Related papers: Bayesian Reasoning in Eternal Inflation: A Solutio…
With present and future observations becoming of higher and higher quality, it is timely and necessary to investigate the most significant theoretical uncertainties in the predictions of inflation. We show that our ignorance of the entire…
At very early times, the universe was not in a vacuum state. Under the assumtion that the deviation from equillibrium was large, in particular that it is higher than the scale of inflation, we analyse the conditions for local transitions…
We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…
I study a model which describes the birth of the universe using a global topological phase transition with a complex manifold where the time, $\tau$, is considered as a complex variable. Before the big bang $\tau$ is a purely imaginary…
The experimental problem of converting a measured binomial quantity, the fraction of events in a sample that pass a cut, into a physical binomial quantity, the fraction of events originating from a signal source, is described as a system of…
In the picture of eternal inflation as driven by a scalar potential with multiple minima, our observable universe resides inside one of many bubbles formed from transitions out of a false vacuum. These bubbles necessarily collide, upsetting…
The primordial bispectrum has been considered in the past decade as a powerful probe of the physical processes taking place in the early Universe. Within the inflationary paradigm, the properties of the bispectrum are one of the keys that…
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
Probabilistic neural networks are typically modeled with independent weight priors, which do not capture weight correlations in the prior and do not provide a parsimonious interface to express properties in function space. A desirable class…
The statistical properties of the primordial density perturbations has been considered in the past decade as a powerful probe of the physical processes taking place in the early universe. Within the inflationary paradigm, the properties of…
We review the paradigm of eternal inflation in the light of the recently proposed corpuscular picture of space-time. Comparing the strength of the average fluctuation of the field up its potential with that of quantum depletion, we show…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
Everlasting inflation has far-reaching implications for cosmology and the standing of self-localizing inferences made by observers, which have been subjects of renewed interest in light of the growing acceptance of theory landscapes and the…
This paper develops Bayesian sample size formulae for experiments comparing two groups. We assume the experimental data will be analysed in the Bayesian framework, where pre-experimental information from multiple sources can be represented…
We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…
We develop a variational Bayes approach for dynamic variable selection in high-dimensional regression models with time-varying parameters and predictors that exhibit a predefined group structure. Through comprehensive simulation studies, we…
The scalar field is considered to have dominated the early Universe. One subtle yet crucial requirement of this assumption is that the solution must be highly stable, i.e., indifferent to any initial conditions because there are no favored…
We consider Bayesian shrinkage predictions for the Normal regression problem under the frequentist Kullback-Leibler risk function. Firstly, we consider the multivariate Normal model with an unknown mean and a known covariance. While the…