Statistical inference under multiterminal rate restrictions: a differential geometric approach

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Abstract
A statistical inference problem for a two-terminal information source emitting mutually correlated signals X and Y is treated. Let sequences Xn and Yn of n independent observations be encoded independently of each other into message sets MX and MY at rates R1 and R 2 per letter, respectively. This compression causes a loss of the statistical information available for testing hypotheses concerning X and Y. The loss of statistical information is evaluated as a function of the amounts R1 and R 2 of the Shannon information. A complete solution is given in the case of asymptotically complete data compression, R1, R2→0 as n→∞. It is shown that the differential geometry of the manifold of all probability distributions plays a fundamental role in this type of multiterminal problem connecting Shannon information and statistical information. A brief introduction to the dually coupled e-affine and m-affine connections together with e -flatness and m-flatness is given

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