## Landscapes of Finite Information

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## Abstract

We propose a novel principle of statistical inference motivated by information theory. In particular, we argue that if the statistician believes, as we do, that the essence of statistical inference is the compression of data, then the domain of statistical enquiry is fundamentally limited to those probability distributions

This stands in stark contrast to what might be expected, namely a principle of finite entropy, i.e. the integrability of

If

By considering the set *En route* we give two simple proofs that there does not exist a universal source code for

Having established the centrality of