The Linear-Gaussian Setting
Daniel Sanz-Alonso, Andrew M. Stuart, Armeen Taeb · Cambridge University Press eBooks · 2023
In this chapter we study the linear-Gaussian setting, where the forward model (·)is linear and both the prior on 𝑢 and the distribution of the observation noise 𝜂 are Gaussian. This setting is highly amenable to analysis and arises frequently in applications. Moreover, as we will see throughout these notes, many methods employed in nonlinear or non-Gaussian settings build on ideas from the linear- Gaussian case by performing linearization or invoking Gaussian approximations.