Related papers: Bayesian analysis of cosmic structures
Accurate analyses of present and next-generation galaxy surveys require new ways to handle effects of non-linear gravitational structure formation in data. To address these needs we present an extension of our previously developed algorithm…
We consider the shape of the posterior distribution to be used when fitting cosmological models to power spectra measured from galaxy surveys. At very large scales, Gaussian posterior distributions in the power do not approximate the…
We present COSMIC BIRTH: COSMological Initial Conditions from Bayesian Inference Reconstructions with THeoretical models: an algorithm to reconstruct the primordial and evolved cosmic density fields from galaxy surveys on the light-cone.…
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
We apply a linear Bayesian model to seismic tomography, a high-dimensional inverse problem in geophysics. The objective is to estimate the three-dimensional structure of the earth's interior from data measured at its surface. Since this…
The large scale structure (LSS) of the universe is generated by the linear density gaussian modes, which are evolved into the observed nonlinear LSS. The posterior surface of the modes is convex in the linear regime, leading to a unique…
The dark sirens method combines gravitational waves and catalogs of galaxies to constrain the cosmological expansion history, merger rates and mass distributions of compact objects, and the laws of gravity. However, the incompleteness of…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modeled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is increasing burden placed…
We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology. Persistent homology is a technique from topological data analysis that quantifies…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
Building on ideas from Castillo and Nickl [Ann. Statist. 41 (2013) 1999-2028], a method is provided to study nonparametric Bayesian posterior convergence rates when "strong" measures of distances, such as the sup-norm, are considered. In…
It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level…
One way of recovering information about the initial conditions of the Universe is by measuring features of the cosmological density field which are preserved during gravitational evolution and galaxy formation. In this paper we study the…
We develop an efficient posterior sampling scheme for the Poisson INGARCH models. The proposed method is based on the approximation of the posterior density that exploits the Poisson limit of the negative binomial distribution. It allows us…
The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point patterns. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the…
We present methods to rigorously extract parameter combinations that are constrained by data from posterior distributions. The standard approach uses linear methods that apply to Gaussian distributions. We show the limitations of the linear…