Posterior convergence for approximated unknowns in non-Gaussian statistical inverse problems

摘要: The statistical inverse problem of estimating the probability distribution an infinite-dimensional unknown given its noisy indirect observation is studied in Bayesian framework. In practice, one often considers only finite-dimensional unknowns and investigates numerically their probabilities. As many are function-valued, it interest to know whether estimated probabilities converge when approximations refined. this work, generalized Bayes formula shown be a powerful tool convergence studies. With help formula, question posterior distributions returned (or any other) unknown. approach allows prior while restrictions mainly for noise model direct theory. Three modes considered -- weak convergence, setwise variation. conditional mean estimates studied. Several examples applicable non-Gaussian models provided, including generalization Cameron-Martin certain measures. Also, well-posedness problems