Estimate the value of an inaccessible random variable X in terms of the observation of an accessible random variable Y

# MAP and ML Estimators

• Maximum a posteriori estimater

$$P[X=x | Y=y]=\frac{P[Y=y | X=x] P[X=x]}{P[Y=y]}$$

$$\max _{x} P[X=x | Y=y]$$

$$\max _{x} P[Y=y | X=x]$$