Online Student-$t$ Processes with an Overall-local Scale Structure for
  Modelling Non-stationary Data
Taole Sha Michael Minyi Zhang
Time-dependent data often exhibit characteristics, such as non-stationarity
and heavy-tailed errors, that would be inappropriate to model with the typical
assumptions used in popular models. Thus, more flexible approaches are required
to be able to accommodate such issues. To this end, we propose a Bayesian
mixture of student-$t$ processes with an overall-local scale structure for the
covariance. Moreover, we use a sequential Monte Carlo (SMC) sampler in order to
perform online inference as data arrive in real-time. We demonstrate the
superiority of our proposed approach compared to typical Gaussian process-based
models on real-world data sets in order to prove the necessity of using
mixtures of student-$t$ processes.