Related papers: An analytical approach to Bayesian evidence comput…

A method is presented for performing joint analyses of cosmological datasets, in which the weight assigned to each dataset is determined directly by it own statistical properties. The weights are considered in a Bayesian context as a set of…

Bayesian evidence is a standard tool used for comparing the ability of different models to fit available data and is used extensively in cosmology. However, since the evidence calculation involves performing an integral of the likelihood…

In this paper we consider the issue of paradigm evaluation by applying Bayes' theorem along the following nested hierarchy of progressively more complex structures: i) parameter estimation (within a model), ii) model selection and…

The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more…

There has been increasing interest by cosmologists in applying Bayesian techniques, such as Bayesian Evidence, for model selection. A typical example is in assessing whether observational data favour a cosmological constant over evolving…

The model evidence is a vital quantity in the comparison of statistical models under the Bayesian paradigm. This paper presents a review of commonly used methods. We outline some guidelines and offer some practical advice. The reviewed…

We introduce a new conservative test for quantifying the consistency of two or more datasets. The test is based on the Bayesian answer to the question, ``How much more probable is it that all my data were generated from the same model…

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…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

Empirical likelihood is a popular nonparametric statistical tool that does not require any distributional assumptions. In this paper, we explore the possibility of conducting variable selection via Bayesian empirical likelihood. We show…

Analyzes of next-generation galaxy data require accurate treatment of systematic effects such as the bias between observed galaxies and the underlying matter density field. However, proposed models of the phenomenon are either numerically…

We use Bayesian model selection techniques to test extensions of the standard flat LambdaCDM paradigm. Dark-energy and curvature scenarios, and primordial perturbation models are considered. To that end, we calculate the Bayesian evidence…

Statistical analysis of max-stable processes used to model spatial extremes has been limited by the difficulty in calculating the joint likelihood function. This precludes all standard likelihood-based approaches, including Bayesian…

Spurred on by recent successes in causal inference competitions, Bayesian nonparametric (and high-dimensional) methods have recently seen increased attention in the causal inference literature. In this paper, we present a comprehensive…

Scientific claims gain credibility by replicability, especially if replication under different circumstances and varying designs yields equivalent results. Aggregating results over multiple studies is, however, not straightforward, and when…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

Model selection aims to determine which theoretical models are most plausible given some data, without necessarily asking about the preferred values of the model parameters. A common model selection question is to ask when new data require…

Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty regarding various physical quantities in a well-defined and self-contained manner. Utilising modern tools, such Bayesian models can be constructed…

We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes' theorem and its applications. In particular we discuss about how to…

Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…