Related papers: Bayesian Reasoning in Eternal Inflation: A Solutio…
The problem of making predictions in eternally inflating universe that thermalizes by bubble nucleation is considered. A recently introduced regularization procedure is applied to find the probability distribution for the ensemble of…
The method of maximum entropy (ME) is extended to address the following problem: Once one accepts that the ME distribution is to be preferred over all others, the question is to what extent are distributions with lower entropy supposed to…
We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
Consider universal data compression: the length $l(x^n)$ of sequence $x^n\in A^n$ with finite alphabet $A$ and length $n$ satisfies Kraft's inequality over $A^n$, and $-\frac{1}{n}\log \frac{P^n(x^n)}{Q^n(x^n)}$ almost surely converges to…
By means of Bayesian techniques, we study how a premature ending of inflation, motivated by geometrical destabilization, affects the observational evidences of typical inflationary models. Large field models are worsened, and inflection…
Since the advent of inflation, several theorems have been proven suggesting that although inflation can (and generically does) continue eternally into the future, it cannot be extended eternally into the past to create a ``steady-state''…
Much is now known about the consistency of Bayesian updating on infinite-dimensional parameter spaces with independent or Markovian data. Necessary conditions for consistency include the prior putting enough weight on the correct…
The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…
Inflationary models of the early universe provide a natural mechanism for the formation of large scale structure. This success brings to forefront the question of naturalness: Does a sufficiently long slow roll inflation occur generically…
Cosmic inflation is arguably the most favoured paradigm of the very early Universe. It postulates an early phase of fast, nearly exponential, and accelerated expansion. Inflationary models are capable of explaining the overall flatness and…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…
We calculate the Bayesian evidences for a class of Ekpyrotic universe models, and compare with a model of single field inflation with a Higgs-type potential. Combining parsimony and observational constraints, this gives us a systematic way…
Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…
We investigate if the observed small and nearly scale-invariant primordial cosmic perturbation, i.e. the perturbation amplitude $P_\zeta\sim10^{-9}$ and the spectral index $n_s \simeq 0.965$, is typical in the landscape of vacua after…
The intuitive reasoning of physicists in conditions of uncertainty is closer to the Bayesian approach than to the frequentist ideas taught at University and which are considered the reference framework for handling statistical problems. The…
By quantising the background as well as the perturbations in a simple one fluid model, we show that there exists an ambiguity in the choice of relevant variables, potentially leading to incompatible observational physical predictions. In a…
In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…
Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…