منابع مشابه
Angles as Probabilities
Almost everyone knows that the inner angles of a triangle sum to 180o. But if you ask the typical mathematician how to sum the solid inner angles over the vertices of a tetrahedron, you are likely to receive a blank stare or a mystified shrug. In some cases you may be directed to the Gram-Euler relations for higher dimensional polytopes [3, 4, 6, 7], a 19th century result unjustly consigned to ...
متن کاملQuantum Probabilities as Behavioral Probabilities
We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial pr...
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A decision maker is asked to express her beliefs by assigning probabilities to certain possible states. We focus on the relationship between her database and her beliefs. We show that, if beliefs given a union of two databases are a convex combination of beliefs given each of the databases, the belief formation process follows a simple formula: beliefs are a similarity-weighted average of the b...
متن کاملExponential Models: Approximations for Probabilities
Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property ...
متن کاملInterpreting Prediction Market Prices as Probabilities
While most empirical analysis of prediction markets treats prices of binary options as predictions of the probability of future events, Manski (2004) has recently argued that there is little existing theory supporting this practice. We provide relevant analytic foundations, describing sufficient conditions under which prediction markets prices correspond with mean beliefs. Beyond these specific...
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ژورنال
عنوان ژورنال: American Mathematical Monthly
سال: 2009
ISSN: 0002-9890,1930-0972
DOI: 10.4169/193009709x460868