The following are the main points you should have learned from this chapter:

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  Probability is a measure of belief in a proposition.

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  The posterior probability is used to update an agent’s beliefs based on evidence.

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  A Bayesian belief network is a representation of conditional independence of random variables.

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  Exact inference can be carried out efficiently for sparse graphs (with low treewidth) by variable elimination.

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  A hidden Markov model or a dynamic belief network can be used for probabilistic reasoning about sequences, such as changes over time or words in sentences, with applications such as robot localization and extracting information from language.

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  Stochastic simulation is used for approximate inference.