Abstract
This chapter presents an overview of some basic concepts in probability theory which are important for understanding probabilistic graphical models. First, the main interpretations and mathematical definition of probability are introduced. Second, the basic rules of probability theory are presented, including the concept of conditional independence and Bayes rule. Third, an overview of random variables and some important distributions are described. Lastly, the basics of information theory are presented.
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Notes
- 1.
It is commonly written P(H) without explicit mention of the conditioning information. In this case we assume that there is still some context under which probabilities are considered even if it is not written explicitly.
- 2.
This means that one and only one of the propositions has a value of TRUE.
References
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Jaynes, E.T.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003)
MacKay, D.J.: Information Theory, Inference and Learning Algorithms. Cambridge University Press, Cambridge (2004)
Sucar, L.E., Gillies, D.F., Gillies, D.A.: Objective Probabilities in Expert Systems. Artif. Intell. 61, 187–208 (1993)
Wasserman, L.: All of Statistcs: A Concise Course in Statistical Inference. Springer, New York (2004)
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Sucar, L.E. (2015). Probability Theory. In: Probabilistic Graphical Models. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-6699-3_2
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DOI: https://doi.org/10.1007/978-1-4471-6699-3_2
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