Abstract
Most computational approaches to Bayesian experimental design require making posterior calculations repeatedly for a large number of potential designs and/or simulated datasets. This can be expensive and prohibit scaling up these methods to models with many parameters, or designs with many unknowns to select. We introduce an efficient alternative approach without posterior calculations, based on optimising the expected trace of the Fisher information, as discussed by Walker (2016). We illustrate drawbacks of this approach, including lack of invariance to reparameterisation and encouraging designs in which one parameter combination is inferred accurately but not any others. We show these can be avoided by using an adversarial approach: the experimenter must select their design while a critic attempts to select the least favourable parameterisation. We present theoretical properties of this approach and show it can be used with gradient based optimisation methods to find designs efficiently in practice.
Highlights
Selecting a good design for an experiment can be crucial to extracting useful information and controlling costs
We focus on the Bayesian approach to optimal experimental design, which takes into account existing knowledge and uncertainty about the process being studied before the experiment is undertaken
We show that using the Hyvarinen score in the decision theoretic framework results in a utility based on the trace of the Fisher information, referred to as Fisher information gain or FIG in the paper (Section 3.3)
Summary
Selecting a good design for an experiment can be crucial to extracting useful information and controlling costs. We focus on the Bayesian approach to optimal experimental design, which takes into account existing knowledge and uncertainty about the process being studied before the experiment is undertaken. In this framework an experimenter must select a design. But not exclusively, concentrate on the case where τ ∈ T ⊆ Rd and θ ∈ Θ ⊆ Rp for some closed sets (under the Euclidean metric) T and Θ, and where y is a vector of n observations Designs τ of this form often represent times or locations for measurements to be taken. In this case τ can be seen as a set of design points, τ1, τ2, . . . , τd
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