Estimation of Random Variables

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

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

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

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