Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics – often criticised for lacking frequentist guarantees – remains underexplored. Recent work has suggested that conformal prediction can serve to “calibrate” Bayesian procedures, thereby imparting frequentist validity and motivating deeper investigation into frequentist–Bayesian hybrids. We further argue that Bayesian inference has the potential to enhance conformal prediction, for instance, through more informative intervals. Thus, in a spirit of modern statistics based less on division and more on synthesis, the two paradigms may be viewed as complementary, jointly striving for a principled balance between validity and efficiency. In this talk, I will outline paths toward bridging this gap. After surveying existing ideas, a formalization of the Bayesian conformal inference framework will be provided, in both its full and split forms. Emphasis will be given to the challenging aspect of computational complexity, with potential solutions. Finally, the advantages of Bayesian conformal inference will be discussed in small-area estimation, a paradigmatic example for this hybrid perspective.
Based on joint work with Brunero Liseo.
17 Ottobre 2025, ore 12
Nina Deliu
Sapienza University of Rome
In person: Room 34 (4th floor) building CU002 Scienze Statistiche
Webinar: https://uniroma1.zoom.us/j/83625004899?pwd=bXCtz0mp759PUh2lkqT0BUoVa0Uegg.1
ID riunione: 836 2500 4899
Passcode: 123456