Detection of extensive air showers with radio antennas is an appealing technique in cosmic ray
physics. However, because of the high level of measurement noise, current reconstruction methods
still leave room for improvement. Furthermore, reconstruction efforts typically focus only on a
single aspect of the signal, such as the energy fluence or arrival time. Bayesian inference is then a
natural choice for a holistic approach to reconstruction, yet, this problem would be ill-posed, since
the electric field is a continuous quantity. Information Field Theory provides the solution for this
by providing a statistical framework to deal with discretised fields in the continuum limit.
We are currently developing models for this novel approach to reconstructing extensive air showers.
The model described here is based on the best current understanding of the emission mechanisms:
It uses parametrisations of the lateral signal strength distribution, charge-excess contribution and
spectral shape. Shower-to-shower fluctuations and narrowband RFI are modelled using Gaussian
processes. Combined with a detailed detector description, this model can infer not only the electric
field, but also the shower geometry, electromagnetic energy and position of shower maximum.
Another big achievement of this approach is its ability to naturally provide uncertainties for the
reconstruction, which has been shown to be difficult in more traditional methods. With such an
open framework and robust computational methods based in Information Field Theory, it will also
be easy to incorporate new insights and additional data, such as timing distributions or particle
detector data, in the future. This approach has a high potential to exploit the full information
content of a complex detector with rigorous statistical methods, in a way that directly includes
domain knowledge.