviolet (EUV) observations provide considerable insight into evolving physical conditions in the active solar atmosphere. For a prescribed density and temperature structure, it is straightforward to construct the corresponding…
Triggered by the study of Carquillat & Prieur (2007, MNRAS, 380, 1064) of Am binaries, I reanalyse their sample of 60 orbits to derive the mass ratio distribution (MRD), assuming as they did a priori functional forms, i.e. a power law or a…
We present a percent-level accurate model of the line-of-sight velocity distribution of galaxies around dark matter halos as a function of projected radius and halo mass. The model is developed and tested using synthetic galaxy catalogs…
In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is…
The density ratio of two probability distributions is one of the fundamental tools in mathematical and computational statistics and machine learning, and it has a variety of known applications. Therefore, density ratio estimation from…
We consider the problem of recovering a distribution function on the real line from observations additively contaminated with errors following the standard Laplace distribution. Assuming that the latent distribution is completely unknown…
In this work we propose a novel method for testing the validity of the fiducial LCDM cosmology by measuring the cumulative distribution function of the most massive haloes in a sample of subvolumes of identical size tiled on the sky at a…
We apply four different mass modelling methods to a suite of publicly available mock data for spherical stellar systems. We focus on the recovery of the density and velocity anisotropy as a function of radius, using either line-of-sight…
This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in…