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For a nonlinear regression model the information matrices of designs depend on the parameter of the model. The adaptive Wynn-algorithm for D-optimal design estimates the parameter at each step on the basis of the employed design points and…
The paper continues the authors' work on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper it is shown that if the mean response function satisfies a condition of `saturated identifiability', which was…
Bayesian optimality criteria provide a robust design strategy to parameter misspecification. We develop an approximate design theory for Bayesian $D$-optimality for non-linear regression models with covariates subject to measurement errors.…
Experimental designs based on the classical D-optimal criterion minimize the volume of the linear-approximation inference regions for the parameters using local sensitivity coefficients. For nonlinear models, these designs can be unreliable…
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…
Optimal designs are usually model-dependent and likely to be sub-optimal if the postulated model is not correctly specified. In practice, it is common that a researcher has a list of candidate models at hand and a design has to be found…
Selecting input variables or design points for statistical models has been of great interest in adaptive design and active learning. Motivated by two scientific examples, this paper presents a strategy of selecting the design points for a…
We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The…
The issue of determining not only an adequate dose but also a dosing frequency of a drug arises frequently in Phase II clinical trials. This results in the comparison of models which have some parameters in common. Planning such studies…
D-Optimal designs for estimating parameters of response models are derived by maximizing the determinant of the Fisher information matrix. For non-linear models, the Fisher information matrix depends on the unknown parameter vector of…
A class of nonlinear models combining a pharmacokinetic compartmental model and a pharmacodynamic Emax model is introduced. The locally D-optimal (LD) design for a four-parameter composed model is found to be a saturated four-point uniform…
In this work we focus on saturated $D$-optimal designs. Using recent results, we identify $D$-optimal designs with the solutions of an optimization problem with linear constraints. We introduce new objective functions based on the geometric…
Cumulative link models have been widely used for ordered categorical responses. Uniform allocation of experimental units is commonly used in practice, but often suffers from a lack of efficiency. We consider D-optimal designs with ordered…
We provide a systematic treatment of $D$-optimal design for binary regression and quantal response models in toxicology studies. For the two-parameter case, we provide an analytical equation (WC equation) for computing the $D$-optimal…
The current work is motivated by the need for robust statistical methods for precision medicine; as such, we address the need for statistical methods that provide actionable inference for a single unit at any point in time. We aim to learn…
We propose an optimistic estimate to evaluate the best possible fitting performance of nonlinear models. It yields an optimistic sample size that quantifies the smallest possible sample size to fit/recover a target function using a…
Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…
Systems with both quantitative and qualitative responses are widely encountered in many applications. Design of experiment methods are needed when experiments are conducted to study such systems. Classic experimental design methods are…
We consider maximin and Bayesian $D$-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes…
Alphabetic optimality criteria, such as the $D$, $A$, and $I$ criteria, require specifying a model to select optimal designs. They are not model free and the optimal designs selected by them are not robust to model uncertainty. Recently,…