Related papers: Bayesian model comparison in cosmology
Frequentist statistical methods, such as hypothesis testing, are standard practice in papers that provide benchmark comparisons. Unfortunately, these methods have often been misused, e.g., without testing for their statistical test…
Measures of discordance between datasets have become an essential part of cosmological analyses. It is important to accurately evaluate the significance of such discordances when present. We propose here a Bayesian interpretation of…
Forecasting techniques for assessing the power of future experiments to discriminate between theories or discover new laws of nature are of great interest in many areas of science. In this paper, we introduce a Bayesian forecasting method…
Bayesian modeling provides a principled approach to quantifying uncertainty in model parameters and model structure and has seen a surge of applications in recent years. Within the context of a Bayesian workflow, we are concerned with model…
Physics increasingly uses Bayesian techniques for systematic data analysis and model-to-data comparison. This paper describes how these methods can be implemented to answer questions of relevance to teaching laboratories. It demonstrates…
Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of…
We review observational tests for the homogeneity of the Universe on large scales. Redshift and peculiar velocity surveys, radio sources, the X-Ray Background, the Lyman-$\alpha$ forest and the Cosmic Microwave Background are used to set…
Correlations between spacelike separated measurements on entangled quantum systems are stronger than any classical correlations and are at the heart of numerous quantum technologies. In practice, however, spacelike separation is often not…
Cosmology is becoming an important tool to test particle physics models. We provide an overview of the standard model of cosmology with an emphasis on the observations relevant for testing fundamental physics.
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
The well-known Bayes theorem assumes that a posterior distribution is a probability distribution. However, the posterior distribution may no longer be a probability distribution if an improper prior distribution (non-probability measure)…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…
Model-independent methods in cosmology has become an essential tool in order to deal with an increasing number of theoretical alternatives for explaining the late-time acceleration of the Universe. In principle, this provides a way of…
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…
A mathematical model is a function taking certain arguments and returning a theoretical prediction of a feature of a physical system. The arguments to the mathematical model can be split into two groups; (a) controllable variables of the…
Models of the Universe like the Concordance Model today used to interpret cosmological observations give expectation values for many cosmological observable so accurate that frequently peoples speak of Precision Cosmology. The quoted…
This paper presents a performance comparison of different estimation and prediction techniques applied to the problem of tracking multiple robots. The main performance criteria are the magnitude of the estimation or prediction error, the…
Gaussian processes provide a method for extracting cosmological information from observations without assuming a cosmological model. We carry out cosmography -- mapping the time evolution of the cosmic expansion -- in a model-independent…
Cosmological models that invoke a multiverse - a collection of unobservable regions of space where conditions are very different from the region around us - are controversial, on the grounds that unobservable phenomena shouldn't play a…