Joint Probability Distribution
A Bayesian network defines a joint probability distribution over its variables. The joint probability of a set of variables can be expressed as the product of the conditional probabilities of each variable given its parents:
[Tex]P(X_1 ,X_2 ,…,X_n )=∏_{i=1}^n P(X_i ∣Parents(X_i )) [/Tex]
This factorization is what allows Bayesian networks to efficiently represent the probabilistic relationships in a system.
Understanding Bayesian Networks: Modeling Probabilistic Relationships Between Variables
Bayesian networks, also known as belief networks or Bayesian belief networks (BBNs), are powerful tools for representing and reasoning about uncertain knowledge. These networks use a graphical structure to encode probabilistic relationships among variables, making them invaluable in fields such as artificial intelligence, bioinformatics, and decision analysis.
This article delves into how Bayesian networks model probabilistic relationships between variables, covering their structure, conditional independence, joint probability distribution, inference, learning, and applications.
Table of Content
- Basic Structure of Bayesian Networks
- Conditional Independence
- Joint Probability Distribution
- Inference in Bayesian Networks
- Learning Bayesian Networks
- Interview Question: “How Do Bayesian Networks Model Probabilistic Relationships Between Variables?”