Related papers: Bayesian Reasoning in Eternal Inflation: A Solutio…
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…
Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a…
We propose a model of inflation with a suitable potential for a single scalar field which falls in the wide class of hilltop inflation. We derive the analytical expressions for most of the physical quantities related to inflation and show…
Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \rightarrow D$, there is a corresponding inference map $I: D \rightarrow…
Inflationary models, especially those with plateau-type potentials, are consistent with the cosmological data, but inflation itself does not resolve the initial singularity. This singularity is resolved, for example, by the idea of the…
There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…
We formulate the basic postulate of pre-big bang cosmology as one of ``asymptotic past triviality'', by which we mean that the initial state is a generic perturbative solution of the tree-level low-energy effective action. Such a…
The theory of eternal inflation in an inflaton potential with multiple vacua predicts that our universe is one of many bubble universes nucleating and growing inside an ever-expanding false vacuum. The collision of our bubble with another…
The recently proposed "reheating-volume" (RV) measure promises to solve the long-standing problem of extracting probabilistic predictions from cosmological "multiverse" scenarios involving eternal inflation. I give a detailed description of…
The Bayesian statistical paradigm provides a principled and coherent approach to probabilistic forecasting. Uncertainty about all unknowns that characterize any forecasting problem -- model, parameters, latent states -- is able to be…
We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…
This article expands the framework of Bayesian inference and provides direct probabilistic methods for approaching inference tasks that are typically handled with information theory. We treat Bayesian probability updating as a random…
Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…
I propose a new mechanism to account for the observed tiny but finite dark energy in terms of a non-Abelian Higgs theory, which has infinitely many perturbative vacua characterized by a winding number, in the framework of inflationary…
During inflation, primordial energy density fluctuations are created from approximate de Sitter vacuum quantum fluctuations redshifted out of the horizon after which they are frozen as perturbations in the background curvature. In this…
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…
The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…
It has been widely claimed that inflation is generically eternal to the future, even in models where the inflaton potential monotonically increases away from its minimum. The idea is that quantum fluctuations allow the field to jump uphill,…
The Bayesian framework is a well-studied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard…