In April 2018,
Ruobin Gong was awarded the Arthur P. Dempster prize for her paper, "Conditioning Rules for Sets of Probabilities: Dilation, Sure Loss, and Simpson's Paradox."
Here is the abstract for her paper:
Statistical modeling using sets of probabilities offer a low-resolution alternative to precise probabilities. They alleviate the need to make unwarranted modeling assumptions, and can help reduce irreplicable findings. However, sets of probabilities pose a novel challenge on how to properly handle model conditioning in light of new information. Different conditioning rules may lead to different posterior inference from the same model, and may exhibit dilation, contraction and sure loss, paradoxical phenomena never to be seen in precise probability conditioning.
In this talk, I reaffirm the indispensability of sets of probabilities in expressing uncertain inference, through demystifying a collection of famous statistical ``paradoxes’’ within a common framework. I show that a logical fallacy stems from a set of marginally plausible yet jointly incommensurable assumptions, well-captured by a set of probabilities. We revisit the three prisoners/Monty Hall problem and Simpson’s paradox, and establish equivalence between each problem with a set-of-probabilities model equipped with a paradox-inducing conditioning rule. I also discuss theoretical posterior discrepancies between the generalized Bayes rule, Dempster's rule and the Geometric rule as alternative conditioning rules for Choquet capacities of order 2. Our findings highlight the invaluable role of judicious judgment in the handling of low-resolution statistical information.
Joint work with Xiao-Li Meng (arXiv:1712.08946).