In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While...

In mathematics, Laplace's principle is a basic theorem in large deviations theory which is similar to Varadhan's lemma. It gives an asymptotic expression...

stationary phase Method of steepest descent Large deviations theory Laplace principle (large deviations theory) Laplace's approximation Tierney, Luke; Kadane...

theorem Large deviations theory Contraction principle (large deviations theory) Varadhan's lemma Tilted large deviation principle Rate function Laplace principle...

large body of mathematical techniques, frequency-domain linear transform methods such as Fourier and Laplace transforms, and linear operator theory,...

Language model Laplace distribution Laplace principle (large deviations theory) LaplacesDemon – software Large deviations theory Large deviations of Gaussian...

Z-transform in control theory (invented by Laplace) in the 1950s. Lev Pontryagin introduced the maximum principle and the bang-bang principle. Pierre-Louis Lions...

Laplace functional Laplace motion Laplace's rule of succession Laplace smoothing Laplace principle (large deviations theory) Laplace series Laplace transform...

sufficiently accurate for many practical purposes and is therefore widely used. Deviations from it are small when the dimensionless quantities ϕ / c 2 {\displaystyle...

orders in perturbation theory, allowing one to express E n ( k ) {\displaystyle E_{n}^{(k)}} in terms of the inverse Laplace transform ρ n , k {\displaystyle...

used in three-phase power systems. De Moivre–Laplace theorem In probability theory, the de Moivre–Laplace theorem, which is a special case of the central...

(}\phi (x)-I(x){\big )}.} Laplace principle (large deviations theory) Dembo, Amir; Zeitouni, Ofer (1998). Large deviations techniques and applications...

kinematics Kirchhoff's circuit laws Kirchhoff's equations laminar flow Laplace transform LC circuit lever L'Hôpital's rule linear actuator linear elasticity...

absolute deviation. It was notably performed by Roger Joseph Boscovich in his work on the shape of the Earth in 1757 and by Pierre-Simon Laplace for the...

surface. To Le Sage's disappointment, Laplace never directly mentioned Le Sage's theory in his works. Because the theories of Fatio, Cramer and Redeker were...

Vin(s) are the Laplace transform of the current and input voltage, respectively, and s is a complex frequency parameter in the Laplace domain. Rearranging...

standard deviations on either side is n S + z n + 2 z {\displaystyle {\frac {n_{S}+z}{n+2z}}} Taking z = 2 {\displaystyle z=2} standard deviations to approximate...

independent histories into the physical theories of gravity: the principle of relativity and non-Euclidean geometry The principle of relativity, introduced by Galileo...

to specify an informed prior, Laplace used uniform priors, according to his "principle of insufficient reason". Laplace assumed uniform priors for mathematical...

alternative) with prior probabilities chosen by using the principle of indifference. Fisher said, "... the theory of inverse probability is founded upon an error...

anl Large deviations theory Contraction principle Cramér's theorem Exponentially equivalent measures Freidlin–Wentzell theorem Laplace principle Large deviations...

Laplace method from integrals on R n {\displaystyle \mathbb {R} ^{n}} to functional Wiener integration. The theorem is used in the large deviations theory...

worth (a+b)/2. More than a hundred years later, in 1814, Pierre-Simon Laplace published his tract "Théorie analytique des probabilités", where the concept...

T. (1939), The Mathematical Theory of Huygens' Principle, Oxford, pp. 36–40. Schrödinger, E. (1926). "An Undulatory Theory of the Mechanics of Atoms and...

available, an uninformative prior may be adopted as justified by the principle of indifference. In modern applications, priors are also often chosen...

low electrolyte concentrations, typically less than 10−3 mol/L. Deviations from the theory occur at higher concentrations and with electrolytes that produce...

Larson, David Royal (eds.). Large Deviations for Additive Functionals of Markov Chains: The 25th Great Plains Operator Theory Symposium, June 7–12, 2005...

Minkowski, H.; Weyl, H. (1952). The Principle of Relativity: a collection of original memoirs on the special and general theory of relativity. Courier Dover...

interpretation. Relative entropy relates to "rate function" in the theory of large deviations. Arthur Hobson proved that relative entropy is the only measure...

squared terms are deviations from the sample mean. ANOVA estimates 3 sample variances: a total variance based on all the observation deviations from the grand...