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Sparse grid hybridized PSO for finding Bayesian optimal designs

Banff International Research Station for Mathematical Innovation and Discovery

Finding Bayesian optimal designs for a nonlinear model is generally a difficult task, especially when there are several factors in the study. Such optimal designs are often analytically intractable and require expensive effort to compute them. A main problem is the unknown number of support points required for the optimal design. The often used Monte Carlo approximations require very large samples from the parameter space to have reasonable accuracy and are thus unrealistic for moderate to high dimensional models. In this talk, we propose an effective and assumptions free approach for finding numerical Bayesian optimal designs with a few real applications to longitudinal models in HIV studies. Our algorithm hybridizes particle swarm optimization and sparse grids methodology (PSOSG) and we demonstrate its potential for finding Bayesian optimal designs for a variety of models using user-specified prior distributions. The optimality of all our generated designs is verified using an equivalence theorem and if time permits, we also discuss applications of PSOSG to find other types of optimal designs.

Mathematics; Statistics

video/mp4

Author affiliation: UCLA

2018-02-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64561

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/