Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian Posteriors Without Bayes' Theorem   The classical Bayesian posterior arises naturally as the unique solution of
several different optimization problems, without the necessity of interpreting
data as conditional probabilities and then using Bayes' Theorem. For example,
the classical Bayesian posterior is the unique posterior that minimizes the
loss of Shannon information in combining the prior and the likelihood
distributions. These results, direct corollaries of recent results about
conflations of probability distributions, reinforce the use of Bayesian
posteriors, and may help partially reconcile some of the differences between
classical and Bayesian statistics.

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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org