I've been watching the 2023 Statistical Rethinking lecture series by Richard McElreath. These cover a complete approach to statistics based on causal reasoning and Bayesian analysis. They are excellent, highly recommend.
Some personal commentary:
- I loved the very practical understanding of the mathematics he was using. This is not a dry application of the correct statistics. He is crafting a "golem", and all its intricate joints allow it to adapt and squirm with the actual data.
- There is a lot going on. I feel like I could follow it mostly from being familiar with simpler versions of a lot of the ideas. This is a presentation of a complete package of ideas, but it would be possible to take it apart and present pieces separately. A lot of the causal reasoning to could be disentangled from the Bayesian.
- A lot of it concerns causal inference from observational data. This depends on bringing a lot of assumptions about causality, which could uncharitably be viewed as already falling into sin. However many medical and social questions only have this type of data. The causal viewpoint clarified for me what adjustments are valid and useful to make in an actual experiment too.
This was also reflected in his choice of priors. Bayesians are sometimes prone to exotic priors, but not here. Mostly normal and exponential distributions chosen to the task at hand. These are moderately informative priors, and can't be used thoughtlessly.
- He will often compare the prior and posterior distributions of parameters. A very useful check. I note this gives the viewer enough information to divide out the prior that was used on these parameters and substitute their own. Some of the author's subjectivity can be removed.
- It's interesting to compare this account of causality to Hill's criteria. As in, while they may be coherent with each other (i.e. not contradict each other), Hill places a lot of emphasis on things McElreath does not. Hill's criteria are (I think?) a decent account of actual medical policy making. How would these enter a causal/statistical analysis?: strong effect sizes and relative risk as preferred effect size, a dose-response curve, specificity, indifference to there being a known mechanism but coherence with known mechanisms, analogy. Maybe only in the interpretation at the end?