Maximilian Siebel

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math.ST2026

Posterior contraction under misspecification and heteroscedasticity in non-linear inverse problems

Fanny Seizilles, Maximilian Siebel

In many practical and numerical inverse problems, the exact data log-likelihood is not fully accessible, motivating the use of surrogate models. We study heteroscedastic nonparamet…

math.ST2024

Convergence Rates for the Maximum A Posteriori Estimator in PDE-Regression Models with Random Design

Maximilian Siebel

We consider the statistical inverse problem of recovering a parameter $θ \in H^{α}$ from data arising from the Gaussian regression problem \begin{equation*} Y = \mathscr{G}(θ)(Z)+\var…

math.ST2024

Lower Bounds for Nonparametric Estimation of Ordinary Differential Equations

Christof Schötz, Maximilian Siebel

We noisily observe solutions of an ordinary differential equation $u ˙ = f (u)$ at given times, where $u$ lives in a $d$ -dimensional state space. The model function $f$ is unknow…