MAP Estimator

Maximum Aposteriori Estimator

(Papolis and Pillai 2014)
Let X be an unknown random variable representing a given phenomena. Y
is a known random variable that represents data collected regarding
the phenomena. MAP Estimator estimates the value of X given the value
of Y.

\[ Xhat_{MAP}(Y) = rgmax_{x}(f_{X}(x)*f_{Y|X}(y|x)\]

References

Papolis, Athanasios, and S. Unnikrishna Pillai. 2014. Probability, Random Variables, and Stochastic Processes. 4th ed. McGraw Hill Education.