Data Analysis, Statistics and Probability
R\'esum\'e: Le principal objet de cette communication est de faire une r\'etro perspective succincte de l'utilisation de l'entropie et du principe du maximum d'entropie dans le domaine du traitement du signal. Apr\`es un bref rappel de…
A new method of quasi-optimal observables allows one to approach the quality of data processing usually associated with the method of maximal likelihood within the simpler algorithmic context of generalized moments.
We study properties of popular near-uniform (Dirichlet) priors for learning undersampled probability distributions on discrete nonmetric spaces and show that they lead to disastrous results. However, an Occam-style phase space argument…
We propose a novel clustering method that is based on physical intuition derived from quantum mechanics. Starting with given data points, we construct a scale-space probability function. Viewing the latter as the lowest eigenstate of a…
We propose an information-theoretic framework for analyzing control systems based on the close relationship of controllers to communication channels. A communication channel takes an input state and transforms it into an output state. A…
Multipath propagation of radio waves in indoor/outdoor environments shows a highly irregular behavior as a function of time. Typical modeling of this phenomenon assumes the received signal is a stochastic process composed of the…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
A novel framework for designing image reconstruction algorithms for linear forward problems is proposed. The framework is based on the novel concept of conserving the information in the data during image reconstruction rather than…
We propose a variational method to solve all three estimation problems for nonlinear stochastic dynamical systems: prediction, filtering, and smoothing. Our new approach is based upon a proper choice of cost function, termed the {\it…
The exponential growth in the rate at which information can be communicated through an optical fiber is a key element in the so called information revolution. However, like all exponential growth laws, there are physical limits to be…
We study memoryless, discrete time, matrix channels with additive white Gaussian noise and input power constraints of the form $Y_i = \sum_j H_{ij} X_j + Z_i$, where $Y_i$ ,$X_j$ and $Z_i$ are complex, $i=1..m$, $j=1..n$, and $H$ is a…
The frequency distribution of different parameters of an EXAFS spectrum can be directly sampled by analysing a population of simulated spectra produced by adding computer-generated noise to a reference pattern. The procedure gives…
In this paper we propose a Bayesian, information theoretic approach to dimensionality reduction. The approach is formulated as a variational principle on mutual information, and seamlessly addresses the notions of sufficiency, relevance,…
A results of numerical procedure for construction of confidence intervals for parameter of Poisson distribution for signal in the presence of background which has Poisson distribution with known value of parameter are presented. It is shown…
Identification of local structure in intensive data -- such as time series, images, and higher dimensional processes -- is an important problem in astronomy. Since the data are typically generated by an inhomogeneous Poisson process, an…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…
Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under…
The possibility of construction of continuous analogue of Poisson distribution with the search of bounds of confidence intervals for parameter of Poisson distribution is discussed. Also, in the article is shown that the true value of a…
Motivated by the study of an important data set for understanding the large-scale structure of the universe, this work considers the estimation of the reduced second moment function, or K-function, of a stationary point process observed…
On contrary to the customary thought, the well-known ``lemma'' that the distribution function of a collisionless Boltzmann gas keeps invariant along a molecule's path represents not the strength but the weakness of the standard theory. One…