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贝叶斯 T 最优模型判别设计AI 解读

The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to the $T$-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57–70] is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally $T$-optimal discriminating design problems with a large number of model comparisons. Current methodology for the numerical construction of…

稳健的 T 最优模型判别设计AI 解读

This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the $T$-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57–70]. $T$-optimal designs depend on unknown model parameters and it is demonstrated that these designs are sensitive with respect to misspecification. As a solution to this problem we propose a Bayesian and standardized maximin approach to construct…

局部最优设计中的 de la Garza 现象札记AI 解读

The celebrated de la Garza phenomenon states that for a polynomial regression model of degree p−1 any optimal design can be based on at most p design points. In a remarkable paper, Yang [Ann. Statist. 38 (2010) 2499–2524] showed that this phenomenon exists in many locally optimal design problems for nonlinear models. In the present note, we present a different view point on these findings using results about moment theory and Chebyshev systems. In particular, we show that…

一类非线性回归模型的最优设计AI 解读

For a broad class of nonlinear regression models we investigate the local E- and c-optimal design problem. It is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the Chebyshev points, which are the local extrema of the equi-oscillating best approximation of the function f0≡0 by a normalized linear combination of the regression functions in the corresponding linearized model. The class of models includes rational,…

傅里叶回归模型中单个系数估计的最优设计AI 解读

In the common trigonometric regression model, we investigate the optimal design problem for the estimation of the individual coefficients, where the explanatory variable varies in the interval $[-a,a]$, $0 <a \le \pi$. It is demonstrated that the structure of the optimal design depends sensitively on the size of the design space. For many important cases, optimal designs can be found explicitly, where the complexity of the solution depends on the value of the parameter a and…

Monod模型中的高效实验设计AI 解读

Summary Estimation and experimental design in a non-linear regression model that is used in microbiology are studied. The Monod model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, water research, pharmacokinetics and plant physiology. It is proved that least squares estimates are asymptotically unbiased and normally distributed. The asymptotic covariance matrix of the estimator is the basis for the construction…