Bayesian regression with multivariate linear splines

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Nonstationary Covariance Functions for Gaussian Process Regression (2003, methodology): “For higher-dimensional inputs, we compare the nonstationary GP to the stationary GP, the neural network models, and two free-knot spline methods, Bayesian multivariate linear splines (BMLS) [14] and Bayesian multivariate automatic regression splines (BMARS) [15], a Bayesian version of MARS [16].”
Spatial modelling using a new class of nonstationary covariance functions (2006, methodology): “The second method (mls) uses free-knot multivariate linear splines (MLS) where the basis functions are truncated linear planes, which gives a surface that is continuous but not differentiable where the planes meet (Holmes and Mallick 2001).”
The Practical Implementation of Bayesian Model Selection (2001, methodology): “It has been applied and extended to nonparametric spline regression by Denison, Mallick and Smith (1998bc), Gustafson (2000), Holmes and Mallick (2001) , Liang,”
Local and Piecewise Affine Approaches to System Identification (2003, methodology): “One such example is [67], which uses a parameterized piecewise affine model with Gaussian a priori distributions for the parameters.”
Generalized Nonlinear Modeling With Multivariate Free-Knot Regression Splines (2003, methodology): “The multivariate linear spline produces a piecewise linear surface that improves interpretability of the model (Breiman 1993; Holmes and Mallick 2001).”