Bayesian Networks

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 (ContD)

• 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.

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Applications (ContD)

• 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
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Bayes Rule

• For any two events A and B,
• P(BA) p(AB) x p(B)/p(A)
• Uses inverse probability
• The probability of a previous event will affect
  the probability of a future event

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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 dont 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)

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References

• http//www.norsys.com/tutorials/netica/secA/tut_A1
  .htmWhatIsABayesNet
• http//en.wikipedia.org/wiki/Bayesian_network