English

Testing whether a Learning Procedure is Calibrated

Statistics Theory 2022-06-17 v5 Statistics Theory

Abstract

A learning procedure takes as input a dataset and performs inference for the parameters θ\theta of a model that is assumed to have given rise to the dataset. Here we consider learning procedures whose output is a probability distribution, representing uncertainty about θ\theta after seeing the dataset. Bayesian inference is a prime example of such a procedure, but one can also construct other learning procedures that return distributional output. This paper studies conditions for a learning procedure to be considered calibrated, in the sense that the true data-generating parameters are plausible as samples from its distributional output. A learning procedure whose inferences and predictions are systematically over- or under-confident will fail to be calibrated. On the other hand, a learning procedure that is calibrated need not be statistically efficient. A hypothesis-testing framework is developed in order to assess, using simulation, whether a learning procedure is calibrated. Several vignettes are presented to illustrate different aspects of the framework.

Keywords

Cite

@article{arxiv.2012.12670,
  title  = {Testing whether a Learning Procedure is Calibrated},
  author = {Jon Cockayne and Matthew M. Graham and Chris J. Oates and T. J. Sullivan and Onur Teymur},
  journal= {arXiv preprint arXiv:2012.12670},
  year   = {2022}
}
R2 v1 2026-06-23T21:17:27.915Z