Related papers: Bayesian Methods in Cosmology
We deal with the analysis of on-off measurements designed for the confirmation of a weak source of events whose presence is hypothesized, based on former observations. The problem of a small number of source events that are masked by an…
In this paper we outline the framework of mathematical statistics with which one may study the properties of galaxy distance estimators. We describe, within this framework, how one may formulate the problem of distance estimation as a…
This paper seeks to provide a thorough account of the ubiquitous nature of the Bayesian paradigm in modern statistics, data science and artificial intelligence. Once maligned, on the one hand by those who philosophically hated the very idea…
For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare…
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…
In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting…
While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures.…
The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…
In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
Reconstructing astrophysical and cosmological fields from observations is challenging. It requires accounting for non-linear transformations, mixing of spatial structure, and noise. In contrast, forward simulators that map fields to…
Understanding the properties of transient gravitational waves and their sources is of broad interest in physics and astronomy. Bayesian inference is the standard framework for astro-physical measurement in transient gravitational-wave…
The Bayesian statistical paradigm uses the language of probability to express uncertainty about the phenomena that generate observed data. Probability distributions thus characterize Bayesian analysis, with the rules of probability used to…
Nowadays, g-mode detection is based upon a priori theoretical knowledge. By doing so, detection becomes more restricted to what we can imagine. De facto, the universe of possibilities is made narrower. Such an approach is pertinent for…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…
In cosmology, we would like to explain our observations and predict future observations from theories of the entire universe. Such cosmological theories make ontological assumptions of what entities exist and what their properties and…
Bayesian statistics is concerned with conducting posterior inference for the unknown quantities in a given statistical model. Conventional Bayesian inference requires the specification of a probabilistic model for the observed data, and the…
We provide four case studies that use Bayesian machinery to making inductive reasoning. Our main motivation relies in offering several instances where the Bayesian approach to data analysis is exploited at its best to perform complex tasks,…