6 Reasoning Under Uncertainty

All of the time, agents are forced to make decisions based on incomplete information. Even when an agent senses the world to find out more information, it rarely finds out the exact state of the world. A robot does not know exactly where an object is. A doctor does not know exactly what is wrong with a patient. A teacher does not know exactly what a student understands. When intelligent agents must make decisions, they have to use whatever information they have. This chapter considers reasoning under uncertainty: determining what is true in the world based on observations of the world. This is used in Chapter 9 as a basis for acting under uncertainty, where the agent must make decisions about what action to take even though it cannot precisely predict the outcomes of its actions. This chapter starts with probability, shows how to represent the world by making appropriate independence assumptions, and shows how to reason with such representations.

• 6.1 Probability
  • 6.1.1 Semantics of Probability
  • 6.1.2 Axioms for Probability
  • 6.1.3 Conditional Probability
  • 6.1.4 Expected Values
  • 6.1.5 Information Theory
• 6.2 Independence
• 6.3 Belief Networks
  • 6.3.1 Constructing Belief Networks
• 6.4 Probabilistic Inference
  • 6.4.1 Variable Elimination for Belief Networks
  • 6.4.2 Approximate Inference Through Stochastic Simulation
• 6.5 Probability and Time
  • 6.5.1 Markov Chains
  • 6.5.2 Hidden Markov Models
  • 6.5.3 Algorithms for Monitoring and Smoothing
  • 6.5.4 Dynamic Belief Networks
  • 6.5.5 Time Granularity
• 6.6 Review
• 6.7 References and Further Reading
• 6.8 Exercises