Relearning statistics with a Bayesian approach. My undergrad education was in social science research methods and I spent 4 years learning the strict frequentist approach of orthodox statistics. It made sense for highly-controlled experiments and simple dice games. But it broke down horribly when faced with any complexity and I never understood why. 25 years later, it's time to fill in the gaps. My reading list:
- E.T. Janes "Probability Theory: The Logic of Science" provides the fundamental theory.
- Robert McElreath "Rethinking Statistics" provides a practical application of the theory in R.
- Andrew Clayton's "Bernoulli's Fallacy" is a non-technical book that provides historical context to the frequentist vs bayesian debate.
I'm fairly convinced now that Bayesian approaches have more mathematical rigor than the crusty old heuristics of traditional statistics. But in terms of user-experience, doing Bayesian calculations still requires more effort on model design and more compute power. It's flexible to a fault, without a well-defined workflow. There is a strong temptation to follow the easy path - shove your data into a black box and publish if p<0.05. It's going to take a generation of (re)training and improvements to statistical software before Bayesian methods are widespread.
+1 for the Statistical Rethinking book by McElreath. I recently took the 2024 edition of the self-paced course https://github.com/rmcelreath/stat_rethinking_2024 and the lectures on youtube are amazing. He's not just teaching stats, but how to do science!
Another, more basic, book on Bayesian stats is: https://allendowney.github.io/ThinkBayes2/ The author uses the grid approximation for everything, so there is no need to get into Stan or other framework.
Myself, I'm still trying to (re)learn frequentist stuff properly (will post a separate comment about that), but the deeper I go the more convinced I am that it is total crap, and my desire to convert to the church of Bayes increases...
- E.T. Janes "Probability Theory: The Logic of Science" provides the fundamental theory.
- Robert McElreath "Rethinking Statistics" provides a practical application of the theory in R.
- Andrew Clayton's "Bernoulli's Fallacy" is a non-technical book that provides historical context to the frequentist vs bayesian debate.
I'm fairly convinced now that Bayesian approaches have more mathematical rigor than the crusty old heuristics of traditional statistics. But in terms of user-experience, doing Bayesian calculations still requires more effort on model design and more compute power. It's flexible to a fault, without a well-defined workflow. There is a strong temptation to follow the easy path - shove your data into a black box and publish if p<0.05. It's going to take a generation of (re)training and improvements to statistical software before Bayesian methods are widespread.