Error Estimates of Theoretical Models: a Guide - INSPIRE

DataBETA

Error Estimates of Theoretical Models: a Guide

Feb 19, 2014

20 pages

Published in:

J.Phys.G 41 (2014) 074001

Published: 2014

e-Print:

1402.4657 [nucl-th]

DOI:

10.1088/0954-3899/41/7/074001

Report number:

INT-PUB-14-004

View in:

ADS Abstract Service

reference search261 citations

Citations per year

Abstract: (arXiv)

This guide offers suggestions/insights on uncertainty quantification of nuclear structure models. We discuss a simple approach to statistical error estimates, strategies to assess systematic errors, and show how to uncover inter-dependencies by correlation analysis. The basic concepts are illustrated through simple examples. By providing theoretical error bars on predicted quantities and using statistical methods to study correlations between observables, theory can significantly enhance the feedback between experiment and nuclear modeling.

Note:

24 pages, 9 figures, submitted to Journal of Physics G

nuclear models
error estimates
error propagation
uncertainty quantification
systematic and statistical errors
correlation analysis
model-based extrapolations
regression analysis

References(50)

Figures(9)

[1]

Empirical Model Building and Response Surfaces. John & Sons, New York, 1987

G.E.P. Box
,
N.R. Draper

[2]

The Editors. Editorial: Uncertainty estimates

- Phys.Rev.A 83 (2011) 040001

[3]

Data Reduction and Error Analysis for the Physical Sciences 2003

P.R. Bevington
,
D.K. Robinson

[4]

Statistical and computational methods in data analysis New York, 1997

S. Brandt

[5]

When all models are wrong. Issues in Science and Technology, Fall 2013:79, 2013

A. Saltelli
,
S. Funtowicz

[6]

Inverse problem theory and methods for model parameter estimation Philadelphia, 2005

A. Tarantola

[7]

Error analysis of nuclear mass fits

J. Toivanen
(
- Jyvaskyla U.
)
,
J. Dobaczewski
(
- Jyvaskyla U. and
- Warsaw U.
)
,
M. Kortelainen
(
- Jyvaskyla U.
)
,
K. Mizuyama
(
- Jyvaskyla U.
)

- Phys.Rev.C 78 (2008) 034306
•
e-Print:
- 0806.1914
•
DOI:
- 10.1103/PhysRevC.78.034306

[8]

The Equation of State from Observed Masses and Radii of Neutron Stars

- Astrophys.J. 722 (2010) 33-54
•
e-Print:
- 1005.0811
•
DOI:
- 10.1088/0004-637X/722/1/33

[9]

Statistical approaches for combining model runs with experimental data. 2013. Presentation at ISNET Meeting 2013, Glasgow

D. Higdon

[9]

- http://indico.cern.ch/event/253381/

[10]

Bayesian inference and nuclear structure models. 2013. Presentation at ISNET Meeting 2013, Glasgow

B. Szpak

[10]

- http://indico.cern.ch/event/253381/

[11]

Information content of the weak-charge form factor

P.-G. Reinhard
(
- Erlangen - Nuremberg U., Theorie III
)
,
J. Piekarewicz
(
- Florida State U.
)
,
W. Nazarewicz
(
- Tennessee U. and
- Oak Ridge and
- Warsaw U.
)
,
B.K. Agrawal
(
- Saha Inst.
)
,
N. Paar
(
- Zagreb U.
)

et al.

- Phys.Rev.C 88 (2013) 3, 034325
•
e-Print:
- 1308.1659
•
DOI:
- 10.1103/PhysRevC.88.034325

[12]

Propagation of uncertainties in the Skyrme energy-density-functional model

- Phys.Rev.C 87 (2013) 3, 034324
•
e-Print:
- 1301.6151
•
DOI:
- 10.1103/PhysRevC.87.034324

[13]

Neutron skin uncertainties of Skyrme energy density functionals

et al.

