What can the foundations discussion contribute to data analysis? And what may be some of the future directions in robust methods and data analysis?

Abstract

The discussion of the philosophical foundations of statistics is not necessarily far remote from practical data analysis, even though, fortunately, a good data analysis does not depend very much on the philosophical framework adopted. Some clarification for data analysis can be provided about the purposes of estimation and testing, the choice between parameter estimation and prediction, the role of parametric models, the difference between epistemic and physical probabilities, the interpretation of confidence intervals and fiducial probabilities, the description of a state of partial knowledge, including the use of upper and lower probabilites, and other topics. This paper contains first some remarks on future directions in robust methods, in loose connection with foundations, but in close connection with the title of the workshop. It then gives a brief description of a new approach to the foundations of statistics, and in the main part it discusses a number of suggestions and consequences for data analysis as mentioned above, which can be derived from the study and discussion of the foundations of statistics.