Field Dynamics Inference for Local and Causal Interactions

@article{Frank2019FieldDI,
  title={Field Dynamics Inference for Local and Causal Interactions},
  author={Philipp Frank and Reimar H. Leike and Torsten A. Ensslin},
  journal={Annalen der Physik},
  year={2019},
  volume={533}
}
Inference of fields defined in space and time from observational data is a core discipline in many scientific areas. This work approaches the problem in a Bayesian framework. The proposed method is based on statistically homogeneous random fields defined in space and time and demonstrates how to reconstruct the field together with its prior correlation structure from data. The prior model of the correlation structure is described in a non‐parametric fashion and solely builds on fundamental… 
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References

SHOWING 1-10 OF 31 REFERENCES
Field dynamics inference via spectral density estimation.
TLDR
This work describes how the underlying laws of a stochastic process can be approximated by the spectral density of the corresponding process and shows how the density can be inferred from possibly very noisy and incomplete measurements of the dynamical field.
Information Theory for Fields
  • T. Ensslin
  • Computer Science, Physics
    Annalen der Physik
  • 2019
TLDR
Information field theory is built upon the language of mathematical physics, in particular, on field theory and statistical mechanics and permits the mathematical derivation of optimal imaging algorithms, data analysis methods, and even computer simulation schemes.
Reconstruction of Gaussian and log-normal fields with spectral smoothness
TLDR
It is shown that the minimization of the Gibbs free energy, corresponding to a Gaussian approximation to the posterior marginalized over the power spectrum, is equivalent to the empirical Bayes ansatz, in which the power Spectrum is fixed to its maximum a posteriori value.
MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster
TLDR
An approach to modifying a whole range of MCMC methods, applicable whenever the target measure has density with respect to a Gaussian process or Gaussian random field reference measure, which ensures that their speed of convergence is robust under mesh refinement.
Inverse problems: A Bayesian perspective
TLDR
The Bayesian approach to regularization is reviewed, developing a function space viewpoint on the subject, which allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion.
A step towards holistic discretisation of stochastic partial differential equations
The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply
Discretization-invariant Bayesian inversion and Besov space priors
Bayesian solution of an inverse problem for indirect measurement $M = AU + {\mathcal{E}}$ is considered, where $U$ is a function on a domain of $R^d$. Here $A$ is a smoothing linear operator and $
Handbook of Markov Chain Monte Carlo
TLDR
A Markov chain Monte Carlo based analysis of a multilevel model for functional MRI data and its applications in environmental epidemiology, educational research, and fisheries science are studied.
Time-discretised Galerkin approximations of parabolic stochastic PDE's
The global discretisation error is estimated for strong time discretisations of finite dimensional Ito stochastic differential equations (SDEs) which are Galerkin approximations of a class of
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