Notes to Myself what we covered

The purpose here is to record roughly what topics are covered each lecture (mostly for my own purposes for future planning)

• L1: Introduced the key idea that Bayesian Statistics uses probability to represent uncertainty. Uncertainty is formally distinct from randomness, or long run frequency, although the concepts overlap. For example, randomness creates uncertainty, but uncertainty can also arise due to incomplete information. Also introduces basic concepts in Bayesian statistics - including prior, posterior and Bayes Factors. notes0.pdf

• L2: could be titled "The problem with p values". Started by noting the difficulty of defining p values, or more precisely the dangers of mis-defining them. (But we got there in the end!). Then introduced the problem addressed by Sellke et al, and asked students to guess answer. Did example from notes0 showing p value of 0.01 can correspond to BF>1 and BF<1. Then noted the difficulty of interpreting confidence intervals. What does [1,3] is a 95% CI for theta mean? Could do with better notes on what CIs are as some students have not been formally introduced to them, or at least not seen them for a while

• L3: Jumped ahead in notes to do examples of Bayesian calculations from notes2.pdf. Skipped notes1 for now because I thought these examples may be helpful in completing the first homework, which is due on Wed (L4). When introducing predictive distributions emphasised that Bayes approach takes account of uncertainty in theta (would be good to include in notes; contrast with plug-in approach). Introduced beta as conjugate prior for binomial, did simple normal example, + savage's potato example.

• L4: Summarise the situation when a Confidence interval is OK to interpret as a Credible interval - eg opinion polling. Also situation where it is not (eg anywhere testing is natural; Sellke et al example). Do more complex example; go through meaning of probability notes and Lindley chapter.