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Center for Nonlinear Studies |
Problems ranging from Climate Modelling and Prediction, Brain Machine Interfaces, Attitude Control of Satellites can be formulated as Bayesian Inference Problems where the physical system is described by a Stochastic Differential Equation forced by a scaled Brownian motion or Poisson, Point Process. Information about the full state of the system is usually not available but some noisy nonlinear function of the state is available. In Climate change science only some coarse grained observations of functions such as statistical information on temperature, information on greenhouse gases or large scale horizontal winds are available . In problems of Brain Machine interface it is required to infer functions such as predicting arm movements from an ensemble of temporal neural signals . In this talk I give a variational and information‐theoretic interpretation of the Bayes formula . This is related to the description of the state of a statistical mechanical system as the state which minimizes the Free Energy . In the limiting case, infinite volume limit, this leads to the characterization of translation Invariant Gibbs Measure as a limit Free Energy Minimization problem, Lanford Ruelle Theorem. By analogy , Shannon’s Noisy Channel Coding Theorem has an interpretation as a limiting Free Energy Minimization Problem . Joint work with Nigel Newton , University of Essex
Host: Frank Alexander