Related papers: Bayesian Methods in Cosmology
This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
Constraints on cosmological parameters are often distilled from sky surveys by fitting templates to summary statistics of the data that are motivated by a fiducial cosmological model. However, recent work has shown how to estimate the…
A probabilistic technique for the joint estimation of background and sources with the aim of detecting faint and extended celestial objects is described. Bayesian probability theory is applied to gain insight into the coexistence of…
As the amount of economic and other data generated worldwide increases vastly, a challenge for future generations of econometricians will be to master efficient algorithms for inference in empirical models with large information sets. This…
This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…
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…
This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimised software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the…
This paper introduces and reviews some of the principles and methods used in Bayesian reliability. It specifically discusses methods used in the analysis of success/no-success data and then reminds the reader of a simple Monte Carlo…
The advent of large data-set in cosmology has meant that in the past 10 or 20 years our knowledge and understanding of the Universe has changed not only quantitatively but also, and most importantly, qualitatively. Cosmologists rely on data…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
After the discovery of the gravitational waves and the observation of neutrinos of cosmic origin, we have entered a new and exciting era where cosmic rays, neutrinos, photons and gravitational waves will be used simultaneously to study the…
Data analysis methods have always been of critical importance for quantitative sciences. In astronomy, the increasing scale of current and future surveys is driving a trend towards a separation of the processes of low-level data reduction…
To understand their data better, astronomers need to use statistical tools that are more advanced than traditional ``freshman lab'' statistics. As an illustration, the problem of combining apparently incompatible measurements of a quantity…
We argue here about the relevance and the ultimate unity of the Bayesian approach in a neutral and agnostic manner. Our main theme is that Bayesian data analysis is an effective tool for handling complex models, as proven by the increasing…
In this chapter, we will first present the most standard computational challenges met in Bayesian Statistics, focussing primarily on mixture estimation and on model choice issues, and then relate these problems with computational solutions.…
A common problem in disciplines of applied Statistics research such as Astrostatistics is of estimating the posterior distribution of relevant parameters. Typically, the likelihoods for such models are computed via expensive experiments…
Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social…
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…
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…