Bayesian data analysis
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The goal of Bayesian <ref>D.S. Sivia, Data Analysis: A Bayesian Tutorial, Oxford University Press, USA (1996) ISBN 0198518897</ref> <ref>P. Gregory, Bayesian Logical Data Analysis for the Physical Sciences, Cambridge University Press, Cambridge (2005) ISBN 052184150X</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. <ref>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>R. Fischer, A. Dinklage, and E. Pasch, Bayesian modelling of fusion diagnostics, Plasma Phys. Control. Fusion 45 (2003) 1095-1111</ref> <ref>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>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>J. Svensson, A. Werner, Large Scale Bayesian Data Analysis for Nuclear Fusion Experiments, IEEE International Symposium on Intelligent Signal Processing (2007) 1</ref> <ref>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
References
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