Related papers: Measure Theoretic Aspects Of Error Terms
In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
This article proposes a link between statistics and the theory of Dirichlet forms used to compute errors. The error calculus based on Dirichlet forms is an extension of classical Gauss' approach to error propagation. The aim of this paper…
Science students must deal with the errors inherent to all physical measurements and be conscious of the need to expressvthem as a best estimate and a range of uncertainty. Errors are routinely classified as statistical or systematic.…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
Properties of weighted averages are studied for the general case that the individual measurements are subject to hidden correlations and have asymmetric statistical as well as systematic errors. Explicit expressions are derived for an…
The uncertainty principle places a fundamental limit on the accuracy with which we can measure conjugate physical quantities. However, the fluctuations of these variables can be assessed in terms of different estimators. We propose a new…
Asymmetric statistical errors arise for experimental results obtained by Maximum Likelihood estimation, in cases where the number of results is finite and the log likelihood function is not a symmetric parabola. This note discusses how…
We demonstrate that description of fluctuations observed in multiparticle production processes using Tsallis statistics approach (in which fluctuations are described by the nonextensivity parameter q) leads to a specific sum rule for…
Fluctuation theorems are fundamental results in non-equilibrium thermodynamics. Considering the fluctuation theorem with respect to the entropy production and an observable, we derive a new thermodynamic uncertainty relation which also…
The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical…
Typical experimental measurement is set up as a study of the system's response to a stationary external excitation. This approach considers any random fluctuation of the signal as spurious contribution which is to be eliminated via…
We present theoretical analysis and the results of measurements of fundamental thermorefractive fluctuations in microspheres. Experimentally measured noise spectra are consistent with the theoretical model.
The aim of this work is to expose some asymptotic series associated to some expressions involving the volume of the n-dimensional unit ball. All proofs and the methods used for improving the classical inequalities announced in the final…
In the stochastic frontier model, the composed error term consists of the measurement error and the inefficiency term. A general assumption is that the inefficiency term follows a truncated normal or exponential distribution. In a wide…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
We introduce from an experimental point of view the main concepts of fluctuation theorems for work, heat and entropy production in out of equilibrium systems. We will discuss the important difference between the applications of these…
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…