Subjective Probability (The Real Thing)
... to agree (well, they gave me “carte blanche”, so the recycling remained my job) and have obtained the necessary permission from the other interested parties, so that the second, bigger part of chapter 5 is their work. Parts of it use mathematics a bit beyond the general level of this book, but I tho ...
... to agree (well, they gave me “carte blanche”, so the recycling remained my job) and have obtained the necessary permission from the other interested parties, so that the second, bigger part of chapter 5 is their work. Parts of it use mathematics a bit beyond the general level of this book, but I tho ...
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... ambiguity. It is also possible that player i may be aware that there is more than one interpretation of p, but believes that player j is aware of only one interpretation. For example, think of a politician making an ambiguous statement which he realizes that different constituencies will interpret d ...
... ambiguity. It is also possible that player i may be aware that there is more than one interpretation of p, but believes that player j is aware of only one interpretation. For example, think of a politician making an ambiguous statement which he realizes that different constituencies will interpret d ...
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... now on). Roughly speaking, a strategy is strongly rationalizable if it is rationalizable using beliefs that are compatible, in the sense that if one player assigns positive probability to a strategy profile, then all players assign positive probability to it. HP show that in the centipede game, the ...
... now on). Roughly speaking, a strategy is strongly rationalizable if it is rationalizable using beliefs that are compatible, in the sense that if one player assigns positive probability to a strategy profile, then all players assign positive probability to it. HP show that in the centipede game, the ...
The Temporal Logic of Causal Structures
... and “smoking kills within 10 years”, we might make very different decisions than when confronted with one that simply says “smoking kills.” Note that we have not yet mentioned the probability of death in either case. The first case could be with probability 1 with the latter being much smaller. This ...
... and “smoking kills within 10 years”, we might make very different decisions than when confronted with one that simply says “smoking kills.” Note that we have not yet mentioned the probability of death in either case. The first case could be with probability 1 with the latter being much smaller. This ...
Test martingales, Bayes factors, and p-values
... Nonnegative martingales with initial value 1, Bayes factors, and p-values can all be regarded as measures of evidence against a probabilistic hypothesis (i.e., a simple statistical hypothesis). In this article, we review the well-known relationship between Bayes factors and nonnegative martingales a ...
... Nonnegative martingales with initial value 1, Bayes factors, and p-values can all be regarded as measures of evidence against a probabilistic hypothesis (i.e., a simple statistical hypothesis). In this article, we review the well-known relationship between Bayes factors and nonnegative martingales a ...
Ars Conjectandi
Ars Conjectandi (Latin for The Art of Conjecturing) is a book on combinatorics and mathematical probability written by Jakob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way, and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations—the aforementioned problems from the twelvefold way—as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work.