Maximum Likelihood Estimation

Context

• 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.

Example

Let's consider this simple network:

Maximum Likelihood Estimation

The marginal probability distribution of $Pa$ is estimated as:

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