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Yingnian Wu 与 Weng Kee Wong 对机器学习概率与统计讨论会的评论AI 解读

We thank the authors for the interesting and timely article. Our commentaries are as follows: From equilibrium Langevin dynamics to non-equilibrium ordinary and stochastic differential equations. We wish to add a little background explanation, with no claim of originality, to this deep and elegant paper that greatly expands the scope of diffusion/score-based models. The diffusion-based model can be viewed as a refined variational auto-encoder and a non-equilibrium Langevin…

Choi 与 Wong 对《广义线性模型参数的弱假设推断》的讨论AI 解读

We congratulate the authors for major advances in the methodology of estimands, in particular assumption-lean reference for the estimands in possibly misspecified generalised linear models. Whereas the simulation studies in Section 6 indeed support the ‘assumption-lean’ claim and the authors’ software in Practice of Epidemiology187 (pp. 1079–1084, 2018) facilitates such inference, the empirical example in Section 7 seems problematic to illustrate applications of the…

检测误差不确定时估计患病率的最优合并检测设计AI 解读

Summary We construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait by using a test with uncertain sensitivity and specificity. Using optimal design theory for approximate designs, we show that the most efficient design for simultaneously estimating the prevalence, sensitivity and specificity requires three different group sizes with equal frequencies. However, if estimating prevalence as accurately as possible is the…

Michaelis–Menten 酶动力学函数拟合优度的最优设计AI 解读

We construct efficient designs for the Michaelis–Menten enzyme kinetic model capable of checking model assumptions. An extended model called EMAX is also considered for this purpose. This model is widely used in pharmacokinetics and reduces to the Michaelis–Menten model for a specific choice of parameter settings. Our strategy is to find efficient designs for estimating the parameters in the EMAX model and at the same time test the validity of the Michaelis–Menten model…

部分指定异方差结构模型的最优贝叶斯设计AI 解读

We consider the problem of finding a nonsequential optimal design for estimating parameters in a generalized exponential growth model. This problem is solved by first considering polynomial regression models with error variances that depend on the covariate value and unknown parameters. A Bayesian approach is adopted, and optimal Bayesian designs supported on a minimal number of support points for estimating the coefficients in the polynomial model are found analytically.…

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异方差 G 最优设计AI 解读

SUMMARY This paper addresses the issue of constructing large sample G-optimal designs when the variability of the response varies across a compact design space. A useful characterization theorem is presented along with a computer algorithm for generating (heteroscedastic) G-optimal designs. to facilitate comparisons between D- and G-optimal designs, Atwood's inequality for comparing D- and G-efficiencies in homoscedastic models is generalized to heteroscedastic models. Some…

图形辅助回归：应用统计的进阶课程AI 解读

1. Variable Distributions 2. Bivariate Regression Analysis 3. Basics of Multiple Regression 4. Regression Criticism 5. Fitting Curves 6. Robust Regressions 7. Logit Regression 8. Principle Components and Factor Analysis