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1 Correction to: JABES https://doi.org/10.1007/s13253-019-00377-z
Unfortunately, in the original publication of the article, several definitional mistakes crept into the manuscript during writing. A complete, corrected version of the manuscript can be found at https://arxiv.org/abs/2001.07623. The results of the paper are unchanged, but the errors and their corrections are listed below.
- 1.
Definition of c(x, y) in Sect. 2.3. The Matérn formulation should be
$$\begin{aligned} c(x, y) = \dfrac{2^{1-\nu }}{(4\pi )^{d/2}\kappa ^{2\nu }\tau ^2\Gamma (\nu + d/2)} (\kappa \Vert x - y\Vert )^{\nu }K_{\nu }(\kappa \Vert x - y\Vert ) \end{aligned}$$ - 2.
At end of second paragraph in Sect. 2.3 should be \(\alpha = \nu + d/2\).
- 3.
In Sect. 3.1, the thin plate penalties should have squared integrands, i.e., \(J(\varvec{\beta }, \lambda ) = \lambda \int \left( \partial ^2 f / \partial x^2\right) ^2 + 2\left( \partial ^2 f / \partial x \partial y\right) ^2 + \left( \partial ^2 f / \partial y^2\right) ^2 \mathrm {d}x\mathrm {d}y\).
- 4.
In Sect. 3.3, in paragraph 2, the expression should be \(\langle Df, Df \rangle = \tau ^2(\kappa ^4 \langle f, f \rangle + 2\kappa ^2 \langle \nabla f, \nabla f \rangle + \langle \Delta f, \Delta f \rangle )\). Following on from that, the definitions of \(\varvec{G}_1, \varvec{G}_2\) should be \(\langle \nabla \psi _i, \nabla \psi _j \rangle \) and \(\langle \Delta \psi _i, \Delta \psi _j \rangle \), respectively.
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Miller, D.L., Glennie, R. & Seaton, A.E. Correction to: Understanding the Stochastic Partial Differential Equation Approach to Smoothing. JABES 25, 276 (2020). https://doi.org/10.1007/s13253-020-00383-6
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DOI: https://doi.org/10.1007/s13253-020-00383-6