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何时应停止软件测试？AI 解读

We derive an optimal rule for stopping the testing of a module of software prior to release, based on the trade-off between the cost of continued testing and the expected losses due to any bugs that remain in the released code. Our economic assumptions are that testing costs are perfectly predictable, but of arbitrary form f(t), and that the costs of fixing a bug, both during testing and subsequent to release, are known constants. Our stochastic assumptions are as follows:…

用非参数贝叶斯模型逼近参数贝叶斯模型AI 解读

Let $\tau$ be a prior distribution over the parameter space $\Theta$ for a given parametric model $P_\theta, \theta \in \Theta$. For the sample space $\mathscr{X}$ (over which $P_\theta$'s are probability measures) belonging to a general class of topological spaces, which include the usual Euclidean spaces, it is shown that this parametric Bayes model can be approximated by a nonparametric Bayes model of the form of a mixture of Dirichlet processes prior, so that (i) the…

位置参数的最节省样本稳健选择程序AI 解读

Consider samples of size $n$ from each of $k$ symmetric populations, differing only in their location parameters. The decision problem is to select the best population--the one with the largest location parameter--with control on the probability of correct selection (PCS) whenever the largest parameter is at least $\Delta$ units larger than all others, and whenever the common error distribution belongs to a specified neighborhood of the standard normal. It is shown that, if…

单变量与多变量 Behrens–Fisher 型问题的同时置信程序AI 解读

Given independent samples of size ni from normal populations with mean μi and variance σi2 both unknown, it is possible to construct simultaneous confidence intervals for all linear combinations of μi's with an exact predetermined confidence coefficient by using the tabulated values of Student's t distribution and a generalization of the maximum modulus method of multiple comparisons. These bounds are shown to be a special case of a class of exact bounds based on a variant…