GK
G.J. Koers
info
Please Note
<p>This page displays the records of the person named above and is not linked to a unique person identifier. This record may need to be merged to a profile.</p>
2 records found
1
We derive a Bernstein–von Mises theorem in the context of misspecified, non-i.i.d., hierarchical models parametrised by a finite-dimensional parameter of interest. We apply our results to hierarchical models containing non-linear operators, including the squared integral operator, and PDE-constrained inverse problems. More specifically, we consider the elliptic, time-independent Schrödinger equation with parametric boundary condition and general parabolic PDEs with parametric potential and boundary constraints. Our theoretical results are com-plemented with a numerical analysis of synthetic data sets, considering both the square integral operator and the Schrödinger equation.
...
We derive a Bernstein–von Mises theorem in the context of misspecified, non-i.i.d., hierarchical models parametrised by a finite-dimensional parameter of interest. We apply our results to hierarchical models containing non-linear operators, including the squared integral operator, and PDE-constrained inverse problems. More specifically, we consider the elliptic, time-independent Schrödinger equation with parametric boundary condition and general parabolic PDEs with parametric potential and boundary constraints. Our theoretical results are com-plemented with a numerical analysis of synthetic data sets, considering both the square integral operator and the Schrödinger equation.
Imagine you need to navigate through a completely dark cave. A well-known 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.
...
Imagine you need to navigate through a completely dark cave. A well-known 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.