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Posterior Consistency under dependent errors in non-linear inverse problems with applications to time evolution equations
arXiv stat.TH0 views
arXiv:2610.07240v1 Announce Type: new Abstract: Let $\theta \to \mathcal G(\theta)$ be a map from a parameter to the solution of some non-linear partial differential equation modelling a dynamical system. We provide conditions to show posterior consistency for $\theta$ under observations of $\mathcal G(\theta)$ with dependent noise, modelling potential time-correlations of the sensors used to make the measurements. We provide two examples, namely the Navier-Stokes equations with unknown viscosity and initial condition, as well as a Reaction-Diffusion type equation with diffusivity coefficient that is varying (heterogeneous) in space, which requires novel stability estimates for a Darcy transport operator with accumulation in time.
Source：https://arxiv.org/abs/2610.07240PreviousHistory-Conditioned Inference of Memory and Stochastic Forcing in Generalized Langevin Equations under L\'evy NoiseNextMinimax Operator Learning for Holomorphic Maps between Hilbert Spaces
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