Bayesian Recovery of the Initial Condition for the Heat Equation

@article{Knapik2013BayesianRO,
  title={Bayesian Recovery of the Initial Condition for the Heat Equation},
  author={Bartek Knapik and Aad van der Vaart and John H van Zanten},
  journal={Communications in Statistics - Theory and Methods},
  year={2013},
  volume={42},
  pages={1294 - 1313}
}
We study a Bayesian approach to recovering the initial condition for the heat equation from noisy observations of the solution at a later time. We consider a class of prior distributions indexed by a parameter quantifying “smoothness” and show that the corresponding posterior distributions contract around the true parameter at a rate that depends on the smoothness of the true initial condition and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the… 

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