# Maximum Likelihood Estimation

- BayesiaLab estimates the parameters of a Bayesian network using
**Maximum Likelihood Estimation***.* - The probability of a state${x_0}$of a node${X}$corresponds to the frequency the state${x_0}$is observed in the dataset.

Let's consider this simple network:

The marginal probability distribution of

$Pa$

is estimated as:$\hat P(Pa = p{a_i}) = \frac{{N(Pa = p{a_i})}}{{\sum\nolimits_j {N(Pa = p{a_j})} }}$

where

$N\left( \cdot \right)$

*represents the number of occurrences of the specified configuration in the dataset.*The conditional probability distribution of X|Pa is estimated as

$\hat P(X = {x_i}|Pa = p{a_i}) = \frac{{N(X = {x_i},Pa = p{a_i})}}{{\sum\nolimits_j {N(X = {x_j},Pa = p{a_j})} }}$

Last modified 7mo ago