• stochastic
  • These sources are frequently described in terms of probability distributions to account for the stochastic nature of complex engineering systems. (wikipedia.org)
  • Travel distance and residence time probability distributions are the key components of stochastic models for coarse sediment transport. (wiley.com)
  • As in many fields with stochastic approaches to particle transport, the conceptual model used to represent sediment transport through time in gravel bed rivers equates the distribution of overall travel distance at time t of a single particle as the sum of a random number of randomly sized step lengths. (wiley.com)
  • In this setting, the process is often used in mathematical models and in the related fields of spatial point processes, stochastic geometry, spatial statistics and continuum percolation theory. (wikipedia.org)
  • Within a probabilistic framework, we describe the characterization of uncertainties using mathematical statistics methods, the propagation of uncertainties through computational models using either Monte Carlo sampling or stochastic expansion methods, and the sensitivity analysis of uncertainties using variance- and differentiation-based methods. (ac.be)
  • Not every probability measure is infinitely divisible, and a characterization of infinitely divisible measures is of central importance in the abstract theory of stochastic processes. (wikipedia.org)
  • Besides these and related disciplines such as algebraic topology and supersymmetric field theories, STS is also connected with the traditional theory of stochastic differential equations and the theory of pseudo-Hermitian operators. (wikipedia.org)
  • The first relation between supersymmetry and stochastic dynamics was established by Giorgio Parisi and Nicolas Sourlas who demonstrated that the application of the BRST gauge fixing procedure to Langevin SDEs, i.e., to SDEs with linear phase spaces, gradient flow vector fields, and additive noises, results in N=2 supersymmetric models. (wikipedia.org)
  • finite
  • It represents the limiting distribution for a sum of independent, identically distributed random variables with finite variance and covariance where the number of elements to be summed is itself an independent random variable distributed according to a geometric distribution. (wikipedia.org)
  • The distribution may also be applicable in broader situations to model multivariate data with heavier tails than a normal distribution but finite moments. (wikipedia.org)
  • Learning algorithms based on this framework exhibit good generalization ability and finite sample convergence, while often being simpler and more effective than information theoretic methods Thus, learning via the kernel embedding of distributions offers a principled drop-in replacement for information theoretic approaches and is a framework which not only subsumes many popular methods in machine learning and statistics as special cases, but also can lead to entirely new learning algorithms. (wikipedia.org)
  • This definition makes sense if x is an integrable function (in L1), a compactly supported distribution, or is a finite Borel measure. (wikipedia.org)
  • Some statistical methods that were originally motivated by the study of the normal distribution have good performance for general elliptical distributions (with finite variance), particularly for spherical distributions (which are defined below). (wikipedia.org)
  • seismology
  • It has applications in statistical mechanics, quantum chemistry, quantum optics, classical optics and signal analysis in diverse fields such as electrical engineering, seismology, time-frequency analysis for music signals, spectrograms in biology and speech processing, and engine design. (wikipedia.org)
  • The Quake Markup Language (QuakeML) is a flexible, extensible and modular XML representation of seismological data (e.g. epicenter, hypocenter, magnitude) which is intended to cover a broad range of fields of application in modern seismology. (wikipedia.org)
  • statistical
  • Handbook of Exploration Geochemistry, Volume 2: Statistics and Data Analysis in Geochemical Prospecting aims to survey the techniques available for the quality control of laboratory data, storage and retrieval of field and laboratory information, statistical analysis of single- and multi-element data, and presentation of geochemical data as maps. (elsevier.com)
  • We include some recent advances in the propagation and sensitivity analysis of uncertainties that are characterized by arbitrary probability distributions that may exhibit statistical dependence. (ac.be)
  • The American Statistical Association has described him as "a living legend whose work has influenced not just statistics, but has had far reaching implications for fields as varied as economics, genetics, anthropology, geology, national planning, demography, biometry, and medicine. (wikipedia.org)
