MAP estimation

Maximum a posteriori (MAP) estimation is a method of Bayesian statistics that finds the mode of the posterior distribution — the parameter value with the highest probability density given the data and the prior. Unlike full Bayesian inference, which computes the entire posterior distribution, MAP reduces the inferential problem to an optimization problem, discarding uncertainty information in exchange for computational tractability. MAP is the foundation of the Laplace approximation and the starting point of many Bayesian computational pipelines. But it is also a conceptual trap: by collapsing the posterior to a single point, it reproduces the worst habits of point estimation and can be misleading when the posterior is multimodal or asymmetric.