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2.5.3 Estimation Based on Maximal Conditional Probabilities

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There are two ways to do an estimation given a conditional problem. The first is to seek a maximal probability based on the optimal choice of outcome (maximum a posteriori [MAP]), versus a maximal probability (referred to as a “likelihood” in this context) given choice of conditioning (maximum likelihood [ML]).

MAP Estimate:

Provides an estimate of r.v. X given that Y = yj in terms of the posterior probability:


ML Estimate:

Provides an estimate of r.v. X given that Y = yj in terms of the maximum likelihood:


Informatics and Machine Learning

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