Discontinuity Bayesian Forecasting

I’m finalizing a paper presentation for the ABCP meeting, where I explore poor polling forecast in local elections in Brazil. I drew upon the Jackman (2005)’s paper “Pooling the Polls” to explore a bit about “house effects” in the Brazilian context. However, during the analysis I found myself extending his original model to fit the local election in Sao Paulo.
In Brazil, political parties have incentives for canvassing free of charge in the aired media (radio and TV). The whole point is that this thing sometimes produces drastic changes to the vote distribution in a short period of time, so we can’t simply apply a Bayesian linear model because that would break up some linearity assumptions.
In order to account for the advertising effect on the popular support, therefore, I had to develop a Bayesian model, where the transition component–the random walk–breaks at the last poll before the ads season began, and restarting with the first poll after it. The following chart says more about the problem. The black spots are the observed polls by the major pollsters.

Over 58 weeks before the ads season began, the Workers’s Party candidate, Fernando Haddad, showed a weekly growth rate of 2.6%, but in the 5 weeks next to the beginning of the political advertising on radio and television, the same rate jumped to 9.46%. To put it simple, whiting a week of media exposition made his popular support increase in more than 5%; it is more than he could achieve in one year of “informal campaigning”.