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Game-theoretic foundations for statistical testing and imprecise probabilities

Remote lectures by Glenn Shafer. December 9th and 10th, 2020.

  • Two 90-minute lectures, divided by a discussion period and a break, will be given each day, starting at 9:00 am New York time (14:00 GMT, 15:00 CET) and concluding four hours later.
  • The readings listed will deepen readers' understanding, but students should be able to follow the lectures without reading them in advance.

Wednesday 9th December 2020

14:00 GMT Lecture 1. Testing predictions by betting against them. Reading: Testing by betting: A strategy for statistical and scientific communication, with discussion and response, by Glenn Shafer. To appear in the Journal of the Royal Statistical Society, Series A.
15:30 GMT Questions and discussion  
16:00 GMT Break  
16:30 GMT Lecture 2. Betting protocols Reading: Borel's law of large numbers, Chapter 1 of Game-Theoretic Foundations for Probability and Finance, by Glenn Shafer and Vladimir Vovk, Wiley, 2019.
15:00 CET Lecture 1. Testing predictions by betting against them. Reading: Testing by betting: A strategy for statistical and scientific communication, with discussion and response, by Glenn Shafer. To appear in the Journal of the Royal Statistical Society, Series A.
16:30 CET Questions and discussion  
17:00 CET Break  
17:30 CET Lecture 2. Betting protocols Reading: Borel's law of large numbers, Chapter 1 of Game-Theoretic Foundations for Probability and Finance, by Glenn Shafer and Vladimir Vovk, Wiley, 2019.
09:00 EST Lecture 1. Testing predictions by betting against them. Reading: Testing by betting: A strategy for statistical and scientific communication, with discussion and response, by Glenn Shafer. To appear in the Journal of the Royal Statistical Society, Series A.
10:30 EST Questions and discussion  
11:00 EST Break  
11:30 EST Lecture 2. Betting protocols Reading: Borel's law of large numbers, Chapter 1 of Game-Theoretic Foundations for Probability and Finance, by Glenn Shafer and Vladimir Vovk, Wiley, 2019.

Thursday 10th December 2020

14:00 GMT Lecture 3. Basing probability theory on betting. Reading: Bernoulli’s and De Moivre’s theorems, Chapter 2 of Game-Theoretic Foundations for Probability and Finance, by Glenn Shafer and Vladimir Vovk, Wiley, 2019.
15:30 GMT Questions and discussion  
16:00 GMT Break  
16:30 GMT Lecture 4. Making and testing predictions with imprecise probabilities. Reading: Betting on a single outcome, Chapter 6 of Game-Theoretic Foundations for Probability and Finance, by Glenn Shafer and Vladimir Vovk, Wiley, 2019.
15:00 CET Lecture 3. Basing probability theory on betting. Reading: Bernoulli’s and De Moivre’s theorems, Chapter 2 of Game-Theoretic Foundations for Probability and Finance, by Glenn Shafer and Vladimir Vovk, Wiley, 2019.
16:30 CET Questions and discussion  
17:00 CET Break  
17:30 CET Lecture 4. Making and testing predictions with imprecise probabilities. Reading: Betting on a single outcome, Chapter 6 of Game-Theoretic Foundations for Probability and Finance, by Glenn Shafer and Vladimir Vovk, Wiley, 2019.
09:00 EST Lecture 3. Basing probability theory on betting. Reading: Bernoulli’s and De Moivre’s theorems, Chapter 2 of Game-Theoretic Foundations for Probability and Finance, by Glenn Shafer and Vladimir Vovk, Wiley, 2019.
10:30 EST Questions and discussion  
11:00 EST Break  
11:30 EST Lecture 4. Making and testing predictions with imprecise probabilities. Reading: Betting on a single outcome, Chapter 6 of Game-Theoretic Foundations for Probability and Finance, by Glenn Shafer and Vladimir Vovk, Wiley, 2019.

The lecture material can also be accessed at: http://glennshafer.com/liverpool-lectures.html

For additional information on this topic, see these working papers and this syllabus.