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Information theory for fields

A physical field has an infinite number of degrees of freedom since it has a field value at each location of a continuous space. Therefore, it is impossible to know a field from finite measurements alone and prior information on the field is essential for field inference. An information theory for fields is needed to join the measurement and prior information into probabilistic statements on field configurations. Such an information field theory (IFT) is built upon the language of mathematical physics, in particular on field theory and statistical mechanics. IFT permits the mathematical derivation of optimal imaging algorithms, data analysis methods, and even computer simulation schemes. The application of IFT algorithms to astronomical datasets provides high fidelity images of the Universe and facilitates the search for subtle statistical signals from the Big Bang. The concepts of IFT might even pave the road to novel computer simulations that are aware of their own uncertainties.