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利用参数与半参数贝叶斯折点回归分析 SEER 癌症发生率AI 解读

Cancer is the second leading cause of death in the United States. Cancer incidence and mortality rates measure the progress against cancer; these rates are obtained from the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute (NCI). Lung cancer has the highest mortality rate among all cancers, whereas prostate cancer has the highest number of new cases among males. In this article, we analyze the incidence rates of these two cancers,…

狄利克雷过程混合模型的边际似然与贝叶斯因子AI 解读

We present a method for comparing semiparametric Bayesian models, constructed under the Dirichlet process mixture (DPM) framework, with alternative semiparameteric or parameteric Bayesian models. A distinctive feature of the method is that it can be applied to semiparametric models containing covariates and hierarchical prior structures, and is apparently the first method of its kind. Formally, the method is based on the marginal likelihood estimation approach of Chib (1995)…

偏离正态分布时位置参数标准置信区间的稳健性AI 解读

Let $X_i = \theta + \sigma Z_i$, where $Z_i$ are i.i.d. from a distribution $F$, and $-\infty < \theta < \infty$ and $\sigma > 0$ are unknown parameters. If $F$ is $N(0, 1)$, a standard confidence interval for the unknown mean $\theta$ is the $t$-interval $\bar{X} \pm t_{\alpha/2} s/\sqrt n$. The question of conservatism of this interval under nonnormality is considered by evaluating the infimum of its coverage probability when $F$ belongs to a suitably chosen class of…