A Variational Approach to Nonlinear Estimation

@article{Mitter2003AVA,
  title={A Variational Approach to Nonlinear Estimation},
  author={Sanjoy K. Mitter and Nigel J. Newton},
  journal={SIAM J. Control and Optimization},
  year={2003},
  volume={42},
  pages={1813-1833}
}
We consider estimation problems, in which the estimand, X, and observation, Y , take values in measurable spaces. Regular conditional versions of the forward and inverse Bayes formula have variational characterisations involving the minimisation of an apparent information, and the maximisation of a compatible information. These both have natural information theoretic interpretations, according to which Bayes’ formula and its inverse are optimal information processors. The variational… CONTINUE READING

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