Student's T-process Regression on the Space of Probability Density Functions

This study provides an extension of the Student's t-process regression (TPR) on the space of probability density functions as a method of system identification for the data set consist of noisy inputs and deterministic outputs with additive noises. With introducing the distance metrics of the probability density functions, the TPR can be naturally extended to the space of the probability density functions and thus prediction and hyper parameter estimation can be implemented by the same fashion of the ordinary model. In addition, with a numerical example of the proposed model, we introduce the Markov Chain Monte Carlo method for hyper parameter estimation.