Bayesian data analysis: Difference between revisions

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 The goal of [[:Wikipedia:Bayesian inference|Bayesian]]
 <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://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 ==