This week my research group dis­cussed Adrian Raftery’s recent paper on “Use and Com­mu­ni­ca­tion of Prob­a­bilis­tic Fore­casts” which pro­vides a fas­ci­nat­ing but brief sur­vey of some of his work on mod­el­ling and com­mu­ni­cat­ing uncer­tain futures. Coin­ci­den­tally, today I was also sent a copy of David Spiegelhalter’s paper on “Visu­al­iz­ing Uncer­tainty About the Future”. Both are well-​​worth reading.

It made me think about my own efforts to com­mu­ni­cate future uncer­tainty through graph­ics. Of course, for time series fore­casts I nor­mally show pre­dic­tion inter­vals. I pre­fer to use more than one inter­val at a time because it helps con­vey a lit­tle more infor­ma­tion. The default in the fore­cast pack­age for R is to show both an 80% and a 95% inter­val like this:

It is some­times prefer­able to use a 50% and a 95% inter­val, rather like a box­plot:

In some cir­cles (espe­cially macro­eco­nomic fore­cast­ing), fan charts are pop­u­lar:

Per­son­ally, I don’t like these at all as they lose any spe­cific prob­a­bilis­tic inter­pretabil­ity. What does the darker shaded region actu­ally refer to? At least in the pre­vi­ous ver­sion, it is clear that the dark region con­tains 50% of the probability.

The above three exam­ples are eas­ily pro­duced using the fore­cast package:

For multi-​​modal dis­tri­b­u­tions I like to use high­est den­sity regions. Here is an exam­ple applied to Nicholson’s blowfly data using a thresh­old model:

The dark region has 50% cov­er­age and the light region has 95% cov­er­age. The fore­cast dis­tri­b­u­tions become bimodal after the first ten iter­a­tions, and so the 50% region is split in two to show that. This graphic was taken from a J. Fore­cast­ing paper I wrote in 1996, so these ideas have been around for a while!

It is easy enough to pro­duce fore­cast HDR with time series. Here is some R code to do it:

We can apply it using the exam­ple I started with: