Adaptive Bayesian multivariate spline knot inference with prior specifications on model complexity

Inferring the number and locations of knots in spline regression remains a difficult problem due to the varying dimensionality of the parameter space and the non-differentiability of the likelihood function. In this paper, we propose a Bayesian framework for knot inference in multivariate spline regression, supported by prior specifications that account for model complexity. By accurately estimating the knot number and locations, this approach addresses several complex tasks, including fitting discontinuous multivariate functions, detecting univariate change points, and identifying peak locations in multivariate regression. We evaluate the proposed method through extensive simulation studies and demonstrate its practical utility by analyzing real-world datasets, including triceps skinfold thickness measurements and functional magnetic resonance imaging data from the Human Connectome Project. The results underscore the superior performance of our approach compared to existing methods.