Abstract
Imagine you need to navigate through a completely dark cave. A wellknown way of achieving this is echolocation, which works by making sounds and listening to how they are reflected back. The problem of determining the geometric shape of a space from a mixture of reflections of emitted sounds, is an example of an inverse problem. In many fields of science, there are situations where it is impossible to measure a parameter of interest directly and instead, the only available method is to measure a different object that is affected by the parameter of interest. These statistical problems can become challenging when it is difficult, or even impossible, to invert the observations directly into the parameter that one is interested in.
In many cases, a statistician has a belief about the true value of the parameter before even starting the experiment. The Bayesian paradigm is an attractive method of combining the new information coming from observations with this prior belief. It gives a sound mechanism, namely the posterior distribution, to update the beliefs about the truth.
In many cases, a statistician has a belief about the true value of the parameter before even starting the experiment. The Bayesian paradigm is an attractive method of combining the new information coming from observations with this prior belief. It gives a sound mechanism, namely the posterior distribution, to update the beliefs about the truth.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  5 Dec 2023 
DOIs  
Publication status  Published  2023 
Keywords
 Statistics
 Bayesian
 Inverse Problems
 Posterior contraction rate
 Bernstein–von Mises theorems
 Distributed methods
 Asymptotics
 Misspecification