Greg Kochanski

Hilary Term 2005.

Week 1

• Why probabilities? and A Condensed Summary of Probability. [Source] (This include definitions and basic math on probabilities.)
• Case studies of pathological science and systematic errors. [Source]

Week 2

• A few examples on the logic and math of Probabilities.
• Begin example: How to test Optimality Theory [Source]
• Monte-Carlo simulations. Monte-Carlo techniques allow you to simply test complicated and messy models. Question: If you flip a coin, how often do you get three heads in a row? Answer Let's do a million flips on the computer and see! [Source]

Week 3

• Handout2B: Bayes' Theorem. [Source]
• Odds-ratio form of Bayes Theorem, practical problems and considerations in applying Bayes' Theorem. [Source]
• Relating Bayes Theorem to tests of Optimality Theory

Week 4

• Hypothesis testing via Bayes Theorem. Statistical significance and confidence intervals. [Source]
• Applying Monte-Carlo Simulations to testing Optimality Theory.

Week 5

• Applying Monte-Carlo Simulations to testing Optimality Theory.

Week 6

• Good-Turing Estimation: how to estimate the probability that the Sun will not rise tomorrow, or other rare events. How do you compute the probability that the word ``immunological'' will appear in the next sentence, given a small corpus of text? [Source]

Week 7

• Bootstrap resampling: An easy-to-remember but computer-intensive way to look at complex problems or to handle non-Gaussian data. [Source]

Week 8

• Markov Chains. [Source]