Related papers: On Probability and Cosmology: Inference Beyond Dat…
Theory testing in the physical sciences has been revolutionized in recent decades by Bayesian approaches to probability theory. Here, I will consider Bayesian approaches to theory extensions, that is, theories like inflation which aim to…
Our knowledge about the universe has increased tremendously in the last three decades or so --- thanks to the progress in observations --- but our understanding has improved very little. There are several fundamental questions about our…
The averaging problem in cosmology is of considerable importance for the correct interpretation of cosmological data. We review cosmological observations and discuss some of the issues regarding averaging. We present a precise definition of…
In astronomical and cosmological studies one often wishes to infer some properties of an infinite-dimensional field indexed within a finite-dimensional metric space given only a finite collection of noisy observational data. Bayesian…
In these lectures I focus on early universe models which can explain the currently observed structure on large scales. I begin with a survey of inflationary cosmology, the current paradigm for understanding the origin of the universe as we…
The main objective of this study is to investigate the phenomenon of the bouncing scenario of the universe. The most widely recognized cosmological framework is the standard cosmological model, sometimes referred to as the Big Bang model.…
Probabilities in eternal inflation are traditionally defined as limiting frequency distributions, but a unique and unambiguous probability measure remains elusive. In this paper, we present a different approach, based on Bayesian reasoning.…
In this talk we discuss three different issues. First of all, there exist several proposals how to solve cosmological problems by adiabatic expansion of the Universe, without any use of inflation. We explain why these models do not solve…
The standard Bayesian model formalism comparison cannot be applied to most cosmological models as they lack well-motivated parameter priors. However, if the data-set being used is separable then it is possible to use some of the data to…
Bayesian model averaging is a procedure to obtain parameter constraints that account for the uncertainty about the correct cosmological model. We use recent cosmological observations and Bayesian model averaging to derive tight limits on…
The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of…
Observational cosmology is in its "golden age" with a vast amount of recent data on the distribution of matter and light in the universe. This data can be used to probe theories of the very early universe. It is small amplitude cosmological…
We consider the properties of an ensemble of universes as function of size, where size is defined in terms of the asymptotic value of the Hubble constant (or, equivalently, the value of the cosmological constant). We assume that standard…
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…
Mathematical models connect theory with the real world through data, enabling us to interpret, understand, and predict complex phenomena. However, scientific knowledge often extends beyond what can be empirically measured, offering valuable…
Observational tests during the next decade may determine if the evolution of the Universe can be understood from fundamental physical principles, or if special initial conditions, coincidences, and new, untestable physical laws must be…
Astrophysics and cosmology can be used to test the standard model of particle physics under conditions and over distance and time scales not accessible to laboratory experiments. Most of the astrophysical observations are in good agreement…
Cosmic inflation is envisioned as the ``most likely'' start for the observed universe. To give substance to this claim, a framework is needed in which inflation can compete with other scenarios and the relative likelihood of all scenarios…
There has been significant recent progress in observational cosmology. This, in turn, has provided an unprecedented picture of the early universe and its evolution. In this review I will present a (biased) view of how one can use these…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…