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Time-dependent data often exhibit characteristics, such as non-stationarityand heavy-tailed errors, that would be inappropriate to model with the typicalassumptions used in popular models. Thus, more flexible approaches are requiredto be able to accommodate such issues. To this end, we propose a Bayesianmixture of student-$t$ processes with an overall-local scale structure for thecovariance. Moreover, we use a sequential Monte Carlo (SMC) sampler in order toperform online inference as data arrive in real-time. We demonstrate thesuperiority of our proposed approach compared to typical Gaussian process-basedmodels on real-world data sets in order to prove the necessity of usingmixtures of student-$t$ processes.

Online Student-$t$ Processes with an Overall-local Scale Structure for Modelling Non-stationary Data