Maximum a posteriori estimation selects a parameter value maximizing its posterior density relative to a specified reference measure. Its output is a maximum a posteriori estimate. The maximizing value need not be invariant under a nonlinear reparameterization, because a density transforms with a Jacobian.
A maximum a posteriori estimate maximizes the posterior density of a parameter or latent configuration. Equivalently, it maximizes the sum of the log likelihood and log prior, relative to the chosen reference measure.
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Maximum a Posteriori (MAP) estimation is a statistical technique used in the context of Bayesian inference. It provides a method for estimating an unknown parameter by maximizing the posterior distribution of that parameter, given observed data. Here’s a breakdown of the concept: 1. **Bayesian Framework**: In Bayesian statistics, we start with a prior belief about a parameter, expressed as a prior probability distribution \( P(\theta) \).