Bayesian approach to inverse problems
Joint probability distribution function (pdf): p(x,y)
- Associated marginal probability densities
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A priori pdf P(x): probability of x=xt
- Example: the Gaussian case in which we know the error covariance and we have xb as the only realization of x.
- The variable x in normally distributed with mean xb and covariance B
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In absence of any other information, x = xb is the most probable state (maximum likelihood)