In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form ∫ a b e M f ( x ) d x , {\displaystyle...

solutions of Laplace's equation. Laplace's equation in spherical coordinates, such as are used for mapping the sky, can be simplified, using the method of separation...

Laplace's approximation provides an analytical expression for a posterior probability distribution by fitting a Gaussian distribution with a mean equal...

In mathematics, the method of steepest descent or saddle-point method is an extension of Laplace's method for approximating an integral, where one deforms...

This method originates from the 19th century, and is due to George Gabriel Stokes and Lord Kelvin. It is closely related to Laplace's method and the...

Wallis. Wallis derived this infinite product using interpolation, though his method is not regarded as rigorous. A modern derivation can be found by examining...

-t^{2}/2} , which is why we are able to perform Laplace's method. In order to extend Laplace's method to higher orders, we perform another change of variables...

Gauss published the precise integral in 1809, attributing its discovery to Laplace. The integral has a wide range of applications. For example, with a slight...

Integrated nested Laplace approximations (INLA) is a method for approximate Bayesian inference based on Laplace's method. It is designed for a class of...

X(x)e^{-ax}a^{x}\,dx,} which resembles a Laplace transform. These types of integrals seem first to have attracted Laplace's attention in 1782, where he was following...

of Laplace's equation. Laplace's equation and Poisson's equation are the simplest examples of elliptic partial differential equations. Laplace's equation...

reference to Laplace's method of probability (developed in a 1774 paper, which independently discovered and popularized Bayesian methods, and a 1812 book)...

Bayesian information criterion, Variational Bayesian methods, false discovery rate, and Laplace's method are used. Many artificial intelligence researchers...

perturbation Watson's lemma Mellin transform Laplace's method Stationary phase approximation Method of dominant balance Method of steepest descent Jahnke, Hans Niels...

column and the smallest element in its row. Saddle-point method is an extension of Laplace's method for approximating integrals Maximum and minimum Derivative...

typically arise in the approximation of certain integrals (Laplace's method, saddle-point method, method of steepest descent) or in the approximation of probability...

Some numerical approximation families of algorithms include Laplace's method (Laplace approximation), numerical integration (iterative quadrature),...

mathematics, the Laplace transform is a powerful integral transform used to switch a function from the time domain to the s-domain. The Laplace transform can...

this equation is the Laplace operator, and the entire equation Δu = 0 is known as Laplace's equation. Solutions of the Laplace equation, i.e. functions...

Expansions Based on Laplace's Method". In Geisser, S.; Hodges, J. S.; Press, S. J.; Zellner, A. (eds.). Bayesian and Likelihood Methods in Statistics and...

can be derived by integrating out the parameters of the model using Laplace's method, starting with the following model evidence:: 217  p ( x ∣ M ) = ∫...

harmonics originate from solving Laplace's equation in the spherical domains. Functions that are solutions to Laplace's equation are called harmonics. Despite...

which was anticipated by Laplace for exponential families). The same result is used when approximating the posterior with Laplace's approximation, where the...

^{2}}}e^{-t}\sin(\pi x).} Comparison of Finite Difference Methods The (continuous) Laplace operator in n {\displaystyle n} -dimensions is given by Δ u...

Laplace transform Laplace–Carson transform Laplace–Stieltjes transform Inverse Laplace transform Laplace's method for approximating integrals Laplace...

uniform random variables. This distribution is often referred to as "Laplace's first law of errors". He published it in 1774, modeling the frequency...

methods similar to those of Laplace, but his favorite object was Pallas, because of its great eccentricity and orbital inclination, whereby Laplace's...

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...

equivalence is based on this transformation. Laplace principle, a large deviations principle in Rd Laplace's method Schilder's theorem, a large deviations principle...

analytically intractable but can be approximated to quite high accuracy using Laplace's method. Smoothing parameter inference is the most computationally taxing part...