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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