Laplace's method

Laplace's method is a mathematical technique used to approximate complex integrals, especially when one part of the integrand sharply peaks at a certain point. Imagine trying to find the total area under a curve that rises steeply at one location; Laplace's method focuses on that peak because it contributes most to the total. By analyzing the behavior near this maximum, the method simplifies the integral into an easier-to-calculate form. It’s especially useful in probability and statistics for estimating distributions and likelihoods when exact calculations are difficult.