Bayesian inverse problem
= Bayesian inverse problem
{wiki}
A Bayesian inverse problem combines a prior measure $\mu_0$ on an unknown $u$ with a likelihood for observed data $y$. When the likelihood is proportional to $e^{-\Phi(u;y)}$, Bayes' formula gives
$$
\frac{d\mu^y}{d\mu_0}(u)=\frac1{Z(y)}e^{-\Phi(u;y)}.
$$