This chapter discusses the features that are characteristic for the problems most typically treated under the umbrella of inverse problems. It begins by listing representative examples of inverse problems followed by a discussion of the key mathematical property of ill-posedness. It then discusses deterministic and regularization methods, and presents some history of Bayesian analysis, as viewed from physics. Next, it provides the framework for current methodology and describes some of the recent advances in Markov chain Monte Carlo (MCMC) algorithms. The chapter concludes with a glimpse of future directions.
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