Search results
Results from the WOW.Com Content Network
Information geometry. The set of all normal distributions forms a statistical manifold with hyperbolic geometry. Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. [1] It studies statistical manifolds, which are Riemannian manifolds whose points ...
Lectures on finite Markov chains, in Lectures on Probability Theory and Statistics, Lecture Notes in Mathematics, Band 1665, 1997, S. 301-413 with Nicholas Varopoulos , T. Coulhon Analysis and geometry on groups , Cambridge Tracts in Mathematics, Band 100, Cambridge University Press 1992
The convolution/sum of probability distributions arises in probability theory and statistics as the operation in terms of probability distributions that corresponds to the addition of independent random variables and, by extension, to forming linear combinations of random variables. The operation here is a special case of convolution in the ...
Probability theory. The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. [1] These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. [2]
Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [ note 1 ][ 1 ][ 2 ] A simple example is the tossing of a fair (unbiased) coin.
The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations[2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same probability space, then.
File:High School Probability and Statistics (Basic).pdf. Size of this JPG preview of this PDF file: 463 × 599 pixels. Other resolutions: 185 × 240 pixels | 371 × 480 pixels | 593 × 768 pixels | 1,275 × 1,650 pixels. This is a file from the Wikimedia Commons. Information from its description page there is shown below.
Divergence (statistics) In information geometry, a divergence is a kind of statistical distance: a binary function which establishes the separation from one probability distribution to another on a statistical manifold. The simplest divergence is squared Euclidean distance (SED), and divergences can be viewed as generalizations of SED.