- Phys.Rev.C 88 (2013) 3, 031305
•
e-Print:
- 1307.4223
•
DOI:
- 10.1103/PhysRevC.88.031305

[14]

Corrections to nuclear energies and radii in finite oscillator spaces

R.J. Furnstahl
(
- Ohio State U.
)
,
G. Hagen
(
- Oak Ridge and
- Tennessee U.
)
,
T. Papenbrock
(
- Oak Ridge and
- Tennessee U.
)

- Phys.Rev.C 86 (2012) 031301
•
e-Print:
- 1207.6100
•
DOI:
- 10.1103/PhysRevC.86.031301

[15]

Nuclear ground state masses and deformations

- Atom.Data Nucl.Data Tabl. 59 (1995) 185-381
•
e-Print:
- nucl-th/9308022
•
DOI:
- 10.1006/adnd.1995.1002

[16]

Optimized Chiral Nucleon-Nucleon Interaction at Next-to-Next-to-Leading Order

et al.

- Phys.Rev.Lett. 110 (2013) 19, 192502
•
e-Print:
- 1303.4674
•
DOI:
- 10.1103/PhysRevLett.110.192502

[17]

Variations on a theme by Skyrme: A systematic study of adjustments of model parameters

P. Klupfel
(
- Erlangen - Nuremberg U.
)
,
P.-G. Reinhard
(
- Erlangen - Nuremberg U.
)
,
T.J. Burvenich
(
- Frankfurt U., FIAS
)
,
J.A. Maruhn
(
- Frankfurt U.
)

- Phys.Rev.C 79 (2009) 034310
•
e-Print:
- 0804.3385
•
DOI:
- 10.1103/PhysRevC.79.034310

[18]

Fitting theories of nuclear binding energies

G.F. Bertsch
(
- Washington U., Seattle
)
,
B. Sabbey
(
- Washington U., Seattle
)
,
M. Uusnakki
(
- Washington U., Seattle
)

- Phys.Rev.C 71 (2005) 054311
•
e-Print:
- nucl-th/0412091
•
DOI:
- 10.1103/PhysRevC.71.054311

[19]

Dependence of single-particle energies on coupling constants of the nuclear energy density functional

M. Kortelainen
(
- Jyvaskyla U.
)
,
J. Dobaczewski
(
- Jyvaskyla U. and
- Warsaw U.
)
,
K. Mizuyama
(
- Jyvaskyla U.
)
,
J. Toivanen
(
- Jyvaskyla U.
)

- Phys.Rev.C 77 (2008) 064307
•
e-Print:
- 0803.2291
•
DOI:
- 10.1103/PhysRevC.77.064307

[20]

Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization

M. Stoitsov
(
- Tennessee U. and
- Oak Ridge
)
,
M. Kortelainen
(
- Tennessee U. and
- Oak Ridge
)
,
S.K. Bogner
(
- Michigan State U., NSCL and
- Michigan State U.
)
,
T. Duguet
(
)
,
R.J. Furnstahl
(
- Ohio State U.
)

et al.

- Phys.Rev.C 82 (2010) 054307
•
e-Print:
- 1009.3452
•
DOI:
- 10.1103/PhysRevC.82.054307

[21]

Accurate calibration of relativistic mean-field models: correlating observables and providing meaningful theoretical uncertainties

F.J. Fattoyev
(
- Florida State U. and
- Tashkent, IYF
)
,
J. Piekarewicz
(
- Florida State U.
)

- Phys.Rev.C 84 (2011) 064302
•
e-Print:
- 1109.1576
•
DOI:
- 10.1103/PhysRevC.84.064302

[22]

private communication, 2013

G.F. Bertsch

[23]

From finite nuclei to the nuclear liquid drop: Leptodermous expansion based on the self-consistent mean-field theory

P.-G. Reinhard
(
- Erlangen - Nuremberg U., Theorie III and
- JIHIR, Oak Ridge
)
,
M. Bender
(
)
,
W. Nazarewicz
(
- Tennessee U. and
- Oak Ridge and
- Warsaw U.
)
,
T. Vertse
(
)

- Phys.Rev.C 73 (2006) 014309
•
e-Print:
- nucl-th/0510039
•
DOI:
- 10.1103/PhysRevC.73.014309

1-25 of 50
1
2
25 / page