  In this article we focus on dynamic network data which describe interactions
among a fixed population through time. We model this data using the latent
space framework, in which the probability of a connection forming is expressed
as a function of low-dimensional latent coordinates associated with the nodes,
and consider sequential estimation of model parameters via Sequential Monte
Carlo (SMC) methods. In this setting, SMC is a natural candidate for estimation
which offers greater scalability than existing approaches commonly considered
in the literature, allows for estimates to be conveniently updated given
additional observations and facilitates both online and offline inference. We
present a novel approach to sequentially infer parameters of dynamic latent
space network models by building on techniques from the high-dimensional SMC
literature. Furthermore, we examine the scalability and performance of our
approach via simulation, demonstrate the flexibility of our approach to model
variants and analyse a real-world dataset describing classroom contacts.
