Predictive Inference and Scientific Reproducibility

ABSTRACT

Most statistical analyses use hypothesis tests or estimation about parameters to form inferential conclusions. I think this is noble, but misguided. The point of view expressed here is that observables are fundamental, and that the goal of statistical modeling should be to predict future observations, given the current data and other relevant information. Further, the prediction of future observables provides multiple advantages to practicing scientists, and to science in general. These include an interpretable numerical summary of a quantity of direct interest to current and future researchers, a calibrated prediction of what’s likely to happen in future experiments, a prediction that can be either “corroborated” or “refuted” through experimentation, and avoidance of inference about parameters; quantities that exists only as convenient indices of hypothetical distributions. Finally, the predictive probability of a future observable can be used as a standard for communicating the reliability of the current work, regardless of whether confirmatory experiments are conducted. Adoption of this paradigm would improve our rigor for scientific accuracy and reproducibility by shifting our focus from “finding differences” among hypothetical parameters to predicting observable events based on our current scientific understanding.

KEYWORDS:

• Observables
• Prediction
• Predictive distribution
• Scientific inference