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Bayesian data analysis: Difference between revisions
→Parametric formulation
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:<math>p(\alpha|D) = \frac{p(D|\alpha)p(\alpha)}{p(D)}</math> | :<math>p(\alpha|D) = \frac{p(D|\alpha)p(\alpha)}{p(D)}</math> | ||
where ''D'' represents the available data. | where ''D'' represents the available data. | ||
The likelihood ''p(D|α)'' | The likelihood ''p(D|α)'' specifies the probability of a specific measurement outcome ''D'' for a given choice of parameters ''α''. | ||
The advantage of the parametric representation is that the abstract 'system state' is reduced to a finite set of parameters, greatly facilitating numerical analysis. | The advantage of the parametric representation is that the abstract 'system state' is reduced to a finite set of parameters, greatly facilitating numerical analysis. | ||
This parametrization may involve, e.g., smooth (orthogonal) expansion functions such as [[:Wikipedia:Fourier-Bessel_series|Fourier-Bessel functions]], or discretely defined functionals on a grid. | |||
<ref>[[doi:10.1088/0741-3335/50/8/085002|J. Svensson et al, ''Current tomography for axisymmetric plasmas'', Plasma Phys. Control. Fusion '''50''' (2008) 085002</ref> | |||
=== Maximization === | === Maximization === | ||