Bayesian data analysis: Difference between revisions

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The goal of [[:Wikipedia:Bayesian inference|Bayesian]]
The goal of [[:Wikipedia:Bayesian inference|Bayesian]]
<ref>D.S. Sivia, ''Data Analysis: A Bayesian Tutorial'', Oxford University Press, USA (1996) ISBN 0198518897</ref>
<ref>D.S. Sivia, ''Data Analysis: A Bayesian Tutorial'', Oxford University Press, USA (1996) ISBN 0198518897</ref>
or integrated data analysis is to combine the information from a set of diagnostics providing complementary information in order to recover the best possible reconstruction of the actual state of the system subjected to measurement.
<ref>P. Gregory, ''Bayesian Logical Data Analysis for the Physical Sciences'', Cambridge University Press, Cambridge (2005) ISBN 052184150X</ref>
<ref>[http://link.aip.org/link/?RSINAK/75/4237/1 R. Fischer, A. Dinklage, ''Integrated data analysis of fusion diagnostics by means of the Bayesian probability theory'', Rev. Sci. Instrum. '''75''' (2004) 4237]</ref><ref>[http://dx.doi.org/10.1109/WISP.2007.4447579 J. Svensson, A. Werner, ''Large Scale Bayesian Data Analysis for Nuclear Fusion Experiments'', IEEE International Symposium on Intelligent Signal Processing (2007) 1]</ref>
or integrated data analysis (IDA) is to combine the information from a set of diagnostics providing complementary information in order to recover the best possible reconstruction of the actual state of the system subjected to measurement.
Like [[Function parametrization]], this technique requires having a model to predict the measurement readings for any given state of the physical system; however, the handling of error propagation is more sophisticated with the Bayesian method, and additionally, it provides a systematic way to include prior knowledge into the analysis.
<ref>[http://dx.doi.org/10.1088/0741-3335/44/8/306 R. Fischer, C. Wendland, A. Dinklage, et al, '' Thomson scattering analysis with the Bayesian probability theory'', Plasma Phys. Control. Fusion '''44''' (2002) 1501]</ref>
<ref>[http://dx.doi.org/10.1088/0741-3335/45/7/304 R. Fischer, A. Dinklage, and E. Pasch, ''Bayesian modelling of fusion diagnostics'', Plasma Phys. Control. Fusion '''45''' (2003) 1095-1111]</ref>
<ref>[http://dx.doi.org/10.1088/0741-3335/45/7/304 R. Fischer, A. Dinklage, and E. Pasch, ''Bayesian modelling of fusion diagnostics'', Plasma Phys. Control. Fusion '''45''' (2003) 1095-1111]</ref>
<ref>[http://link.aip.org/link/?RSINAK/75/4237/1 R. Fischer, A. Dinklage, ''Integrated data analysis of fusion diagnostics by means of the Bayesian probability theory'', Rev. Sci. Instrum. '''75''' (2004) 4237]</ref>
<ref>[http://www.new.ans.org/pubs/journals/fst/a_575 A. Dinklage, R. Fischer, and J. Svensson, ''Topics and Methods for Data Validation by Means of Bayesian Probability Theory'', Fusion Sci. Technol. '''46''' (2004) 355]</ref>
<ref>[http://dx.doi.org/10.1109/WISP.2007.4447579 J. Svensson, A. Werner, ''Large Scale Bayesian Data Analysis for Nuclear Fusion Experiments'', IEEE International Symposium on Intelligent Signal Processing (2007) 1]</ref>
<ref>[http://www.new.ans.org/pubs/journals/fst/a_10892 R. Fischer, C.J. Fuchs, B. Kurzan, et al., ''Integrated Data Analysis of Profile Diagnostics at ASDEX Upgrade'', Fusion Sci. Technol. '''58''' (2010) 675]</ref>
Like [[Function parametrization]] (FP), this technique requires having a ''forward model'' to predict the measurement readings for any given state of the physical system; however 
* instead of computing an estimate of the inverse of the forward model (as with FP), IDA finds the best model state corresponding to a specific measurement by a maximization procedure (maximization of the likelihood);
* the handling of error propagation is more sophisticated within IDA, allowing non-Gaussian error distributions and absolutely general parameter interdependencies; and
* additionally, it provides a systematic way to include prior knowledge into the analysis.


== See also ==
== See also ==

Revision as of 11:01, 20 November 2010

The goal of Bayesian [1] [2] or integrated data analysis (IDA) is to combine the information from a set of diagnostics providing complementary information in order to recover the best possible reconstruction of the actual state of the system subjected to measurement. [3] [4] [5] [6] [7] [8] Like Function parametrization (FP), this technique requires having a forward model to predict the measurement readings for any given state of the physical system; however

  • instead of computing an estimate of the inverse of the forward model (as with FP), IDA finds the best model state corresponding to a specific measurement by a maximization procedure (maximization of the likelihood);
  • the handling of error propagation is more sophisticated within IDA, allowing non-Gaussian error distributions and absolutely general parameter interdependencies; and
  • additionally, it provides a systematic way to include prior knowledge into the analysis.

See also

References

  1. ↑ D.S. Sivia, Data Analysis: A Bayesian Tutorial, Oxford University Press, USA (1996) ISBN 0198518897
  2. ↑ P. Gregory, Bayesian Logical Data Analysis for the Physical Sciences, Cambridge University Press, Cambridge (2005) ISBN 052184150X
  3. ↑ R. Fischer, C. Wendland, A. Dinklage, et al, Thomson scattering analysis with the Bayesian probability theory, Plasma Phys. Control. Fusion 44 (2002) 1501
  4. ↑ R. Fischer, A. Dinklage, and E. Pasch, Bayesian modelling of fusion diagnostics, Plasma Phys. Control. Fusion 45 (2003) 1095-1111
  5. ↑ R. Fischer, A. Dinklage, Integrated data analysis of fusion diagnostics by means of the Bayesian probability theory, Rev. Sci. Instrum. 75 (2004) 4237
  6. ↑ A. Dinklage, R. Fischer, and J. Svensson, Topics and Methods for Data Validation by Means of Bayesian Probability Theory, Fusion Sci. Technol. 46 (2004) 355
  7. ↑ J. Svensson, A. Werner, Large Scale Bayesian Data Analysis for Nuclear Fusion Experiments, IEEE International Symposium on Intelligent Signal Processing (2007) 1
  8. ↑ R. Fischer, C.J. Fuchs, B. Kurzan, et al., Integrated Data Analysis of Profile Diagnostics at ASDEX Upgrade, Fusion Sci. Technol. 58 (2010) 675
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