Editorial: Forum on recent developments on finitely additive probabilities and coherence

摘要

The foundations of probability theory-as we know it now-and its connection to the theory of statistics date back to the first half of the twentieth century. One of the main contributors to these developments was certainly Bruno de Finetti (1906-1985, BdF in the sequel). Starting from the late twenties, just after his graduation in 1927, BdF wrote a sequence of papers concerning various fundamental issues. Most of such papers have been recently collected in a volume (de Finetti 2006) edited by U.M.I. (Unione Matematica Italiana) and A.M.A.S.E.S. (Associazione per la Matem-atica Applicata alle Scienze Economiche e Sociali). Restricting on probability theory and statistics (and neglecting mathematical economics), the topics where BdF had the greatest impact are: (ⅰ) Finitely additive probabilities and coherence; (ⅱ) Exchangeability and Bayesian inference; (ⅲ) Processes with independent increments. All these arguments were treated within his subjective approach to probability. However, while many basic ideas on (ⅲ) were introduced by BdF, a systematic theory of independent increment processes was developed by other people, mainly by Paul Levy. Issues (ⅰ) and (ⅱ), instead, are entirely due to BdF. Coherence and exchangeability merely did not exist before BdF.