O'Reilly logo

Fundamentals of Stochastic Networks by Oliver C. Ibe

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

8

BAYESIAN NETWORKS

8.1 INTRODUCTION

A probabilistic network, which is sometimes referred to as a probabilistic graphical model, is a tool that enables us to visually illustrate and work with conditional independencies among variables in a given problem. Specifically, nodes represent variables and the lack of an edge between two nodes represents conditional independence between the variables. There are two types of graphical models: directed graphical models and undirected graphical models. Undirected graphical models are called Markov random fields or Markov networks and are popularly used in the physics and vision communities. Directed graphical models have no directed cycles and are called Bayesian networks (BNs) or belief networks; they are popularly used in the artificial intelligence and statistics communities.

In an undirected graphical model, two nodes A and B are defined to be conditionally independent given a third node C, written AB|C, if all paths between A and B are separated by C. If the joint distribution of A, B, and C is known, then we may write:

c08ue001

In a directed graphical model, conditional independence can be displayed graphically. For example, consider the distribution:

c08ue002

For each conditional distribution we add a directed arc from the node corresponding to the ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required