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The process convolution framework for constructing a Gaussian Process (GP) model is a computationally efficient approach for larger datasets in lower dimensions. Bayesian inference or specifically, Markov chain Monte Carlo, is commonly used for estimating the parameters of this model. However, applications where data arrive sequentially require re-running the Markov chain for each new data arrival, which can be computationally inefficient. This paper presents a sequential inference method for the process convolution GP model based on a Sequential Monte Carlo method called Particle Learning. This model is illustrated on a synthetic example and an optimization problem in hydrology.

Sequential process convolution Gaussian process models via particle learning