  In this paper, Bayesian optimisation is used to simultaneously search the
optimal values of the shape parameter and the radius in radial basis function
partition of unity interpolation problem. It is a probabilistic iterative
approach that models the error function with a step-by-step self-updated
Gaussian process, whereas partition of unity leverages a mesh-free method that
allows us to reduce cost-intensive computations when the number of scattered
data is very large, as the entire domain is decomposed into several smaller
subdomains of variable radius. Numerical experiments on the scattered data
interpolation problem show that the combination of these two tools sharply
reduces the search time with respect to other techniques such as the leave one
out cross validation.
