# Posterior Concentration Rates for Bayesian Penalized Splines

@inproceedings{Bach2021PosteriorCR, title={Posterior Concentration Rates for Bayesian Penalized Splines}, author={Paul Bach and Nadja Klein}, year={2021} }

Despite their widespread use in practice, the asymptotic properties of Bayesian penalized splines have not been investigated so far. We close this gap and study posterior concentration rates for Bayesian penalized splines in a Gaussian nonparametric regression model. A key feature of the approach is the hyperprior on the smoothing variance, which allows for adaptive smoothing in practice but complicates the theoretical analysis considerably as it destroys conjugacy and precludes analytic…

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