Related papers: Reducing parametric uncertainties through informat…
In problems of parameter estimation from sensor data, the Fisher Information provides a measure of the performance of the sensor; effectively, in an infinitesimal sense, how much information about the parameters can be obtained from the…
Image-based simulation, the use of 3D images to calculate physical quantities, fundamentally relies on image segmentation to create the computational geometry. However, this process introduces image segmentation uncertainty because there is…
The information rates achievable by using electromagnetic radiation affected by thermal noise and signal decoherence are studied. The standard coherent Gaussian model is compared with an alternative photon gas model which represents lack of…
This paper presents a novel method for analyzing the latent space geometry of generative models, including statistical physics models and diffusion models, by reconstructing the Fisher information metric. The method approximates the…
A model in statistical mechanics, characterised by the corresponding Gibbs measure, is a subset of the totality of probability distributions on the phase space. The shape of this subset, i.e., the geometry, then plays an important role in…
Information geometry and Wasserstein geometry are two main structures introduced in a manifold of probability distributions, and they capture its different characteristics. We study characteristics of Wasserstein geometry in the framework…
Motivated by the analysis of the distribution of university grades, which is usually asymmetric, we discuss two informative priors for the shape parameter of the skew-normal distribution, showing that they lead to closed-form…
In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and…
Technology of data collection and information transmission is based on various mathematical models of encoding. The words "Geometry of information" refer to such models, whereas the words "Moufang patterns" refer to various sophisticated…
Probabilistic machine learning techniques can learn both complex relations between input features and output quantities of interest as well as take into account stochasticity or uncertainty within a data set. In this initial work, we…
The time-dependent generator coordinate method with the gaussian overlap approximation (TDGCM+GOA) formalism is applied to describe the fission of $^{252}$Cf. We perform analysis of fission from the initial states laying in the energetic…
We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…
Wasserstein geometry and information geometry are two important structures to be introduced in a manifold of probability distributions. Wasserstein geometry is defined by using the transportation cost between two distributions, so it…
Parameter inference with an estimated covariance matrix systematically loses information due to the remaining uncertainty of the covariance matrix. Here, we quantify this loss of precision and develop a framework to hypothetically restore…
Fine-tuning and naturalness, the sensitivity of low-energy observables to small changes in the fundamental parameters of a theory, are cornerstones of physics beyond the Standard Model. We propose a new measure of fine-tuning based on…
We present a framework for the detection and estimation of deformations applied to a grid of sources. Our formalism uses the Hamiltonian formulation of the quantum Fisher information matrix (\textsc{qfim}) as the figure of merit to quantify…
Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…
The response of a vibrating beam to a force depends on many physical parameters including those determined by material properties. Damage caused by fatigue or cracks result in local reductions in stiffness parameters and may drastically…
The Gaussian function (GF) is widely used to explain the behavior or statistical distribution of many natural phenomena as well as industrial processes in different disciplines of engineering and applied science. For example, the GF can be…
Image segmentation is a complex mathematical problem, especially for images that contain intensity inhomogeneity and tightly packed objects with missing boundaries in between. For instance, Magnetic Resonance (MR) muscle images often…