Bayesian data analysis: Difference between revisions

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== Parametric formulation ==
== Parametric formulation ==


The description of the system state is usually done by defining a parametric representation, e.g., by defining spatial density or temperature profiles as a function of space via a vector of ''N'' parameters, α: ''n(r,α)'' or ''T(r,α)''.
The description of the system state is usually done by defining a parametric representation, e.g., by defining density or temperature profiles as a function of space via a vector of ''N'' parameters, α: ''n(r,α)'' or ''T(r,α)''.
The parameters obey a prior distribution ''p(α)'', expressing physical or other constraints.
The parameters obey a prior distribution ''p(α)'', expressing physical or other constraints.
Applying Bayes theorem one obtains
Applying Bayes theorem one obtains

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