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Finite-Dimensional Distributions and Tail Behavior in Stationary Interval-Valued Probability Models
平稳区间值概率模型的有限维分布与尾部行为
We consider the relationship between the finite-dimensional distributions of a stationary time series model and its asymptotic behavior in the framework of interval-valued probability (IVP), a simple generalization of additive probability measures. By Caratheodory's theorem, the specification of a countably additive probability measure on the algebra of cylinders $\mathscr{C}$ uniquely defines its behavior on $\sigma(\mathscr{C})$ (containing the tail events). If the measure…
Bayes-like Decision Making with Upper and Lower Probabilities
使用上下概率进行类贝叶斯决策
We consider the use of interval-valued probabilities to represent the support lent to the hypothesis that the parameter value θ lies in a subset A of the parameter set Θ when we observe x, know the likelihoods {fΘ: θεΘ}, and have some prior information concerning the parameter. Our model for prior information is that of a salient prior distribution in which we have little confidence, although we have much less confidence in any alternative prior. We consider notions of…