Annual Sobel Lecture (Remote Lecture via Zoom at HSSB 1173) 

Title: Statistical Learning with Low-resolution Information: There is No Free Lunch

Speaker: Xiao-Li Meng (Harvard University) 

Abstract:
Imprecise probabilities alleviate the need for high-resolution and unwarranted assumptions in statistical modeling. They present an alternative strategy to reduce irreplicable findings. However, updating imprecise models requires the user to choose among alternative updating rules. Competing rules can result in incompatible inferences, and exhibit dilation, contraction and sure loss, unsettling phenomena that cannot occur with precise probabilities and the regular Bayes rule. We revisit some famous statistical paradoxes and show that the logical fallacy stems from a set of marginally plausible yet jointly incommensurable model assumptions akin to the trio of phenomena above. Discrepancies between the generalized Bayes (B) rule, Dempster's (D) rule, and the Geometric (G) rule as competing updating rules are discussed. We note that 1) B-rule cannot contract nor induce sure loss, but is the most prone to dilation due to “overfitting'' in a certain sense; 2) in absence of prior information, both B-rule and G-rule are incapable to learn from data however informative they may be; 3) D-rule and G-rule can mathematically contradict each other by contracting while the other dilating. These findings highlight the invaluable role of judicious judgment in handling low-resolution information, and the care that needs to be taken when applying updating rules to imprecise probability models.   [This talk is based on the discussion article in Statistical Science:  Gong and Meng (2021) Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss, and Simpson’s Paradox.] 

Bio:
Xiao-Li Meng is the Whipple V. N. Jones Professor of Statistics at Harvard University. Professor Meng is the recipient of numerous awards and honors, including the COPSS Presidents' Award in 2001. Professor Meng has written more than 150 publications in at least a dozen theoretical and methodological areas, as well as in areas of pedagogy and professional development. In 2020, he was elected to the American Academy of Arts and Sciences.