Supporting Automatic Differentiation in CMS Combine profile likelihood scans

One common task in data analysis is the determination of model parameters in order to describe a given dataset.
This can be done in various ways, one of which is the discrete profiling method, which was developed as part of the
analysis of data at the CMS experiment. In essence, the discrete profiling method is a generalization of the profile
likelihood method: while the latter handles continuous nuisance parameters by profiling over them, the former extends
the approach to also include discrete parameters that switch between different candidate models. However, datasets
are continually growing in size and the number of parameters increases, thus making statistical analysis computa-
tionally expensive. Implementation of Automatic Differentiation (AD) would significantly reduce the computational
cost of discrete profiling, thus enabling a more efficient data analysis. In the following summer student report, a
documentation of the discrete profiling method is provided along with a report on the work done in order to support
AD in Combine—the main software for statistical analysis used in the CMS experiment.