Abstract
We describe the R package acebayes and demonstrate its use to find Bayesian optimal experimental designs. A decision-theoretic approach is adopted, with the optimal design maximizing an expected utility. Finding Bayesian optimal designs for realistic problems is challenging, as the expected utility is typically intractable and the design space may be high-dimensional. The package implements the approximate coordinate exchange algorithm to optimize (an approximation to) the expected utility via a sequence of conditional one-dimensional optimization steps. At each step, a Gaussian process regression model is used to approximate, and subsequently optimize, the expected utility as the function of a single design coordinate (the value taken by one controllable variable for one run of the experiment). In addition to functions for bespoke design problems with user-defined utility functions, acebayes provides functions tailored to finding designs for common generalized linear and nonlinear models. The package provides a step-change in the complexity of problems that can be addressed, enabling designs to be found for much larger numbers of variables and runs than previously possible. We provide tutorials on the application of the methodology for four illustrative examples of varying complexity where designs are found for the goals of parameter estimation, model selection and prediction. These examples demonstrate previously unseen functionality of acebayes.
Highlights
A well-planned and executed experiment is an efficient and effective way of learning the effect of an intervention on a process or system (Box et al 2005), and design of experiments is a key contribution of statistics to the scientific method (Stigler 2016, ch. 6)
A Bayesian optimal design is found by maximising the expectation of this utility over the space of all possible designs, where expectation is with respect to the joint distribution of all unknown quantities including the, as yet, unobserved responses (Chaloner and Verdinelli 1995)
We demonstrate using acenlm to generate a pseudo-Bayesian D-optimal design for a compartmental model commonly used in pharmacokinetics (PK)
Summary
A well-planned and executed experiment is an efficient and effective way of learning the effect of an intervention on a process or system (Box et al 2005), and design of experiments is a key contribution of statistics to the scientific method (Stigler 2016, ch. 6). Overstall and Woods (2017) recently presented the first general methodology for finding highdimensional Bayesian optimal designs using the approximate coordinate exchange (ACE) algorithm. We describe the R package acebayes (Overstall et al 2018c) which implements the ACE algorithm, and introduce functionality that facilitates finding optimal designs for common classes of models, including nonlinear and generalised linear models. For special classes of nonlinear models, locally optimal designs, with a point mass prior for γ and utility functions not depending on y, can be found by packages LDOD (Masoudi et al 2013), designGLMM (Bush and Ruggiero 2016) and PopED (Nyberg et al 2012).
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