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.

翻译：在使用贝叶斯非参数回归建模生物响应时，关于响应形态的先验信息可能以非线性函数空间的形式存在，这些函数空间定义了响应的一般形态。为了将此类信息纳入分析，我们提出了一种非线性函数收缩方法，该方法将非参数拟合函数均匀收缩至非线性函数空间，同时当数据表明存在其他形态时，允许在该空间外进行拟合。该方法通过泰勒级数展开及相应的非线性参数更新，将现有线性子空间函数收缩方法扩展至非线性函数空间。我们以具有生物学基础的经典Hill模型为例展示了该通用方法，并证明收缩至复合函数空间（即先验存在两个或更多非线性函数的情况）具有直接可行性。通过合成数据与真实数据验证了该方法的有效性。关于底层MCMC采样的计算细节随附于在线补充材料中，其中包含相关数据与分析结果。