  • As Head and later Director of the Research and Training School at the Indian Statistical Institute for a period of over 40 years, Rao developed research and training programs and produced several leaders in the field of Mathematics. (wikipedia.org)
  • Elliptical distributions are also used in robust statistics to evaluate proposed multivariate-statistical procedures. (wikipedia.org)
  • empirical
  • However, bed elevation time series collected using sonar transducers and lidar can be translated into empirical residence time distributions at each elevation in the bed and for the entire bed thickness. (wiley.com)
  • The distribution patterns and volumes of coarse-grained channel-fill deposits developed mainly during falling- and lowstand stages can be estimated from outcrop and seismic data on the basis of several empirical relationships among width, depth, and sinuosity of deep-water channels. (go.jp)
  • Statistics
  • The analysis of distributions is fundamental in machine learning and statistics, and many algorithms in these fields rely on information theoretic approaches such as entropy, mutual information, or Kullback-Leibler divergence. (wikipedia.org)
  • random
  • We introduce an automated segmentation method, extended Markov Random Field ( eMRF ) to classify 21 neuroanatomical structures of mouse brain based on three dimensional (3D) magnetic resonance imaging (MRI). (pubmedcentralcanada.ca)
  • The distribution can be represented by a random variable describing the time until absorption of a Markov process with one absorbing state. (wikipedia.org)
  • functions
  • See below for a characterization of pure states whose Wigner functions are non-negative. (wikipedia.org)
  • In 1949, José Enrique Moyal elucidated how the Wigner function provides the integration measure (analogous to a probability density function) in phase space, to yield expectation values from phase-space c-number functions g(x,p) uniquely associated to suitably ordered operators Ĝ through Weyl's transform (cf. (wikipedia.org)
  • spaces
  • One could apply non-separable Hilbert spaces, such as a rigged Hilbert space, but that takes the argument away why physics must contain fields. (science20.com)
  • laboratory
  • Residence time for individual grains is difficult to measure, and residence time distributions appropriate to field and laboratory settings are typically inferred theoretically or from overall transport characteristics. (wiley.com)
  • frequency
  • The Wigner distribution P(x,p) of a pure state is defined as: where ψ is the wavefunction and x and p are position and momentum but could be any conjugate variable pair (i.e. real and imaginary parts of the electric field or frequency and time of a signal). (wikipedia.org)
  • These moments can then be used to determine an appropriate frequency distribution, which can then be used as a probability model. (wikipedia.org)
  • The frequency of extremal events, such as severe droughts and storms, often requires the use of distributions that focus on the tail of the distribution, rather than the data nearest the mean. (wikipedia.org)
  • infinite
  • In those set-ups Jean-François Mertens provided an extension of the characterization of the minmax and maxmin value for the infinite game in the dependent case with state independent signals. (wikipedia.org)
  • Deterministic distribution (or constant) - The limiting case of an Erlang distribution, as the number of phases become infinite, while the time in each state becomes zero. (wikipedia.org)
  • results
  • Smoothing the Wigner distribution through a filter of size larger than ħ (e.g., convolving with a phase-space Gaussian, a Weierstrass transform, to yield the Husimi representation, below), results in a positive-semidefinite function, i.e., it may be thought to have been coarsened to a semi-classical one. (wikipedia.org)
  • From the results of the 2D and 3D seismic survey acquired in the Nankai Trough area by METI in 2001 and 2002, widely-distributed BSR was recognized in the area, which was expected the wide distribution of methane hydrate. (go.jp)
  • Class
  • In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which a probability distribution is represented as an element of a reproducing kernel Hilbert space (RKHS). (wikipedia.org)
  • Science
  • Rao was awarded the United States National Medal of Science, that nation's highest award for lifetime achievement in fields of scientific research, in June 2002. (wikipedia.org)
  • neural
  • Neural decoding is a neuroscience-related field concerned with the reconstruction of sensory and other stimuli from information that has already been encoded and represented in the brain by networks of neurons. (wikipedia.org)
  • known
  • Mertens and Zamir implemented John Harsanyi's proposal to model games with incomplete information by supposing that each player is characterized by a privately known type that describes his feasible strategies and payoffs as well as a probability distribution over other players' types. (wikipedia.org)