Probability

Machine Learning and Pattern Recognition

Chris Williams

School of Informatics, University of Edinburgh

August 2014

(All of the slides in this course have been adapted from

previous versions by Charles Sutton, Amos Storkey, David Barber.)

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Outline

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What is probability?

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Random Variables (discrete and continuous)

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Expectation

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Joint Distributions

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Marginal Probability

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Conditional Probability

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Chain Rule

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Bayes' Rule

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Independence

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Conditional Independence

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Some Probability Distributions (for reference)

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Reading: Murphy secs 2.1-2.4

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What is probability?

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Quantication of uncertainty

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Frequentist

interpretation: long run frequenies of events

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Example: The probability of a particular coin landing heads up

is 0.43

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Bayesian

interpretation: quantify our degrees of belief about

something

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Example: the probability of it raining tomorrow is 0.3

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Not possible to repeat \tomorrow" many times

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Basic rules of probability are the same, no matter which

interpretation is adopted

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notes on probability