Abstract
When a model-based approach is appropriate, an optimal design can guide how to collect data judiciously for making reliable inference at minimal cost. However, finding optimal designs for a statistical model with several possibly interacting factors can be both theoretically and computationally challenging, and this issue is rarely discussed in the literature. We propose nature-inspired metaheuristic algorithms, like particle swarm optimization (PSO) and its variants, to solve such optimization problems. We demonstrate that such techniques, which are easy to implement, can find different types of optimal designs for models with several factors efficiently. To facilitate use of such algorithms, we provide computer codes to generate tailor made optimal designs and evaluate efficiencies of competing designs. As applications, we apply PSO and find Bayesian optimal designs for Exponential models useful in HIV studies and re-design a car-refuelling study for a Logistic model with ten factors and some interacting factors.
Highlights
Statistical models are getting increasingly complex to capture the finer features of a problem
In the optimal design literature, we typically assume that the statistical model is fully parametrized, known and defined on a user-selected design space, apart from the unknown parameters in the model
Given a design criterion and a predetermined n of independent observations to take for the study, the design questions are the optimal number (k) of design points to take from X, the optimal locations x1, . . . , xk’s in X to observe the responses, and the optimal proportion of observations to take at xi, i = 1, . . . , k
Summary
Statistical models are getting increasingly complex to capture the finer features of a problem. (Royle 2002) reported that the traditional exchange algorithms are not practical for finding large spatial designs when the criterion is computationally expensive to evaluate or the discretized design space is large. These may be reasons why the bulk of the optimal experimental designs reported in the literature concern a small number of factors. Nature-inspired metaheuristic algorithms, such as particle swarm optimization (PSO) or one of its enhanced versions, such as competitive swarm optimizer (CSO), are more likely to solve optimization problems with a large number of variables to optimize These algorithms are general purpose optimization tools and by construction, do not require any assumptions on the optimization problem. We conclude with a discussion on future work and a cautionary remark on use of optimal designs in practice
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