The mathematical and philosophical foundations of statistical science. As Deborah Mayo notes in Statistical inference as severe testing:
Some readers may be surprised to learn that the field of statistics, arid and staid as it seems, has a fascinating and colorful history of philosophical debate, marked by unusual heights of passion, personality, and controversy for at least a century. Others know them all too well and regard supporting any one side largely as proselytizing. I’ve heard some refer to statistical debates as “theological.” (pg 11)
Particular issues in the foundations of statistics involve:
- Perspectives on hypothesis testing. Eg: Fisher’s paradigm vs Neyman-Pearson paradigm vs Jeffreys’ paradigm of hypothesis testing vs Mayo’s error statistics. See also current statistical practice combines the Fisherian and Neyman-Pearson perspectives.
- Perspectives on the correct role and interpretation of statistics and probability. See Bayesian statistics, frequentist statistics, and game-theoretic statistics.
- Perspectives on the correct interpretation and/or use of probability: Bayesian interpretation of probability, frequentist interpretation of probability, instrumentalist theory of probability.