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Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a…
We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the…
We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters.…
We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. The focus is on problems where one seeks to optimize the…
We consider the problem of designing experiments for the estimation of a target in regression analysis if there is uncertainty about the parametric form of the regression function. A new optimality criterion is proposed, which minimizes the…
This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class…
Among the major difficulties that one may encounter when estimating parameters in a nonlinear regression model are the nonuniqueness of the estimator, its instability with respect to small perturbations of the observations and the presence…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
We consider the problem of computing optimal experimental design on a finite design space with respect to a compound Bayes risk criterion, which includes the linear criterion for prediction in a random coefficient regression model. We show…
In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is…
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…
Improvements in technology lead to increasing availability of large data sets which makes the need for data reduction and informative subsamples ever more important. In this paper we construct $ D $-optimal subsampling designs for…
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…
The subject of this work is multiple group random coefficients regression models with several treatments and one control group. Such models are often used for studies with cluster randomized trials. We investigate A-, D- and E-optimal…
We consider the problem of obtaining D-optimal designs for factorial experiments with a binary response and $k$ qualitative factors each at two levels. We obtain a characterization for a design to be locally D-optimal. Based on this…
The ability to design effective experiments is crucial for obtaining data that can substantially reduce the uncertainty in the predictions made using computational models. An optimal experimental design (OED) refers to the choice of a…
Many chemical and biological experiments involve multiple treatment factors and often it is convenient to fit a nonlinear model in these factors. This nonlinear model can be mechanistic, empirical or a hybrid of the two. Motivated by…
We consider minimax-optimal designs for the prediction of individual parameters in random coefficient regression models. We focus on the minimax-criterion, which minimizes the "worst case" for the basic criterion with respect to the…
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 design is an approach for selecting samples among a given set so as to obtain the best estimator for a given criterion. In the context of linear regression, several optimal designs have been derived, each associated with a…