We investigate posterior contraction rates for priors on multivariate functions that are constructed using tensor-product B-spline expansions. We prove that using a hierarchical prior with an appropriate prior distribution on the partition size and Gaussian prior weights on the B-spline coefficients, procedures can be obtained that adapt to the degree of smoothness of the unknown function up to the order of the splines that are used. We take a unified approach including important nonparametric statistical settings like density estimation, regression, and classification.
"Adaptive estimation of multivariate functions using conditionally Gaussian tensor-product spline priors." Electron. J. Statist. 6 1984 - 2001, 2012. https://doi.org/10.1214/12-EJS735