Statistics and Its Interface

Volume 7 (2014)

Number 4

Special Issue on Modern Bayesian Statistics (Part I)

Guest Editor: Ming-Hui Chen (University of Connecticut)

Sequential process convolution Gaussian process models via particle learning

Pages: 465 – 475



Waley W. J. Liang (Analytic Scientist, FICO, U.S.A.)

Herbert K. H. Lee (Department of Applied Mathematics and Statistics, University of California at Santa Cruz)


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 Monte Carlo, optimization, spatial modeling, Bayesian statistics

2010 Mathematics Subject Classification

Primary 62L12, 62M30. Secondary 90C26.

Published 23 December 2014