Work
De Finetti emphasized a predictive inference approach to statistics; he proposed a thought experiment along the following lines (described in greater detail at coherence (philosophical gambling strategy)): You must set the price of a promise to pay $1 if there was life on Mars 1 billion years ago, and $0 if there was not, and tomorrow the answer will be revealed. You know that your opponent will be able to choose either to buy such a promise from you at the price you have set, or require you to buy such a promise from your opponent, still at the same price. In other words: you set the odds, but your opponent decides which side of the bet will be yours. The price you set is the "operational subjective probability" that you assign to the proposition on which you are betting. This price has to obey the probability axioms if you are not to face certain loss, as you would if you set a price above $1 (or a negative price). By considering bets on more than one event de Finetti could justify additivity. Prices, or equivalently odds, that do not expose you to certain loss through a Dutch book are called coherent.
De Finetti is also noted for de Finetti's theorem on exchangeable sequences of random variables. De Finetti was not the first to study exchangeability but he brought the subject to greater visibility. He started publishing on exchangeability in the late 1920s but the 1937 article is his most famous treatment.
In 1929, de Finetti introduced the concept of infinitely divisible probability distributions.
He also introduced de Finetti diagrams for graphing genotype frequencies.
The 1974 English translation of his book is credited with reviving interest in predictive inference in the Anglophone world, and bringing the idea of exchangeability to its attention.
The de Finetti Award, presented annually by the European Association for Decision Making, is named after him.
Read more about this topic: Bruno De Finetti
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