  We develop and describe online algorithms for performing real-time
semiparametric regression analyses. Earlier work on this topic is in Luts,
Broderick & Wand (J. Comput. Graph. Statist., 2014) where online mean field
variational Bayes was employed. In this article we instead develop sequential
Monte Carlo approaches to circumvent well-known inaccuracies inherent in
variational approaches. Even though sequential Monte Carlo is not as fast as
online mean field variational Bayes, it can be a viable alternative for
applications where the data rate is not overly high. For Gaussian response
semiparametric regression models our new algorithms share the online mean field
variational Bayes property of only requiring updating and storage of sufficient
statistics quantities of streaming data. In the non-Gaussian case accurate
real-time semiparametric regression requires the full data to be kept in
storage. The new algorithms allow for new options concerning accuracy/speed
trade-offs for real-time semiparametric regression.
