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Lavine 与 Hodges 对《广义线性模型参数的弱假设推断》的讨论AI 解读

The authors advocate a style and rhetoric of statistical analysis that begins with specifying an estimand and ends with an estimate and interval. They say, ‘The starting point… is to come up with an estimand that is meaningful when the above [generalized partially linear] model [(4)] does not hold, but reduces to [the familiar regression coefficient] β when the model holds; this… allows for nonparametric inference to be developed for that estimand’. However, in our opinion,…

多重集采样器AI 解读

We introduce the multiset sampler (MSS), a new Metropolis–Hastings algorithm for drawing samples from a posterior distribution. The MSS is designed to be effective when the posterior has the feature that the parameters can be divided into two sets, X, the parameters of interest and Y, the nuisance parameters. We contemplate a sampler that iterates between X moves and Y moves. We consider the case where either (a) Y is discrete and lives on a finite set or (b) Y is continuous…

用于评估海洋混合层深度趋势的主观似然AI 解读

This article describes a Bayesian statistical analysis of long-term changes in the depth of the ocean's mixed layer. The data are thermal profiles recorded by ships. For these data, there is no good sampling model and thus no obvious likelihood function. Our approach is to elicit posterior distributions for training data directly from the expert. We then infer the likelihood function and use it on large datasets.

给定先验边际分布时的贝叶斯推断AI 解读

We show how to find bounds on posterior expectations of arbitrary functions of the parameters when the prior marginals are specified but when the complete joint prior is unspecified. We also give a theorem that is useful for finding posterior bounds in a wide range of Bayesian robustness problems. We apply these techniques to two examples. The first example involves a recent clinical trial for extracorporeal membrane oxygenation (ECMO). Our analysis may be regarded as a…

多维参数空间中的稳健贝叶斯分析方法AI 解读

In some multiparameter Bayesian problems the prior is more naturally described as a joint density for all of the parameters and in others it is more naturally described as a product of marginal and conditional densities. Although ordinary quantile, ε-contamination, and density-ratio classes of priors may be sensible choices for robust Bayesian analyses in the former case, they may be less satisfactory in the latter. This article shows how to construct product classes of…

贝叶斯统计中的敏感性：先验与似然AI 解读

One paradigm for sensitivity analyses in Bayesian statistics is to specify Γ, a reasonable class of priors, and to compute the corresponding class of posterior inferences. The class Γ is chosen to represent uncertainty about the prior. There is often additional uncertainty, however, about the family of sampling distributions. This article introduces a method for computing ranges of posterior expectations over reasonable classes of sampling distributions that lie “close to” a…