Laplace Approximation: Integral Estimation

This lecture covers the Laplace approximation method for estimating integrals, focusing on smooth convex functions and the application of an improper Gaussian distribution. The Laplace approximation provides a simple way to obtain numerical estimates, with a focus on the second derivative of the function. The lecture also discusses the accuracy and convergence of the method, highlighting the importance of the normal probability distribution within three standard deviations of the mean. The Laplace approximation is demonstrated through examples and its application in higher dimensions.