A Hierarchical Bayesian Setting for an Inverse Problem in Linear Parabolic PDEs with Noisy Boundary Conditions

@article{Ruggeri2017AHB,
  title={A Hierarchical Bayesian Setting for an Inverse Problem in Linear Parabolic PDEs with Noisy Boundary Conditions},
  author={Fabrizio Ruggeri and Zaid A Sawlan and Marco Scavino and Ra{\'u}l Tempone},
  journal={Bayesian Analysis},
  year={2017},
  volume={12},
  pages={407-433}
}
In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial dierential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution eld subject to Gaussian noise. Given Gaussian priors for the time-dependent Dirichlet boundary values, we analytically… 
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