|148||Probability and Induction||Holliday||TuTh 11-12:30||Barrows 56|
An introduction to the fundamental concepts of probability and inductive logic (the axioms of probability, conditional probability, Bayes’ rule, and expected value), the subjective Bayesian approach to probability (degrees of belief, coherence, and updating on evidence), and the frequentist approach to probability (long-run frequencies, normal approximations, significance and power, and confidence intervals). Discussion of the philosophical problem of induction from the subjectivist and frequentist perspectives. Applications to the ethics of statistics and risk: e.g., is it morally acceptable to convict someone on the basis of merely statistical evidence? What is it to make a judgement of guilt “beyond a reasonable doubt”? How should we weigh the risks of public policies with uncertain effects?
Prerequisites: 12A (or equivalent) or consent of the instructor