Non-Gaussian statistical inverse problems. II: Posterior convergence for approximated unknowns (Q435840)

[For the review of part I of this paper see ibid., 215--266 (2012; Zbl 1263.62041).]NEWLINENEWLINE As announced in part I, the paper addresses the following question: (iii) Convergence of posterior distributions and posterior means for approximated unknowns. Especially finding conditions that guarantee the convergence of the posterior distributions when the corresponding approximated prior distributions converge.NEWLINENEWLINE It is of interest to know whether the estimated probabilities converge when the finite-dimensional approximations are refined. The use of a generalized Bayesian formula allows to turn the question of the convergence of the posterior distributions to that of the convergence of the finite-dimensional approximations. The author investigates three modes of convergence: weak, setwise and convergence in variation.