Research On Quasi-Bayesian Theory

Based on bayesian theory, quasi-bayesian theory is presented by Giron and Rios in 1980. Giron and Rios discuss decision-making problems under a group of prior distributions, which start from preference. But the theory also has its shortcomings, it did not discuss the conditionalization and the independence, and the decision-making rules didn't been discussed too much. On the basis of quasi-bayesian theory, Cozman discusses conditionalization and the independence in quasi-bayesian theory by adopting Wallers irrelevance and independence concepts, and updates the quasi-bayesian theory under the basic research on preference. This thesis gives a further discussion of relevant contents of quasi-bayesian theory on the basis of Cozman's work.At first, this thesis briefly introduces the background and the recent works of bayesian theory at home and aborad, and the quasi-bayesian theory presented by Giron and Rios. On the basis of preference, the equivalence between Giron-Rios' axioms and Walley's almost preferences axioms is discussed. Then this thesis researches the applications of Giron-Rios axioms. According to the definition and properties of lower expectations presented by Walley, this thesis starts from preferences, and gives the definition of the preference operator and a kind of preference pattern. The relevant properties of preference operator are discussed. This thesis derives the convex sets of probability distribution from lower expectation anddiscusses the relation between lower expectation and dominating distributions, including some properties of conditional preference. At last, Based on bayesian interval estimation, this thesis gives the definition of quasi-bayesian confidence set, and then discusses the quasi-bayesian interval estimation in the normal case in which the mean is unknown while the variance is known and makes comparisons with the Bayesian interval estimation.