Related papers: Einstein from Noise: Statistical Analysis
We present a simple stochastic mechanism which generates pulse trains exhibiting a power law distribution of the pulse intervals and a $1/f^\alpha$ power spectrum over several decades at low frequencies with $\alpha$ close to one. The…
Objective: Tinnitus affects 10-15% of the population yet lacks objective diagnostic biomarkers. This study applied machine learning to EEG and fMRI data to identify neural signatures distinguishing tinnitus patients from healthy controls.…
Sensor noise sources cause differences in the signal recorded across pixels in a single image and across multiple images. This paper presents a Bayesian approach to decomposing and characterizing the sensor noise sources involved in imaging…
Statistical mechanics is used to study unrealizable generalization in two large feed-forward neural networks with binary weights and output, a perceptron and a tree committee machine. The student is trained by a teacher being larger, i.e.…
We present an estimation of the noise induced by scattered light inside the main arms of the Einstein Telescope (ET) gravitational wave detector. Both ET configurations for high- and low-frequency interferometers are considered, for which…
We study the performance of the Topological Uncertainty (TU) constructed with a trained feedforward neural network (FNN) for Anomaly Detection. Generally, meaningful information can be stored in the hidden layers of the trained FNN, and the…
This study is devoted to the inference problem of extracting the nuclear matter properties directly from a set of mass-radius observations. We employ Bayesian neural networks (BNNs), which is a probabilistic model capable of estimating the…
Gene expression is stochastic and displays variation ("noise") both within and between cells. Intracellular (intrinsic) variance can be distinguished from extracellular (extrinsic) variance by applying the law of total variance to data from…
The space-based detector LISA may observe gravitational waves from the early inspiral of stellar-mass black hole binaries, some of which could have significant eccentricity. Current gravitational waveform templates are only valid for small…
The Einstein Telescope is a proposed third generation gravitational wave detector that will operate in the region of 1 Hz to a few kHz. As well as the inspiral of compact binaries composed of neutron stars or black holes, the lower…
Current AI systems excel at pattern recognition but fail at causal reasoning. We argue this is not an engineering limitation but reveals something fundamental about the nature of understanding itself. We propose that causal cognition…
Weak lensing experiments are a powerful probe of cosmology through their measurement of the mass distribution of the universe. A challenge for this technique is to control systematic errors that occur when measuring the shapes of distant…
While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set --`inferring the uncertainty of model parameters on the basis of observations' -- has been continually pursued by many statisticians. To…
Gravitational wave (GW) observations from extreme-mass-ratio inspirals (EMRIs) are powerful tools for testing general relativity (GR). However, systematic errors arising from waveform models could potentially lead to incorrect scientific…
Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…
We study the quantum to classical transition in Boson Sampling by analysing how $N$-boson interference is affected by inevitable noise in an experimental setup. We adopt the Gaussian noise model of Kalai and Kindler for Boson Sampling and…
In this study, we explore the effects of including noise predictors and noise observations when fitting linear regression models. We present empirical and theoretical results that show that double descent occurs in both cases, albeit with…
Cellular processes do not follow deterministic rules; even in identical environments genetically identical cells can make random choices leading to different phenotypes. This randomness originates from fluctuations present in the…
Spatially entangled twin photons provide a test of the Einstein-Podolsky-Rosen (EPR) paradox in its original form of position (image plane) versus impulsion (Fourier plane). We show that recording a single pair of images in each plane is…
Recent algebraic parametric estimation techniques led to point-wise derivative estimates by using only the iterated integral of a noisy observation signal. In this paper, we extend such differentiation methods by providing a larger choice…