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贝叶斯样本量的闭式表达AI 解读

Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the data. Thus, when a sample size criterion is formalized in terms of a functional of the posterior, its value is a random variable. Generally, such functionals have means under the true distribution. We give asymptotic expressions for the…

若干潜在性质的可观测表征与检验AI 解读

Work due to Junker and more recently due to Junker and Ellis characterized desired latent properties of an educational testing procedure in terms of a collection of other manifest properties. This is important because one can only propose tests for manifest quantities, not latent ones. Here, we complete the conversion of a pair of latent properties to equivalent conditions in terms of four manifest quantities and identify a general method for producing tests for manifest…

给定样本均值的后验收敛AI 解读

For various applications one wants to know the asymptotic behavior of $w(\theta | \overline{X})$, the posterior density of a parameter $\theta$ given the mean $\overline{X}$ of the data rather than the full data set. Here we show that $w(\theta | \overline{X})$ is asymptotically normal in an $L^1$ sense, and we identify the mean of the limiting normal and its asymptotic variance. The main results are first proved assuming that $X_1, \dots, X_n, \dots$ are independent and…