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贝叶斯推断中自适应求积的随机收敛速率及应用AI 解读

We provide the first stochastic convergence rates for a family of adaptive quadrature rules used to normalize the posterior distribution in Bayesian models. Our results apply to the uniform relative error in the approximate posterior density, the coverage probabilities of approximate credible sets, and approximate moments and quantiles, therefore, guaranteeing fast asymptotic convergence of approximate summary statistics used in practice. The family of quadrature rules…

唐彦博对《广义线性模型参数的弱假设推断》的讨论AI 解读

The method proposed by Vansteelandt and Dukes is an interesting combination of non-parametric and machine learning techniques with traditional ideas in statistics. We note in this discussion that the authors' argument is easily extended to obtain a quantitative rate in terms of the quality of the nonparametric conditional mean estimate, and comment on how this may impact a practitioner's choice of the machine learning model used to estimate the conditional mean. However the…

高维情形下的修正似然根AI 解读

Summary We examine a higher order approximation to the significance function with increasing numbers of nuisance parameters, based on the normal approximation to an adjusted log-likelihood root. We show that the rate of the correction for nuisance parameters is larger than the correction for non-normality, when the parameter dimension p is O(nα) for α<12. We specialize the results to linear exponential families and location–scale families and illustrate these with…