ABSTRACT
Gaussian process regression places priors on the functions describing the relationship between the predictor(s) and the response which are Gaussian processes. This chapter implements these methods in integrated nested Laplace approximations but we need to make some compromises to achieve reasonable computational efficiency. It introduces the methodology and demonstrates some extensions. The existence of the dip depends crucially on how much we smooth the data. In most smoothing methods, this choice of smoothness is either chosen by the user or by some automated method which produces a point estimate of the best choice. The chapter shows that the fitted function is too rough on the left but too smooth on the right. This function is difficult to fit because it has varying smoothness. All stationary smoothers struggle with this test function for this reason. Required quantities such as the hazard and survival function can be computed via the linear predictor.
