Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian Methods for Parameter Estimation in Effective Field Theories   We demonstrate and explicate Bayesian methods for fitting the parameters that
encode the impact of short-distance physics on observables in effective field
theories (EFTs). We use Bayes' theorem together with the principle of maximum
entropy to account for the prior information that these parameters should be
natural, i.e.O(1) in appropriate units. Marginalization can then be employed to
integrate the resulting probability density function (pdf) over the EFT
parameters that are not of specific interest in the fit. We also explore
marginalization over the order of the EFT calculation, M, and over the
variable, R, that encodes the inherent ambiguity in the notion that these
parameters are O(1). This results in a very general formula for the pdf of the
EFT parameters of interest given a data set, D. We use this formula and the
simpler "augmented chi-squared" in a toy problem for which we generate
pseudo-data. These Bayesian methods, when used in combination with the
"naturalness prior", facilitate reliable extractions of EFT parameters in cases
where chi-squared methods are ambiguous at best. We also examine the problem of
extracting the nucleon mass in the chiral limit, M_0, and the nucleon sigma
term, from pseudo-data on the nucleon mass as a function of the pion mass. We
find that Bayesian techniques can provide reliable information on M_0, even if
some of the data points used for the extraction lie outside the region of
applicability of the EFT.

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The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
1
The categories of this paper are: cs