Design of Experiments in Nonlinear Models

Convex optimization of measurement allocation for magnetic tracking systems

“…We have not considered in full the characteristics of the estimation problem that is obtained with the optimized measurement allocation during the optimization procedure; for example, if the parameters can be uniquely determined everywhere in the measurement domain and if there are local minima present in the estimation problem. This is related to the concepts of identifiability and estimability and the reader is referred to Pronzato and Pázman (2013) for further information.…”

“…If the model V k ðpÞ is linear in p, the D-optimal solution minimizes the volume of the lower bound for the confidence ellipsoid described by M À1 in (12). The volume of the b-confidence ellipsoid is given by Pronzato and Pázman (2013) …”

“…The reader is referred to Walter and Pronzato (1997), Uciński (2005), Pukelsheim (2006), Atkinson et al (2007), and Pronzato and Pázman (2013) for an introduction to the subject. Joshi and Boyd (2009) studied sensor selection by means of convex optimization without a specific application in mind.…”

Sizing up the regions of unique minima in the least squares nonlinear regression

“…We obtain a formula for computing the maximum radius of any RIGM region based on the properties of an equidistant function that the first two authors introduced in [6]. This function also plays a prominent role in the definition of extended intrinsic curvature of a nonlinear model presented in [8]. While closely related to the intrinsic curvature locally, the equidistant function reflects global rather than local properties of a nonlinear model.…”

Designs for Generalized Linear Models

“…The focus of Silvey (1980) and Fedorov and Hackl (1997) is on the mathematical theory; Atkinson, Donev, and Tobias (2007) and Berger and Wong (2009) are more concerned with applications, whereas Goos and Jones (2011) introduce theory and examples via the JMP software. Pronzato and Pázman (2013) present the theory of optimal design for nonlinear models, while Fedorov and Leonov (2014) illustrate their theory with pharmaceutical applications, particularly dose finding.…”