  When modeling biological responses using Bayesian non-parametric regression,
prior information may be available on the shape of the response in the form of
non-linear function spaces that define the general shape of the response. To
incorporate such information into the analysis, we develop a non-linear
functional shrinkage (NLFS) approach that uniformly shrinks the non-parametric
fitted function into a non-linear function space while allowing for fits
outside of this space when the data suggest alternative shapes. This approach
extends existing functional shrinkage approaches into linear subspaces to
shrinkage into non-linear function spaces using a Taylor series expansion and
corresponding updating of non-linear parameters. We demonstrate this general
approach on the Hill model, a popular, biologically motivated model, and show
that shrinkage into combined function spaces, i.e., where one has two or more
non-linear functions a priori, is straightforward. We demonstrate this approach
through synthetic and real data. Computational details on the underlying MCMC
sampling are provided with data and analysis available in an online supplement.
