Online semiparametric regression via sequential Monte Carlo

Summary We develop and describe online algorithms for performing online semiparametric regression analyses. Earlier work on this topic is by Luts, Broderick and Wand (2014), Journal of Computational and Graphical Statististics , 23 , 589–615, where online mean‐field variational Bayes (MFVB) was employed. In this article we instead develop sequential Monte Carlo approaches to circumvent well‐known inaccuracies inherent in variational approaches. For Gaussian response semiparametric regression models, our new algorithms share the online MFVB property of only requiring updating and storage of sufficient statistics quantities of streaming data. In the non‐Gaussian case, accurate online semiparametric regression requires the full data to be kept in storage. The new algorithms allow for new options concerning accuracy–speed trade‐offs for online semiparametric regression.