Laplace approximation is a method used in statistics and machine learning to approximate a complex posterior distribution with a simpler, Gaussian distribution. This allows for easier calculation of probabilities and inference, as well as more efficient optimization of model parameters.

One example of Laplace approximation is in Bayesian linear regression, where the posterior distribution of model parameters is often complex and difficult to work with. Using Laplace approximation, this posterior distribution can be approximated as a Gaussian distribution, allowing for easier calculation of probabilities and inference.

Another example is in variational inference, where Laplace approximation is used to approximate a complex posterior distribution with a simpler distribution, such as a Gaussian. This allows for more efficient optimization of model parameters and improved inference.

In both of these examples, Laplace approximation allows for more efficient calculation and inference, as well as more effective optimization of model parameters. By approximating complex posterior distributions with simpler, Gaussian distributions, Laplace approximation can help improve the performance of statistical and machine learning models.