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Published online by Cambridge University Press: 27 July 2023
In this chapter we explore the properties of Bayesian inversion from the perspective of an optimization problem which corresponds to maximizing the posterior probability; that is, to finding a maximum a posteriori (MAP) estimator, or mode of the posterior distribution. We demonstrate the properties of the point estimator resulting from this optimization problem, showing its positive and negative attributes, the latter motivating our work in the following three chapters. We also introduce, and study, basic gradient-based optimization algorithms.
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