Related papers: A quasi-Gaussian approximation for the probability…

This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…

We review various methods used to estimate uncertainties in quantum correlation functions, such as parton distribution functions (PDFs). Using a toy model of a PDF, we compare the uncertainty estimates yielded by the traditional Hessian and…

We show that correlation functions have to satisfy contraint relations, owing to the non-negativity of the power spectrum of the underlying random process. Specifically, for any statistically homogeneous and (for more than one spatial…

Working with a toy model whose partition function consists of a discrete summation, we introduce the statistical field-theory methodology by transforming a partition function via a formal Gaussian integral relation (the Hubbard-Stratonovich…

Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…

We study the correlations of the shear signal between triplets of sources in the Canada-France-Hawaii Lensing Survey (CFHTLenS) to probe cosmological parameters via the matter bispectrum. In contrast to previous studies, we adopted a…

Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…

The properties of the probability distribution function of the cosmological continuous density field are studied. We present further developments and compare dynamically motivated methods to derive the PDF. One of them is based on the…

Under ideal conditions, the probability density function (PDF) of a random variable, such as a sensor measurement, would be well known and amenable to computation and communication tasks. However, this is often not the case, so the user…

Fusing probabilistic information is a fundamental task in signal and data processing with relevance to many fields of technology and science. In this work, we investigate the fusion of multiple probability density functions (pdfs) of a…

We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows…

We present an improved method for calculating the parallel and perpendicular velocity correlation functions directly from peculiar velocity surveys using weighted maximum-likelihood estimators. A central feature of the new method is the use…

The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes…

We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…

We describe a Bayesian approach to estimating luminosity functions. We derive the likelihood function and posterior probability distribution for the luminosity function, given the observed data, and we compare the Bayesian approach with…

Approximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy…

We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its…

The gravitational evolution of the cosmic one-point probability distribution function (PDF) has been estimated using an analytic approximation that combines gravitational perturbation theory with the Edgeworth expansion around a Gaussian…

We use the physics of ellipsoidal collapse to model the probability distribution function of the smoothed dark matter density field in real and redshift space. We provide a simple approximation to the exact collapse model which shows…

We develop an accurate and computationally efficient emulator to model the gravitational lensing magnification probability distribution function (PDF), enabling robust cosmological inference of point sources such as supernovae and…