Related papers: On Probability and Cosmology: Inference Beyond Dat…
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…
Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The…
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…
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 discuss the possibility that the inflationary paradigm, undoubtfully today's best framework to understand all the present cosmological data, may still have some viable challengers. The underlying idea for such discussions is that…
We review some of the common methods for model selection: the goodness of fit, the likelihood ratio test, Bayesian model selection using Bayes factors, and the classical as well as the Bayesian information theoretic approaches. We…
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…
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a…
Cosmology has come a long way from being based on a small number of observations to being a data-driven precision science. We discuss the questions "What is observable?", "What in the Universe is knowable?" and "What are the fundamental…
In this paper, using a significantly improved version of the model-independent, cosmographic approach to cosmology (John, M. V. 2004, ApJ, 614, 1), we address an important question: Was there a decelerating past for the universe? To answer…
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…
While Bayesian model selection is a useful tool to discriminate between competing cosmological models, it only gives a relative rather than an absolute measure of how good a model is. Bayesian doubt introduces an unknown benchmark model…
[Abridged] Some cosmological theories propose that the observable universe is a small part of a much larger universe in which parameters describing the low-energy laws of physics vary from region to region. How can we reasonably assess a…
A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of…
We discuss epistemological and methodological aspects of the Bayesian approach in astrophysics and cosmology. The introduction to the Bayesian framework is given for a further discussion concerning the Bayesian inference in physics. The…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
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…
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…
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…