Related papers: Intrinsic probability distributions for physical s…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
The Fisher information matrix can be used to characterize the local geometry of the parameter space of neural networks. It elucidates insightful theories and useful tools to understand and optimize neural networks. Given its high…
We show how to verify the metrological usefulness of quantum states based on the expectation values of an arbitrarily chosen set of observables. In particular, we estimate the quantum Fisher information as a figure of merit of metrological…
We derive a new variational principle for the quantum Fisher information leading to a simple iterative alternating algorithm, the convergence of which is proved. The case of a fixed measurement, i.e. the classical Fisher information, is…
The probability distribution of the order parameter is exploited in order to obtain the criticality of magnetic systems. Monte Carlo simulations have been employed by using single spin flip Metropolis algorithm aided by finite-size scaling…
We describe a statistical method to avoid biased estimation of the content of different particle species. We consider the case when the particle identification information strongly depends on some kinematical variables, whose distributions…
The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and…
Heisenberg-like and Fisher-information-based uncertainty relations which extend and generalize previous similar expressions are obtained for $N$-fermion $d$-dimensional systems. The contributions of both spatial and spin degrees of freedom…
By using concrete scenarios, we present and discuss a new concept of probabilistic Self-Stabilization in Distributed Systems.
We derive general expressions for the multi-tracer Fisher matrix, both assuming that the cross-spectra are constrained by the auto-spectra, and also allowing for independent degrees of freedom in the cross-spectra. We show that, just like…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
The two principal/immediate influences -- which we seek to interrelate here -- upon the undertaking of this study are papers of Zyczkowski and Slomczy\'nski (J. Phys. A 34, 6689 [2001]) and of Petz and Sudar (J. Math. Phys. 37, 2262…
We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. This result…
We consider a drift-diffusion process of $N$ stochastic particles and show that its empirical measure converges, as $N\rightarrow \infty$, to the solution of the Landau equation. We work in the regime of very soft and Coulomb potentials…
A new distribution named intensive natural distribution is introduced with the intent of consolidating statistics and empirical data. Based on the probability derived from the Bernoulli distribution, this method extended also Poisson…
Natural gradient descent, which preconditions a gradient descent update with the Fisher information matrix of the underlying statistical model, is a way to capture partial second-order information. Several highly visible works have…
We have calculated the Tsallis entropy and Fisher information matrix (entropy) of spatially-correlated nonextensive systems, by using an analytic non-Gaussian distribution obtained by the maximum entropy method. Effects of the correlated…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
The Fisher information matrix (FIM) is a foundational concept in statistical signal processing. The FIM depends on the probability distribution, assumed to belong to a smooth parametric family. Traditional approaches to estimating the FIM…
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years,…