Abstract
Experimental design attempts to maximise the information available for modelling tasks. An optimal experiment allows the inferred models or parameters to be chosen with the highest expected degree of confidence. If the true system is faithfully reproduced by one of the models, the merit of this approach is clear - we simply wish to identify it and the true parameters with the most certainty. However, in the more realistic situation where all models are incorrect or incomplete, the interpretation of model selection outcomes and the role of experimental design needs to be examined more carefully. Using a novel experimental design and model selection framework for stochastic state-space models, we perform high-throughput in-silico analyses on families of gene regulatory cascade models, to show that the selected model can depend on the experiment performed. We observe that experimental design thus makes confidence a criterion for model choice, but that this does not necessarily correlate with a model's predictive power or correctness. Finally, in the special case of linear ordinary differential equation (ODE) models, we explore how wrong a model has to be before it influences the conclusions of a model selection analysis.
Highlights
Mathematical models provide a rich framework for biological investigation
In this work we present a computationally efficient method of experimental design for model selection
The contributions of this article are threefold; firstly, we extend a promising and computationally efficient experimental design framework for model selection to the stochastic setting, with nonGaussian prior distributions; secondly, we utilise this efficiency to explore the robustness of model selection outcomes to experimental choices; and we observe that experimental design can give rise to levels of confidence in selected models that may be misleading as a guide to their predictive power or correctness
Summary
Mathematical models provide a rich framework for biological investigation. Depending upon the questions posed, the relevant existing knowledge and alternative hypotheses may be combined and conveniently encoded, ready for analysis via a wealth of computational techniques. The consequences of each hypothesis can be understood through the model behaviour, and predictions made for experimental validation. Values may be inferred for unknown physical parameters and the actions of unobserved components can be predicted via model simulations. Choosing an appropriate formulation (e.g. mechanistic, phenomenological or empirical), identifying the important components to include (and those that may be safely ignored), and defining the laws of interaction between them remains highly challenging, and requires a combination of experimentation, domain knowledge and, at times, a measure of luck. Even the most sophisticated models will still be subject to an unknown level of inaccuracy – how this affects the modelling process, and in particular experimental design for Bayesian inference, will be the focus of this study
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