Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 3 / c / iv / Solution

A Dirichlet process mixture model avoids fixing the number of occupied functions. Let $G_0=N_n(0,K)$ be the finite-dimensional Gaussian process law on the common input grid and specifyA draw from a Dirichlet process is almost surely discrete, so several $f_i$ coincide and thereby form clusters. The number of occupied clusters is random and can grow with the data.