Robust designs for binary data: applications of simulated annealing

Abstract

When the aim of an experiment is the estimation of a Generalised Linear Model (GLM), standard designs from linear model theory may prove inadequate. This paper describes a flexible approach for finding designs for experiments to estimate GLMs through the use of D-optimality and a simulated annealing algorithm. A variety of uncertainties in the model can be incorporated into the design search, including the form of the linear predictor, through use of a robust design selection criterion and a postulated model space. New methods appropriate for screening experiments and the incorporation of correlations between possible model parameters are described through examples. An updating formula for Doptimality under a GLM is presented which improves the computational efficiency of the search.Robust designs for binary data: applications of simulated annealingSouthampton Statistical Sciences Research Institute, University of Southampton, Southampton, UK AbstractWhen the aim of an experiment is the estimation of a Generalised Linear Model (GLM), standard designs from linear model theory may prove inadequate. This paper describes a flexible approach for finding designs for experiments to estimate GLMs through the use of D-optimality and a simulated annealing algorithm. A variety of uncertainties in the model can be incorporated into the design search, including the form of the linear predictor, through use of a robust design selection criterion and a postulated model space. New methods appropriate for screening experiments and the incorporation of correlations between possible model parameters are described through examples. An updating formula for D-optimality under a GLM is presented which improves the computational efficiency of the search.

Design of Experiments for Categorical Repeated Measurements in Packet Communication Networks

“…This approach is valid when the parameters in the prior are not interdependent. Woods (2010) introduced a method for optimizing designs for binary data described by a generalized linear model; he used a simulated annealing algorithm, and by finding updating equations for this algorithm was able to minimize expensive evaluations of information matrices. A generalization of this work could extend to the general (categorical) data described here.…”

Exact optimal experimental designs with constraints

“…Instead of exploring the solution space systematically, heuristic algorithms define criteria (heuristic) that drive the search towards promising regions of the solution space. Some state-of-the-art heuristic algorithms are available in the optimal design literature such as genetic algorithms (Mandal et al 2006;Lin et al 2015), simulated annealing (Woods 2010) and Particle Swarm algorithms (Chen et al 2014). For details, see Mandal et al (2015).…”

On designing experiments for a dynamic response modeled by regression splines

“…The computation time and determinant value of the optimal design obtained by our algorithm are compared with those obtained from an exhaustive search over all possible sampling plans. Woods suggested to build the candidate set by choosing only sampling times around the locations where each basis function reaches its maximal value. Our approach further reduces this candidate set to only N candidate sampling times.…”