Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decision-theoretic justifications for Bayesian hypothesis testing using
  credible sets   In Bayesian statistics the precise point-null hypothesis $\theta=\theta_0$
can be tested by checking whether $\theta_0$ is contained in a credible set.
This permits testing of $\theta=\theta_0$ without having to put prior
probabilities on the hypotheses. While such inversions of credible sets have a
long history in Bayesian inference, they have been criticised for lacking
decision-theoretic justification.
  We argue that these tests have many advantages over the standard Bayesian
tests that use point-mass probabilities on the null hypothesis. We present a
decision-theoretic justification for the inversion of central credible
intervals, and in a special case HPD sets, by studying a three-decision problem
with directional conclusions. Interpreting the loss function used in the
justification, we discuss when test based on credible sets are applicable.
  We then give some justifications for using credible sets when testing
composite hypotheses, showing that tests based on credible sets coincide with
standard tests in this setting.

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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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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: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn