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Advanced Probability Theory Stephen Roberts [email protected]

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Page 1: Advanced Probability Theory - University of Oxford

Advanced Probability Theory

Stephen [email protected]

Page 2: Advanced Probability Theory - University of Oxford

• William of Ockham: model selection

• Thomas Bayes: inference

• Claude Shannon: uncertainty and information

• Edwin Jaynes: logic and inference

Page 3: Advanced Probability Theory - University of Oxford
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(a is just a)

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Belief update – learning – basis of modern ML

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(Proof of this in Lecture 2)

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−10 −8 −6 −4 −2 0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p(x)

p(A|x)

max{p(A|x),p(B|x)}

p(x|A)

Fig 1.2

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