Probability Handouts

I have uploaded here the handouts from my Philosophy of Science class, which focus on how to understand scientific reasoning from a Bayesian perspective. Several philosophers have told me that they have found them helpful as introductions to probability theory and Bayesian reasoning. Teachers should feel free to use or modify these for their own classes.

Handout #1 introduces basic logical concepts necessary for understanding probability theory. Handout #2 introduces the HD model of scientific reasoning and its problems, to illustrate the need for a more sophisticated model of scientific confirmation. Handout #3 lays out the axioms and theorems of probability. (Philosophers referencing this handout should note that the axioms I use are non-standard. They are based on the axioms that E.T. Jaynes derives from Cox's Theorem in chapters 1-2 of his book, Probability Theory: The Logic of Science. Unlike the standard Kolmogorov axioms, they take conditional probabilities as basic. If you want an introduction to Kolmogorov's axioms, I would recommend looking at Alan Hájek's SEP entry instead.) Handout #4 then explores connections between propositional logic and probability theory.

With this background in hand, Handout #5 introduces a Bayesian model of scientific confirmation. Handouts #6-9 develop and apply this model to various problems and case studies in the history and philosophy of science, including Duhem's underdetermination problem and the scientific virtue of theoretical consilience. Handout #10 shows how to expand Bayes' Theorem to continuous probability distributions, and Handout #11 examines the nature and dangers of significance testing from a Bayesian perspective.

Handout #1: Logic for Understanding Probability

Handout #2: The Hypothetico-Deductive Model of Scientific Confirmation

Handout #3: Fundamental Rules of Probability [Note: this handout uses Jaynes' non-standard axioms which take conditional probabilities as basic.]

Handout #4: From Truth Tables to Joint Probability Distributions

Handout #5: The Bayesian Theory of Scientific Confirmation

Handout #6: The Bayesian Analysis of the Duhem Problem

Handout #7: Darwin's Theory as a Case Study in Scientific Reasoning

Handout #8: A Bayesian Account of Consilience

Handout #9: The Relative Odds Form of Bayes' Theorem

Handout #10: Bayes' Theorem and Continuous Probability Distributions

Handout #11: Statistical Significance Tests