Related papers: Bayesian Reasoning in Eternal Inflation: A Solutio…

We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set…

Bayesian clinical trials can benefit of available historical information through the elicitation of informative prior distributions. Concerns are however often raised about the potential for prior-data conflict and the impact of Bayes test…

The capability of Cosmic Inflation to explain the latest Cosmic Microwave Background and Baryonic Acoustic Oscillation data is assessed by performing Bayesian model comparison within the landscape of nearly three-hundred models of…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…

Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…

The hypothesis that the Universe underwent a period of exponential expansion at very early times has become the most popular theory of the early Universe. Not only does it solve some of the problems of standard big bang cosmology, but it…

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…

We propose an intuitive framework for studying the problem of initial conditions in slow-roll inflation. In particular, we consider a universe at high, but sub-Planckian energy density and analyze the circumstances under which it is…

Based on the conventional metric tensor and driven by a nearly constant energy density, cosmic inflation, characterized by a remarkably accelerated expansion, was proposed as an early epoch in the Universe. The energy density is typically…

In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…

We address the problem of reconstructing quantum theory from the perspective of an agent who makes bets about the outcomes of possible experiments. We build a general Bayesian framework that can be used to organize the agent's beliefs and…

Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…

Data sets for statistical analysis become extremely large even with some difficulty of being stored on one single machine. Even when the data can be stored in one machine, the computational cost would still be intimidating. We propose a…

Eternal inflation is studied in the context of warm inflation. We focus on different tools to analyze the effects of dissipation and the presence of a thermal radiation bath on the fluctuation-dominated regime, for which the…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

Following Freivogel {\it et al} we consider inflation in a predictive (or `friendly') region of the landscape of string vacua, as modeled by Arkani-Hamed, Dimopoulos and Kachru. In such a region the dimensionful coefficients of…

Depending on the type and arrangement of metastable vacua in the theory, initial conditions in a de Sitter vacuum with arbitrarily large entropy can be compatible with the observed arrow of time, if the causal patch or related measures are…

The ongoing unprecedented exponential explosion of available computing power, has radically transformed the methods of statistical inference. What used to be a small minority of statisticians advocating for the use of priors and a strict…

We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the…