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非识别模型后验分布的极限是什么，为何值得关注？AI 解读

In health research and other fields, the observational data available to researchers often fall short of the data that ideally would be available, due to the inherent limitations of study design and data acquisition. Were they available, these ideal data might be readily analyzed via straightforward statistical models with such desirable properties as parameter identifiability. Conversely, realistic models for the available data that incorporate uncertainty about the link…

使用近似工具变量的测量误差建模AI 解读

Summary Consider using regression modelling to relate an exposure (predictor) variable to a disease outcome (response) variable. If the exposure variable is measured with error, but this error is ignored in the analysis, then misleading inferences can result. This problem is well known and has spawned a large literature on methods which adjust for measurement error in predictor variables. One theme is that the requisite assumptions about the nature of the measurement error…

参数模型误设敏感性的度量AI 解读

Summary In settings where parametric inference is inconsistent under model misspecification, the discrepancy between correct and misspecified inferences is compared with the discrepancy between correct and misspecified models. To make the comparison tractable, large sample and small misspecification approximations are employed. The ratio of the approximate discrepancy between inferences to the approximate discrepancy between models is regarded as a relative measure of…

包含交互项与平滑效应的贝叶斯回归建模AI 解读

There have been many recent suggestions as to how to build and estimate flexible Bayesian regression models, using constructs such as trees, neural networks, and Gaussian processes. Although there is much to commend these methods, their implementation and interpretation can be daunting for practitioners. This article presents a spline-based methodology for flexible Bayesian regression that is quite simple in terms of computation and interpretation. Smooth bivariate…

含交互项与平滑效应的贝叶斯回归建模AI 解读

There have been many recent suggestions as to how to build and estimate flexible Bayesian regression models, using constructs such as trees, neural networks, and Gaussian processes. Although there is much to commend these methods, their implementation and interpretation can be daunting for practitioners. This article presents a spline-based methodology for flexible Bayesian regression that is quite simple in terms of computation and interpretation. Smooth bivariate…

推断对先验边际分布的局部敏感性AI 解读

The sensitivity of posterior expectations to perturbations of prior marginals is investigated, using a local method. This approach is particularly well suited to high-dimensional parameter spaces. Qualitative and quantitative results are obtained regarding the propagation of sensitivity in multiparameter settings. More specifically, a posterior expectation is treated as a functional of the prior marginal. The derivative of this functional is evaluated at the nominal prior…

后验期望的局部敏感性AI 解读

We investigate the degree to which posterior expectations are sensitive to prior distributions, using a local method based on functional differentiation. Invariance considerations suggest a family of norms which can be used to measure perturbations to the prior. The sensitivity measure is seen to depend heavily on the choice of norm; asymptotic results suggest which norm will yield the most useful results in practice. We find that to maintain asymptotically sensible…

贝叶斯推断的局部敏感性诊断AI 解读

We investigate diagnostics for quantifying the effect of small changes to the prior distribution over a k-dimensional parameter space. We show that several previously suggested diagnostics, such as the norm of the Fréchet derivative, diverge at rate $n^{k/2}$ if the base prior is an interior point in the class of priors, under the density ratio topology. Diagnostics based on $\phi$-divergences exhibit similar asymptotic behavior. We show that better asymptotic behavior can…