Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalizations related to hypothesis testing with the Posterior
  distribution of the Likelihood Ratio   The Posterior distribution of the Likelihood Ratio (PLR) is proposed by
Dempster in 1974 for significance testing in the simple vs composite hypotheses
case. In this hypotheses test case, classical frequentist and Bayesian
hypotheses tests are irreconcilable, as emphasized by Lindley's paradox, Berger
& Selke in 1987 and many others. However, Dempster shows that the PLR (with
inner threshold 1) is equal to the frequentist p-value in the simple Gaussian
case. In 1997, Aitkin extends this result by adding a nuisance parameter and
showing its asymptotic validity under more general distributions. Here we
extend the reconciliation between the PLR and a frequentist p-value for a
finite sample, through a framework analogous to the Stein's theorem frame in
which a credible (Bayesian) domain is equal to a confidence (frequentist)
domain.
  This general reconciliation result only concerns simple vs composite
hypotheses testing. The measures proposed by Aitkin in 2010 and Evans in 1997
have interesting properties and extend Dempster's PLR but only by adding a
nuisance parameter. Here we propose two extensions of the PLR concept to the
general composite vs composite hypotheses test. The first extension can be
defined for improper priors as soon as the posterior is proper. The second
extension appears from a new Bayesian-type Neyman-Pearson lemma and emphasizes,
from a Bayesian perspective, the role of the LR as a discrepancy variable for
hypothesis testing.

12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math