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In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. [ 1][ 2]: 10 It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey ...
Jeffreys prior. In Bayesian statistics, the Jeffreys prior is a non-informative prior distribution for a parameter space. Named after Sir Harold Jeffreys, [ 1] its density function is proportional to the square root of the determinant of the Fisher information matrix: It has the key feature that it is invariant under a change of coordinates for ...
Probability theory. A Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now ."
This is the same as saying that the probability of event {1,2,3,4,6} is 5/6. This event encompasses the possibility of any number except five being rolled. The mutually exclusive event {5} has a probability of 1/6, and the event {1,2,3,4,5,6} has a probability of 1, that is, absolute certainty.
Fermi's golden rule. In quantum physics, Fermi's golden rule is a formula that describes the transition rate (the probability of a transition per unit time) from one energy eigenstate of a quantum system to a group of energy eigenstates in a continuum, as a result of a weak perturbation. This transition rate is effectively independent of time ...
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.The general form of its probability density function is = The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is the variance.
Hopfield network. A Hopfield network ( associative memory or Ising–Lenz–Little model or Nakano-Amari-Hopfield network) is a spin glass system used to model neural networks, based on Ernst Ising 's work with Wilhelm Lenz on the Ising model of magnetic materials. [ 1 ]
Matrix (mathematics) An m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, a2,1 represents the element at the second row and first column of the matrix. In mathematics, a matrix ( pl.: matrices) is a rectangular array or table of ...