Approximate Inference for Nonstationary Heteroscedastic Gaussian process   Regression
  This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over input dependent noise variance (heteroscedasticity) and input dependent signal variance (nonstationarity) by setting independent GP priors for the noise and signal variances. We use expectation propagation (EP) for inference and compare results to Markov chain Monte Carlo in two simulated data sets and three empirical examples. The results show that EP produces comparable results with less computational burden. 
Ville Tolvanen, Pasi Jyl\"anki, Aki Vehtari
stat.ML