A Review of Modern Computational Algorithms for Bayesian Optimal Design

Abstract

Bayesian experimental design is a fast growing area of research with many real-world applications. As computational power has increased over the years, so has the development of simulation-based design methods, which involve a number of algorithms, such as Markov chain Monte Carlo, sequential Monte Carlo and approximate Bayes methods, and which have enabled more complex design problems to be solved. TheBayesian framework provides a unified approach for incorporating prior information and/or uncertainties regarding the statistical model with a utility function which describes the experimental aims. In this paper, we provide a general overview on the concepts involved in Bayesian experimental design, and focus on describing some of the more commonly-used Bayesian utility functions and methods for their estimation, as well as a number of algorithms that are used to search over the design space to find the optimal Bayesian design. We also discuss other computational strategies for further research in Bayesian optimal design.

Experiment design for nonparametric models based on minimizing Bayes Risk: application to voriconazole$$^{1}$$

“…It is worth noting that there is a separate literature on Bayesian optimal design (Ryan et al [42]). Pre-posterior analysis methods from Bayesian optimal design have been applied in the context of PK problems in Merle and Mentre [36].…”

“…However, in contrast to many of the pre-posterior analysis expressions found in modern Bayesian optimal design (cf., Ryan et al [42]), expressions (2)(3) can be calculated analytically without requiring multidimensional integration or stochastic analysis. For the purpose of this paper, a design that minimizes the Bayes Risk overbound (2) is denoted as the Multiple Model optimal experiment design (MMopt).…”

“…This comparison is not intended to be exhaustive as other experiment design methods are possible. Comparisons with methods such as D s optimal design (Goodwin and Payne [21]), T-optimal design (Atkinson et al [2] Vajjah and Duffull [53]), alternative robust D-optimal designs [22][36], and Bayesian design (Chaloner and Verdinelli [12], Ryan et al [42]), are left for future studies.…”

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

“…Hence, it is necessary to efficiently sample from or accurately approximate a larger number of posterior distributions. This poses a significant computational challenge and renders many algorithms such as standard Markov chain Monte Carlo (MCMC) computationally infeasible (Ryan et al 2015). Hence, the requirement for an efficient computational algorithm for Bayesian inference motivates the consideration of the sequential Monte Carlo (SMC) algorithm.…”

“…A recent review of modern computational algorithms for Bayesian design has been given by Ryan et al (2015), and discusses some work in a sequential design context. Approaches based on MCMC techniques have been explored for fixed effects models by Weir et al (2007), McGree et al (2012.…”