At Channel 4 we use ratings forecasts to help advertisers who work with us to reach the right audience. To provide forecasts that respond to the changing tastes and trends in television, we explore general methods of mixed effects modelling and Bayesian filtering which will be of interest to data scientists and researchers from a range of industries.
The use of a random effects model allows us to capture the inherent appeal of a programme, which is not described by predictors such as time and genre. However, as we will illustrate, the ratings of an individual programme often drift slowly, or shift suddenly, up or down. Consequently, the random effects parameters should be treated as time varying. This can be achieved by inclusion of a fixed ‘forgetting factor’ to down-weight older data. This concept is central to the popular recursive least squares algorithm. Similarly, with Bayesian forgetting the posterior is most effected by more recent data. In both cases there is little principled guidance for tuning the forgetting factor, and being fixed means sudden parameter changes are hard to deal with. Recent developments in the field suggest algorithms for Bayesian estimation of a time varying forgetting factor which is appropriate for tracking rapidly changing parameters.
Without dwelling on derivations, we will discuss: