An exchange on statistical inference in memory of Italo Scardovi

On May 14, 2025, at the Statistical Department of the University of Bologna, a roundtable discussion on the foundations of statistical inference took place within a workshop in memory of Italo Scardovi. This paper collects the talks of the four speakers. Hennig presents a framework for interpreting statistical inference, taking into account that statistical model assumptions are not always fulfilled in reality. Liseo reconsiders some of the topics that Scardovi was most passionate about and assesses their impact on today’s statistics. Rigo deals with the advantages/disadvantages of taking prediction as the cornerstone of statistical inference (giving parameters a lesser role than usual). Piccolo provides a wide view of the foundations of statistics and their role in science, taking a subjectivist Bayesian position.