Likelihood

The probability of an observation (the data being what it is) given some parameters

Topics

• Log Likelihood

$L(p_i|Y_i)=P(Y_i=y_i|p_i)$

• Likelihood for a single observation $y_i$ which occurs at a conditional probability of $p_i=P(Y_i=1|X_i)$

$L(p|Y)=\prod _{i}P(Y_i=y_i)=\prod _i{p}_i^{y_i}(1-p_i{)}^{1-y_i}$

• The likelihood of an observation of $p$ given $x$ and $y$