Understanding the Epistemic Utility of Imprecise Probabilities in Statistical Inference
Date:
Imprecise probabilities have many good uses in statistical inference. The analyst may not know what prior to use for a Bayesian model, what mechanism gave rise to the missing data, or how to make probabilistic statements when non-identifiable parameters are involved. Such kinds of uncertainty are structurally intrinsic to the statistical model, and imprecise probabilities can well articulate them without concocting unwarranted assumptions. On the other hand, imprecise probabilities present unique challenges that call for the judicious judgment on the analyst’s part. The plurality of updating rules leads to seemingly paradoxical phenomena such as dilation and sure loss. In addition, while their results are more robust and informative, IP models are generally difficult to compute. In this talk, I deliberate the benefits and difficulties with imprecise probabilities in statistical inference, using a few examples encountered in practice. I call for a principled method to understand the epistemic utility in the statistical application of imprecise probabilities.