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This math is far above me, but I get a feeling like there's some relationship between the Fisher Information Metric and Kalman Filters. I think I'll take another look later tonight


Often in the information-theoretic statistical literature these topics are discussed under the umbrella of prequential coding or inference.

E.g., in this text:

https://www.google.com/books/edition/The_Minimum_Description...


Are you maybe referring to the alternative formulation described in [1]?

[1] https://en.wikipedia.org/wiki/Kalman_filter#Information_filt...




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