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Bayesian Networks

Bayesian Networks

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Bayesian Networks

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  1. Bayesian Networks Team Orange: Harrison, Sheehan, McGregor, & Law

  2. History • Reverend Thomas Bayes (1702-1761) • British theologian and mathematician who wrote the basic law of probability (now called Bayes Rule) • The term "Bayesian networks" was coined by Judea Pearl in 1985 to emphasize three aspects: • The often subjective nature of the input information • The reliance on Bayes's conditioning as the basis for updating information • The distinction between causal and evidential modes of reasoning, which underscores Thomas Bayes’ published paper of 1763

  3. What is a Bayesian network? • A Bayesian Network is a model • It reflects the states of a world that is being modeled and it describes how those states are related by probabilities • All the possible states of the model represent all the possible worlds that can exist(all the possible ways that the parts or states can be configured)

  4. Applications • Anything can be modeled by a Bayesian Network • Bayesian Networks are used for: • Prediction • Modeling ecosystems • Diagnosis • Monitoring and alerting • Artificial Intelligence

  5. Applications (Cont’D) • Prediction • Since Bayes nets are cause-effect, making statistical based predictions from them is common, especially in areas like meteorology or financial risk management. • Diagnostics • The causal relationship of Bayes nets is also very valuable in medical fields. With a thorough network, one can efficiently diagnose diseases from symptoms.

  6. Applications (Cont’D) • Ecosystems • A Bayes net is useful for balancing the interests of industry, community, and nature in any ecosystem • Monitoring • Bayes nets give the best possible decision with available sensor data for alerting when a system it monitors is in a fail state • Artificial Intelligence • The Bayes net is a tool used in the field of machine learning.

  7. Bayesian Network • Directed Acyclic Graph, no cycles • Nodes = variables • Edges = dependence relationship Valid Invalid

  8. A Simple Bayesian network

  9. Bayes Rule • For any two events A and B, P(B|A) = p(A|B) x p(B)/p(A) • Uses “inverse probability” • The probability of a previous event will affect the probability of a future event

  10. Why are Bayesian networks useful? • Modeling Reality • Gives us a better understanding of what we are modeling • Useful to make predictions about how the world will behave • Adaptable • You don’t need complete knowledge of your network, use as much knowledge as is available • Assisting Decision Making • Can lead you to make the right decision (some states are better than others)

  11. References • http://www.norsys.com/tutorials/netica/secA/tut_A1.htm#WhatIsABayesNet • http://en.wikipedia.org/wiki/Bayesian_network