By Andrew Gelman and Aki Vehtari:
The eight ideas below represent a categorization based on our experiences and reading of the literature and are not listed in chronological order or in order of importance. They are separate concepts capturing different useful and general developments in statistics.
Each of these ideas has pre-1970 antecedents, both in the theoretical statistics literature and in the practice of various applied fields. But each has developed enough in the past fifty years to havebecome something new.
The ideas are:
- counterfactual causal inference
- bootstrapping and simulation-based inference
- overparameterised models and regularisation
- multilevel models
- generic computation algorithms
- adaptive decision analysis
- robust inference
- exploratory data analysis
We consider the ideas listed above to be particularly important in that each of them was not so much a method for solving an existing problem, as an opening to new ways of thinking about statistics and new ways of data analysis.
To put it another way, each of these ideas was a codification, bringing inside the tent an approach that had been considered more a matter of taste or philosophy than statistics[.]
There is also a section on the most important ideas of the next few decades.