 Bayesian inverse problem

ID: bayesian-inverse-problem

A Bayesian inverse problem combines a prior measure

μ_{0}

on an unknown

u

with a likelihood for observed data

y

. When the likelihood is proportional to

e^{- Φ (u; y)}

, Bayes' formula gives

\frac{d μ ^{y}}{d μ _{0}} (u) = \frac{1}{Z ( y )} e^{- Φ (u; y)} .

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