Model selection prediction for the mixture of Gaussian processes with RJMCMC

Abstract

Repetition measurements from different sources often occur in data analysis which need to be model and keep track of the original sources. Moreover, data are usually collected as finite vectors which need to be considered as a sample from some certain continuous signal. Actually, these collected finite vectors can be effectively modeled by the mixture of Gaussian processes (MGP) and the key problem is how to make model selection on a given dataset. In fact, model selection prediction of MGP has been investigated by the RJMCMC method. However, the split and merge formula of the RJMCMC method are designed only for the univariables in the past. In this paper, we extend the split and merge formula to the situation of the multivariables. Moreover, we add a Metropolis-Hastings update rule after the RJMCMC process to speed up the convergence. It is demonstrated by simulation experiments that our improved RJMCMC method is feasible and effective.