Abstract The probability distribution of a sequence X = ( X 1 , X 2 , … ) of random variables is determined by its predictive distributions P ( X 1 ∈ ⋅ ) and P ( X n + 1 ∈ ⋅ ∣ X 1 , … , X n ) , n ≥ 1 . Motivated by applications in Bayesian predictive inference, in Berti et al. (2020), a class C of sequences is introduced by specifying such predictive distributions. Each X ∈ C is conditionally identically distributed. The asymptotics of X ∈ C is investigated in this paper. Both strong and weak limit theorems are provided. Conditions for X to converge a.s., and for X not to converge in probability, are given in terms of the predictive distributions. A stable CLT is provided as well. Such a CLT is used to obtain approximate credible intervals.

中文翻译：

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某些条件同分布序列的渐近性

摘要 随机变量序列 X = ( X 1 , X 2 , … ) 的概率分布由其预测分布 P ( X 1 ∈ ⋅ ) 和 P ( X n + 1 ∈ ⋅ ∣ X 1 , … , X 决定n ) , n ≥ 1 。受贝叶斯预测推理中的应用的启发，Berti 等人。(2020)，通过指定这样的预测分布引入了 C 类序列。每个 X ∈ C 是条件同分布的。本文研究了X∈C的渐近性。提供了强极限定理和弱极限定理。X 收敛的条件和 X 不收敛的概率的条件是根据预测分布给出的。还提供了稳定的 CLT。这样的 CLT 用于获得近似的可信区间。