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Bayesian ODE solvers: the maximum a posteriori estimate
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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en
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18
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STATISTICS AND COMPUTING, Volume 31, issue 3
Abstract
There is a growing interest in probabilistic numerical solutions to ordinary differential equations. In this paper, the maximum a posteriori estimate is studied under the class of ν times differentiable linear time-invariant Gauss–Markov priors, which can be computed with an iterated extended Kalman smoother. The maximum a posteriori estimate corresponds to an optimal interpolant in the reproducing kernel Hilbert space associated with the prior, which in the present case is equivalent to a Sobolev space of smoothness ν+ 1. Subject to mild conditions on the vector field, convergence rates of the maximum a posteriori estimate are then obtained via methods from nonlinear analysis and scattered data approximation. These results closely resemble classical convergence results in the sense that a ν times differentiable prior process obtains a global order of ν, which is demonstrated in numerical examples.
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| openaire: EC/H2020/757275 /EU//PANAMA
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Tronarp, F, Särkkä, S & Hennig, P 2021, 'Bayesian ODE solvers : the maximum a posteriori estimate', STATISTICS AND COMPUTING, vol. 31, no. 3, 23. https://doi.org/10.1007/s11222-021-09993-7