Related papers: Einstein from Noise: Statistical Analysis
Mesoscopic systems -- small electric circuits working in quantum regime -- offer us a unique experimental stage to explorer quantum transport in a tunable and precise way. The purpose of this Review is to show how they can contribute to…
Consider the following three important problems in statistical inference, namely, constructing confidence intervals for (1) the error of a high-dimensional ($p>n$) regression estimator, (2) the linear regression noise level, and (3) the…
Aleatoric uncertainty captures the inherent randomness of the data, such as measurement noise. In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance…
Quantum-enhanced metrology surpasses classical metrology by improving estimation precision scaling with a resource $N$ (e.g., particle number or energy) from $1/\sqrt{N}$ to $1/N$. Through the use of nonlinear effects, Roy and…
We propose a semiparametric Bayesian methodology for estimating the average treatment effect (ATE) within the potential outcomes framework using observational data with high-dimensional nuisance parameters. Our method introduces a Bayesian…
Internal mechanism leading to the emergence of the widely occurring 1/f noise still remains an open issue. In this paper we investigate the distinction between internal time of the system and the physical time as a source of 1/f noise.…
An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…
The detectors in mass spectrometers are precise enough to count ion events. In practice, the statistics of chemical noise are affected by large quantization errors and overdispersion because of amplification in the detector. The detector…
The Einstein relation, relating the steady state fluctuation properties to the linear response to a perturbation, is considered for steady states of stochastic models with a finite state space. We show how an Einstein relation always holds…
We present a theoretical background for the data analysis of the gravitational-wave signals from spinning neutron stars for Earth-based laser interferometric detectors. We introduce a detailed model of the signal including both the…
The next generation of ground-based gravitational-wave detectors, Einstein Telescope (ET) and Cosmic Explorer (CE), present a unique opportunity to put constraints on dense matter, among many other groundbreaking scientific goals. In a…
Recent theoretical studies (Kou et al., 2023; Cao et al., 2022) have revealed a sharp phase transition from benign to harmful overfitting when the noise-to-feature ratio exceeds a threshold-a situation common in long-tailed data…
High-dimensional inference refers to problems of statistical estimation in which the ambient dimension of the data may be comparable to or possibly even larger than the sample size. We study an instance of high-dimensional inference in…
We exploit the great potential offered by Bayesian Neural Networks (BNNs) to directly decipher the internal composition of neutron stars (NSs) based on their macroscopic properties. By analyzing a set of simulated observations, namely NS…
The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…
Modern machine learning often operates in the regime where the number of parameters is much higher than the number of data points, with zero training loss and yet good generalization, thereby contradicting the classical bias-variance…
We investigated the use of the Bayesian inference to restore noise-degraded images under conditions of spatially correlated noise. The generative statistical models used for the original image and the noise were assumed to obey…
We introduce a particular construction of an autocorrelation matrix of a time series and its analysis based on the random-matrix theory ideas that is capable of unveiling the type of correlations information which is inaccessible to the…
The Einstein Telescope is the next-generation gravitational wave interferometer which, compared to current detectors, will enable the observation of gravitational signals at lower frequencies with a sensitivity improved by approximately two…
The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…