80-815 Seminar on the Foundations of Statistics
12 units, Carnegie Mellon University
In the first phase well examine Savages theory of subjective expected utility chapters 25 of his book, The Foundations of Statistics. Additional readings Fishburns review, Subjective Expected Utility Theory and Decision, 13 1981, 131199 also, Chapters 8 and 13 of Fishburns Utility Theory for Decision Making. During this part of the course well contrast Savages approach with the von NeumannMorgenstern theory of utility and with the AnscombeAumann theory of preferences for horse lotteries. Also, well discuss some specialized topics, e.g., statedependent utilities and 5.5, relating to Savages postulate P3. In the second phase of the course, well focus on some of the following issues, as the class determines 2.1. A comparison of Savages theory and deFinettis criterion of coherence. 2.2. A comparison of Savages theory and A.Walds Statistical Decision Functions. 2.3. Personal vs. group decisions. Topics to include Arrows impossibility theorem, consensus, Savages position in 7.2 13.5. 2.4. Violations of the surething principle Savages postulate P2. Additional readings will be taken from the psychological and economic literature on descriptive models of risk without the expected utility property Kahneman and Tverskys Prospect Theory, Wakkers Cumulative Prospect Theory, M.Machinas theory, Fishburns SSB theory, etc For the third phase, well discuss some issues related to Savages chapters 3 4 relating to qualitative probability theory.
Prerequisites: none listed
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