Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A robust Bayesian approach to modelling epistemic uncertainty in
  common-cause failure models   In a standard Bayesian approach to the alpha-factor model for common-cause
failure, a precise Dirichlet prior distribution models epistemic uncertainty in
the alpha-factors. This Dirichlet prior is then updated with observed data to
obtain a posterior distribution, which forms the basis for further inferences.
  In this paper, we adapt the imprecise Dirichlet model of Walley to represent
epistemic uncertainty in the alpha-factors. In this approach, epistemic
uncertainty is expressed more cautiously via lower and upper expectations for
each alpha-factor, along with a learning parameter which determines how quickly
the model learns from observed data. For this application, we focus on
elicitation of the learning parameter, and find that values in the range of 1
to 10 seem reasonable. The approach is compared with Kelly and Atwood's
minimally informative Dirichlet prior for the alpha-factor model, which
incorporated precise mean values for the alpha-factors, but which was otherwise
quite diffuse.
  Next, we explore the use of a set of Gamma priors to model epistemic
uncertainty in the marginal failure rate, expressed via a lower and upper
expectation for this rate, again along with a learning parameter. As zero
counts are generally less of an issue here, we find that the choice of this
learning parameter is less crucial.
  Finally, we demonstrate how both epistemic uncertainty models can be combined
to arrive at lower and upper expectations for all common-cause failure rates.
Thereby, we effectively provide a full sensitivity analysis of common-cause
failure rates, properly reflecting epistemic uncertainty of the analyst on all
levels of the common-cause failure model.

11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph