Maximum Likelihood Estimation

Maximum Likelihood Estimation


  • BayesiaLab estimates the parameters of a Bayesian network using Maximum Likelihood Estimation.
  • The probability of a state x0{x_0} of a node X{X} corresponds to the frequency the state x0{x_0} is observed in the dataset.


Let's consider this simple network:

Maximum Likelihood Estimation

The marginal probability distribution of PaPa is estimated as:

P^(Pa=pai)=N(Pa=pai)jN(Pa=paj)\widehat{P}(Pa = p{a_i}) = \frac{{N(Pa = p{a_i})}}{{\sum\nolimits_j {N(Pa = p{a_j})} }}

where N()N\left( \cdot \right) represents the number of occurrences of the specified configuration in the dataset.

The conditional probability distribution of XPaX|Pa is estimated as

P^(X=xiPa=pai)=N(X=xi,Pa=pai)jN(X=xj,Pa=paj)\widehat{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})} }}

For North America

Bayesia USA

4235 Hillsboro Pike
Suite 300-688
Nashville, TN 37215, USA

+1 888-386-8383

Head Office

Bayesia S.A.S.

Parc Ceres, Batiment N 21
rue Ferdinand Buisson
53810 Change, France

For Asia/Pacific

Bayesia Singapore

1 Fusionopolis Place
#03-20 Galaxis
Singapore 138522

Copyright © 2024 Bayesia S.A.S., Bayesia USA, LLC, and Bayesia Singapore Pte. Ltd. All Rights Reserved.