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Bayesian data analysis: Difference between revisions
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<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://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> | <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> | ||
<ref>B.Ph. van Milligen, T. Estrada, E. Ascasíbar, et al, ''Integrated data analysis at TJ-II: the density profile'', Rev. Sci. Instrum. (2011) Accepted for publication</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 | 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); | * 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 | * the handling of error propagation is more sophisticated within IDA, allowing non-Gaussian error distributions and absolutely general and complex parameter interdependencies; and | ||
* additionally, it provides a systematic way to include prior knowledge into the analysis. | * additionally, it provides a systematic way to include prior knowledge into the analysis. | ||
The maximization process is CPU intensive, so that Bayesian analysis is not suited for real-time data analysis (unlike FP). | |||
== Bayes' Theorem == | == Bayes' Theorem == | ||