Related papers: Bayesian model comparison in cosmology
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…
We propose here a \emph{novel} method which singles out the \emph{a priori} unavoidable dependence on the underlying cosmological model when extracting parameter constraints, providing robust limits which only depend on the considered…
Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In…
Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…
Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…
Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In…
A model-independent or non-parametric approach for modeling a database has been widely used in cosmology. In these scenarios, the data has been used directly to reconstruct an underlying function. In this work, we introduce a novel…
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…
Interpretation of cosmological data to determine the number and values of parameters describing the universe must not rely solely on statistics but involve physical insight. When statistical techniques such as "model selection" or…
Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the…
A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…
We introduce a statistical measure of the effective model complexity, called the Bayesian complexity. We demonstrate that the Bayesian complexity can be used to assess how many effective parameters a set of data can support and that it is a…
We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimised for a specific cosmological model or for an ensemble of models, even if based on drastically different physical…
Fine-tuning in physics and cosmology is often used as evidence that a theory is incomplete. For example, the parameters of the standard model of particle physics are "unnaturally" small (in various technical senses), which has driven much…
The ratio of Bayesian evidences is a popular tool in cosmology to compare different models. There are however several issues with this method: Bayes' ratio depends on the prior even in the limit of non-informative priors, and Jeffrey's…
Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for…
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…