Related papers: Bayesian Reasoning in Eternal Inflation: A Solutio…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
In BP models with hundreds of fluxes, we compute the effects of cosmological dynamics on the probability distribution of landscape vacua. Starting from generic initial conditions, we find that most fluxes are dynamically driven into a…
Inflationary cosmology proposes that the early Universe undergoes accelerated expansion, driven, in simple scenarios, by a single scalar field, or inflaton. The form of the inflaton potential determines the initial spectra of density…
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…
I propose a new volume-weighted probability measure for cosmological "multiverse" scenarios involving eternal inflation. The "reheating-volume (RV) cutoff" calculates the distribution of observable quantities on a portion of the reheating…
The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. It is argued that essentially all inflationary models lead to (future-)eternal…
There exists the "entropy problem" of the early universe, that is, why did the universe begin with an extremely low entropy and how did it evolve into such high entropy at late times? It has been long believed that inflation cannot be the…
In this thesis we will primarily demonstrate how additional scalar degrees of freedom - which are motivated from many high-energy embeddings - open up new observational windows onto the physics of inflation. We construct a Bayesian…
In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
We present an interpretation of the physics of space-times undergoing eternal inflation by repeated nucleation of bubbles. In many cases the physics can be interpreted in terms of the quantum mechanics of a system with a finite number of…
The mechanism for triggering the universe inflation could be that at very early periods the time variable was discrete instead of smooth. Alternatively, and perhaps equivalently, it could be the consequence that the metrics of the early…
In this paper we explore the relationship between the existence of eternal inflation and the initial conditions leading to inflation. We demonstrate that past and future completion of inflation is related, in that past-incomplete inflation…
The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…
We consider the problem of integrating a small probability sample (ps) and a non-probability sample (nps). By definition, for the nps, there are no survey weights, but for the ps, there are survey weights. The key issue is that the nps,…
Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are…
Inflation is known to be generically eternal to the future: the false vacuum is thermalized in some regions of space, while inflation continues in other regions. Here, we address the question of whether inflation can also be eternal to the…
After reviewing the general ideas of quantum cosmology (Wheeler-DeWitt equation, boundary conditions, interpretation of $\psi$), I discuss how these ideas can be tested observationally. Observational predictions differ for different choices…
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…
Eternal inflation, the idea that there is always a part of the universe that is expanding exponentially, is a frequent feature of inflationary models. It has been argued that eternal inflation requires the violation of energy conditions,…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…