相关论文: What Do We Mean by Malmquist Bias?
A review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the…
Traditional language models face a challenge from hallucinations. Their very presence casts a large, dangerous shadow over the promising realm of natural language processing. It becomes crucial to understand the various kinds of…
The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…
Cosmic backreaction refers to the general question of whether a homogeneous and isotropic cosmological model is able to predict the correct expansion dynamics of our inhomogeneous Universe. One aspect of this issue concerns the validity of…
Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…
This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean plane, we study the problem of determining their relative…
We introduce the concept of back-reaction in relativistic cosmological modeling. Roughly speaking, this can be thought of as the difference between the large-scale behaviour of an inhomogeneous cosmological solution of Einstein's equations,…
Quantum theory does not provide a unique definition for the joint probability of two non-commuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were…
In this pedagogical lecture, I introduce some of the basic terminology and description of fluctuating fields as they occur on cosmology. I define various statistical, cosmological and sample homogeneity and explain what is meant by the fair…
We propose here selected actual features of measurement problems based on our concerns in our respective fields of research. Their technical similarity in apparently disconnected fields motivate this common communication. Problems of…
Modified theories of gravity have been invoked recently as an alternative to dark energy, in an attempt to explain the apparent accelerated expansion of the universe at the present time. In order to describe inhomogeneities in cosmological…
Formulae for the line-of-sight and transverse comoving distances, proper motion distance, angular diameter distance, luminosity distance, k-correction, distance modulus, comoving volume, lookback time, age, and object intersection…
An alternative to the postulate of dark energy required to explain the accelerated expansion of the universe is to adopt an inhomogeneous cosmological model to explain the supernovae data without dark energy. We adopt a void cosmology…
It is shown that the standard Kolmogorov model for probability spaces cannot in general allow the elimination but of only a small amount of probabilistic redundancy. This issue, a purely theoretical weakness, not necessarily related to…
Cosmological parameter estimation is traditionally performed in the Bayesian context. By adopting an "agnostic" statistical point of view, we show the interest of confronting the Bayesian results to a frequentist approach based on…
We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a…
In this paper, we first provide a brief review of the effective dynamics of two recently well-studied models of modified loop quantum cosmologies (mLQCs), which arise from different regularizations of the Hamiltonian constraint and show the…
Relations are given for the correction of bias when mean absolute magnitudes are derived by the method of reduced parallaxes. The bias in the case of the derivation of the absolute magnitudes of individual objects is also considered.
Ambiguities of the so-called Thiemann regularization in Loop Quantum Cosmology lead to freedom in how to construct a particular quantization prescription. So far three distinct examples of such have been proposed in the literature. For two…
Usually, we assume that there is no inhomogeneity isotropic in terms of our location in our uni- verse. This assumption has not been observationally confirmed yet in sufficient accuracy, and we need to consider the possibility that there…