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中心量族推断：针对一族分布中心的假设检验AI 解读

Summary Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their centre. Tests that assess statistical hypotheses of centre implicitly assume a specific centre, e.g., the mean or median. Yet, scientific hypotheses do not always specify a particular centre. This ambiguity leaves the possibility for a gap between scientific theory and statistical practice that can lead to rejection of a true null.…

统一贝叶斯个案影响分析中的曲率与重要性抽样方法AI 解读

Methods for summarizing case influence in Bayesian models take essentially two forms: (1) use common divergence measures for calculating distances between the full-data posterior and the case-deleted posterior, and (2) measure the impact of infinitesimal perturbations to the likelihood to study local case influence. Methods based on approach (1) lead naturally to considering the behavior of case-deletion importance sampling weights (the weights used to approximate samples…

识别记忆的贝叶斯竞赛模型AI 解读

Many psychological models use the idea of a trace, which represents a change in a person’s cognitive state that arises as a result of processing a given stimulus. These models assume that a trace is always laid down when a stimulus is processed. In addition, some of these models explain how response times (RTs) and response accuracies arise from a process in which the different traces race against each other. In this article, we present a Bayesian hierarchical model of RT…

贝叶斯线性模型中删例重要性抽样权重的变异性AI 解读

I consider a standard specification of the Bayesian linear model and derive necessary and sufficient conditions for the variance of the case-deletion importance sampling weights to be finite. The conditions have an intuitive interpretation in terms of familiar frequentist measures of leverage and influence and are easy to verify. I present two real data examples in which the necessary conditions fail to hold for some observations and the corresponding importance sampling…

地震时间演化的贝叶斯分析AI 解读

We adopt a Bayesian approach to analyze the occurrence times of seismic events and their magnitudes. We choose an epidemic model for the process of occurrence times conditional on the observed magnitude values. The locations of, and dependencies between, the model parameters are determined on the basis of historical and physical information. The overall prior variability is deliberately made diffuse. We generate samples from the joint posterior distribution of the model…

地震时间演化的贝叶斯分析AI 解读

We adopt a Bayesian approach to analyze the occurrence times of seismic events and their magnitudes. We choose an epidemic model for the process of occurrence times conditional on the observed magnitude values. The locations of, and dependencies between, the model parameters are determined on the basis of historical and physical information. The overall prior variability is deliberately made diffuse. We generate samples from the joint posterior distribution of the model…