Abstract
Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism, serves as a foundation for inference. Statistical pragmatism is inclusive and emphasizes the assumptions that connect statistical models with observed data. I argue that introductory courses often mischaracterize the process of statistical inference and I propose an alternative "big picture" depiction.
Highlights
The protracted battle for the foundations of statistics, joined vociferously by Fisher, Jeffreys, Neyman, Savage, and many disciples, has been deeply illuminating, but it has left statistics without a philosophy that matches contemporary attitudes
Once the data themselves were considered random variables, the frequentist-Bayesian debate moved into the theoretical world: it became a debate about the best way to reason from random variables to inferences about parameters
Bayesians responded by treating subjectivity as a virtue on the grounds that all inferences are subjective yet, while there is a kernel of truth in this observation—we are all human beings, making our own judgments— subjectivism was never satisfying as a logical framework: an important purpose of the scientific enterprise is to go beyond personal decision-making
Summary
The protracted battle for the foundations of statistics, joined vociferously by Fisher, Jeffreys, Neyman, Savage, and many disciples, has been deeply illuminating, but it has left statistics without a philosophy that matches contemporary attitudes. Bayesians have denied the utility of confidence and statistical significance, attempting to sweep aside the obvious success of these concepts in applied work. For their part, frequentists have ignored the possibility of inference about unique events despite their ubiquitous occurrence throughout science. I would suggest that it makes more sense to place in the center of our logical framework the match or mis-match of theoretical assumptions with the real world of data This, it 3 seems to me, is the common ground that Bayesian and frequentist statistics share; it is more fundamental than either paradigm taken separately; and as we strive to foster. With the hope of prodding our discipline to right a lingering imbalance, I attempt here to describe the dominant contemporary philosophy of statistics
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