Variable selection approaches are widely used in regression. In many applications, variable selection is used to prioritise variables that may have a causal influence on the response. However, many widely-used approaches are rooted in linear models that may limit ability to discern causal influences. Yet in a number of settings, nonlinear dynamical models of underlying processes are available that define classes of functional relationships between covariates and response. Here, we propose an approach for variable selection that is rooted in such nonlinear dynamical systems. Reversible jump Markov chain Monte Carlo is used to assess putative functional relationships and obtain posterior probabilities for the inclusion of individual covariates. We illustrate the approach in the context of protein biochemistry, using data simulated from a recent mechanistic model and in an application to protein data from cell lines. In the former, the true causal graph is known and is used for assessment, whilst in the latter results are compared against known biochemistry. We find that the proposed method- ology is more effective at identifying causal variates than methods based on linear models. Finally we discuss opportunities and challenges involved in extending these ideas further.

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