Joint likelihood

Sometimes we may wish to analyse multiple datasets simultaneously. For example, we may have two datasets, each containing a set of light curves that for whatever reason are expected to share parameters. In this case, we may wish to fit the two datasets simultaneously, so that the shared parameters are constrained by both datasets. We note that the datasets must be independent, i.e. they must not share any data. Of course this can be extended to arbitrarily many datasets.

A classic example, which is common in this field is analysing EM data alongside GW data for a binary neutron star merger. Thanks to the interface with bilby this is easily achievable with :code`bilby` doing the gravitational-wave part of the analysis and redback doing the EM part of the analysis.

We provide a simplified example of jointly fitting an afterglow and the gravitational waves from a binary neutron star merger in the examples. We note that this framework can also be used to jointly analyse multiple data types from the same source, for example, the optical photometry of a kilonova and a radio afterglow.

We note that in the practice, this is often done with a single likelihood by approximating the magnitude data as a flux density.