Related papers: Einstein from Noise: Statistical Analysis
The Einstein Telescope (ET) is a third-generation underground gravitational-wave observatory designed to extend the detection sensitivity down to a few Hertz. Newtonian noise is expected to limit the low-frequency sensitivity of ET,…
We tackle the problem of template estimation when data have been randomly transformed under an isometric group action in the presence of noise. In order to estimate the template, one often minimizes the variance when the influence of the…
Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…
The noise of signals or currents consisting from a sequence of pulses, elementary events or moving discrete objects (particles) is analyzed. A simple analytically solvable model is investigated in detail both analytically and numerically.…
Stray light represents a significant noise source for gravitational wave detectors, requiring an accurate modeling and mitigation to preserve the experiment's sensitivity. In this article, we present an updated and improved analysis of the…
The Einstein Telescope (ET) is a proposed third-generation gravitational-wave (GW) underground observatory. It will have greatly increased sensitivity compared to current GW detectors, and it is designed to extend the observation band down…
We tackle the problem of template estimation when data have been randomly deformed under a group action in the presence of noise. In order to estimate the template, one often minimizes the variance when the influence of the transformations…
In this article, we study the consistency of the template estimation with the Fr\'echet mean in quotient spaces. The Fr\'echet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We…
Attention mechanism is a fundamental component of the transformer model and plays a significant role in its success. However, the theoretical understanding of how attention learns to select tokens is still an emerging area of research. In…
In this paper, we develop a generalized Bayesian inference framework for a collection of signal-plus-noise matrix models arising in high-dimensional statistics and many applications. The framework is built upon an asymptotically unbiased…
Summary statistics of the likelihood, such as the Bayesian evidence, offer a principled way of comparing models and assessing tension between, or within, the results of physical experiments. Noisy realisations of the data induce scatter in…
In this work we analyze the stochastic dynamics of the Kauffman model evolving under the influence of noise. By considering the average crossing time between two distinct trajectories, we show that different Kauffman models exhibit a…
Distant and weak supervision allow to obtain large amounts of labeled training data quickly and cheaply, but these automatic annotations tend to contain a high amount of errors. A popular technique to overcome the negative effects of these…
Inference and hypothesis testing are typically constructed on the basis that a specific model holds for the data. To determine the veracity of conclusions drawn from such data analyses, one must be able to identify the presence of the…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
The Einstein Telescope is a third-generation underground gravitational wave observatory designed to achieve unprecedented sensitivity down to 3 Hz. Waves propagating in the soil due to anthropogenic or natural vibration sources generate…
Several proposed gravitational wave interferometers have a triangular configuration, such as the Einstein Telescope and the Laser Interferometer Space Antenna. For such a configuration one can construct a unique null channel insensitive to…
This paper addresses the detection of a stochastic process in noise from irregular samples. We consider two hypotheses. The \emph{noise only} hypothesis amounts to model the observations as a sample of a i.i.d. Gaussian random variables…
Consider the estimation of a signal ${\bf x}\in\mathbb{R}^N$ from noisy observations ${\bf r=x+z}$, where the input~${\bf x}$ is generated by an independent and identically distributed (i.i.d.) Gaussian mixture source, and ${\bf z}$ is…
Computer simulations of the Ising model exhibit white noise if thermal fluctuations are governed by Boltzmann's factor alone; whereas we find that the same model exhibits 1/f noise if Boltzmann's factor is extended to include local…