The Gaussian process summer schools have emerged from a long history of organization of Gaussian process meetings by the Sheffield group. These include the Gaussian Process Round Table and the Gaussian Processes in Practice workshops.
The Gaussian Process Round Table was a small meeting of Gaussian process researchers from around Europe that focussed on what the advantages and limitations of Gaussian process models were. Much of the discussion at the meeting on sparse Gaussian process models was summarized by the Quinonero Candela and Rasmussen paper on "A Unifying Review of Sparse Approximate Gaussian Process Regression". Carl Rasmussen and Chris Williams also used the opportunity to get together and finalize their draft of the book Gaussian Processes for Machine Learning.
The Gaussian Processes in Practice meeting was organised to bring Gaussian processes to a wider audience. It was recorded for Video Lectures and the introductory talk given by David MacKay has had over 30,000 views on the site. By this time the Rasmussen and Williams book was published. This explained these models to a wider audience enabling more widespread adoption of these approaches.
The Gaussian Process Summer Schools now continue in the tradition of explaining these powerful approaches to probabilistic inference to a wider audience. The first school was run in June 2013. As well as hosting schools locally in Sheffield we also conduct Gaussian Process Road Shows: reduced versions of the school that can be brought on site to a given University or Company to provide a short course on Gaussian Process models.