Information Theory for Fields by Torsten Enslin in 2019
1.1 Aim
1.2 Structure of the work
- In this Sect. 1, the problem of field inference is approached with Bayesian probability theory.
- In Sect. 2, the free theory of IFT is developed using an illustrative example of a diffusion process driven by white noise and observed at some point in time.
- In Sect. 3, this is then extended into the non-linear regime, leading to interacting IFT in wich the field estimate is not a linear function of the data any more.
- Sect. 4 IFT algorithms and their numerical implementation.
- Sect. 5 future developments in IFT
1.3 Physical fields
1.4 Smoothness and correlations
1.5 Bayes and statistical physics
1.6 Expectation values
1.7 Maximum entropy
1.8 Infinities
2. Free fields
2.1 Simplistic scenario
2.2 Prior regularization
2.3 Wiener filter
2.4 Generalized Wiener filter
2.6 Maximum likelihood
2.7 Optimal estimate
2.8 Critical filter
3. Interacting fields
3.1 Classical field approximation
3.2 Comparison to other estimators
- 3.2.2 Hamiltonian Monte Carlo for fields
3.3 Mean field approximation
3.5 Kullbach-Leibler sampling
4. Applications
4.2 Photon imaging
4.3 Available IFT algorithms
4.4 Non-Gaussianity
5. Outlook