David J.Price a,b , Nigel G. Bean c,d , Joshua V. Ross c,d , Jonathan Tuke c,d. An induced natural selection heuristic for finding optimal Bayesian experimental designs. Computational Statistics & Data Analysis, Volume 126,October 2018, Pages 112-124. https://doi.org/10.1016/j.csda.2018.04.011
Bayesian optimal experimental design has immense potential to inform the collection of data so as to subsequently enhance our understanding of a variety of processes. However, a major impediment is the difficulty in evaluating optimal designs for problems with large, or high-dimensional, design spaces. An efficient search heuristic suitable for general optimisation problems, with a particular focus on optimal Bayesian experimental design problems, is proposed. The heuristic evaluates the objective (utility) function at an initial, randomly generated set of input values. At each generation of the algorithm, input values are “accepted” if their corresponding objective (utility) function satisfies some acceptance criteria, and new inputs are sampled about these accepted points. The new algorithm is demonstrated by evaluating the optimal Bayesian experimental designs for the previously considered death, pharmacokinetic and logistic regression models. Comparisons to the current “gold-standard” method are given to demonstrate the proposed algorithm as a computationally-efficient alternative for moderately-large design problems (i.e., up to approximately 40-dimensions).
a Disease Dynamics Unit, Department of Veterinary Medicine, University of Cambridge, Madingley Road, Cambridge CB3 0ES, United Kingdom
b Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, VIC 3010, Australia
c Victorian Infectious Diseases Reference Laboratory Epidemiology Unit at the Peter Doherty Institute for Infection and Immunity, The University of Melbourne and Royal Melbourne Hospital, VIC 3000, Australia
d School of Mathematical Sciences, University of Adelaide, SA 5005, Australia
e ARC Centre of Excellence for Mathematical & Statistical Frontiers, School of Mathematical Sciences, University of Adelaide, SA 5005, Australia