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 ==

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