PreprintCC BY 4.0arXiv
Posterior Consistency under dependent errors in non-linear inverse problems with applications to time evolution equations
Abstract
Let θ→ 𝒢(θ) 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 θ under observations of 𝒢(θ) 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.
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BibTeX
@misc{jambhale2026posterior,
title = {{Posterior Consistency under dependent errors in non-linear inverse problems with applications to time evolution equations}},
author = {Aditya Jambhale},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07240},
eprint = {2610.07240},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07240},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Posterior Consistency under dependent errors in non-linear inverse problems with applications to time evolution equations
AU - Aditya Jambhale
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07240
UR - https://arxiv.org/abs/2610.07240
AB - Let θ→ 𝒢(θ) 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 θ under observations of 𝒢(θ) 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.
ER -