Related papers: Testing the Multiverse: Bayes, Fine-Tuning and Typ…
Recent developments in cosmology suggest that much of the universe is in a state of explosive, accelerated expansion, called inflation. We live in a "bubble" where inflation has ended, and other bubbles with diverse properties are…
The problem of making practical, useful goodness of fit tests in the Bayesian paradigm is largely open. We introduce a class of special cases (testing for uniformity: have the cards been shuffled enough; does my random generator work) and a…
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors,…
An extension of the Standard Model by extra scalar singlets was considered. Theoretical (unitarity, vacuum stability, triviality) and cosmological (dark matter relic abundance, direct detection experiments, constraints on dark matter…
The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…
We re-analyze the question of the use of cosmological observations to infer the present state and future evolution of our patch of the universe. In particular, we discuss under which conditions one might be able to infer that our patch will…
In this article we review the theory of cosmological inflation with a particular focus on the beautiful connection it provides between the physics of the very small and observations of the very large. We explain how quantum mechanical…
For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare…
Numerical simulations are widely used to predict the behavior of physical systems, with Bayesian approaches being particularly well suited for this purpose. However, experimental observations are necessary to calibrate certain simulator…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
The past five years has seen a surge in research and innovative ideas for the imaging of extrasolar planets, particular terrestrial ones. We expect that within the next decade a space observatory will be launched with the objective of…
In the modern Bayesian view classical probability theory is simply an extension of conventional logic, i.e., a quantitative tool that allows for consistent reasoning in the presence of uncertainty. Classical theory presupposes, however,…
Over the past decade advancements in the understanding of several astrophysical phenomena have allowed us to infer a concordance cosmological model that successfully accounts for most of the observations of our universe. This has opened up…
Astronomers are often confronted with funky populations and distributions of objects: brighter objects are more likely to be detected; targets are selected based on colour cuts; imperfect classification yields impure samples. Failing to…
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 big bang model and the history of the early universe according to the grand unified theories are introduced. The shortcomings of big bang are discussed together with their resolution by inflationary cosmology. Inflation, the subsequent…
In forthcoming years, connections between cosmology and particle physics will be made increasingly important with the advent of a new generation of cosmic microwave background (CMB) experiments. Here, we review a number of these links. Our…
Theory refinement is the task of updating a domain theory in the light of new cases, to be done automatically or with some expert assistance. The problem of theory refinement under uncertainty is reviewed here in the context of Bayesian…
Time-symmetric cosmological theories, in which the initial and final states are arranged to have similar features or are independently fixed, have been quite extensively discussed in the literature. However, a more general and perhaps more…
The terrain that theorists cover in this CMB golden age is described. We ponder early universe physics in quest of the fluctuation generator. We extoll the virtues of inflation and defects. We transport fields, matter and radiation into the…