  Latent position network models are a versatile tool in network science;
applications include clustering entities, controlling for causal confounders,
and defining priors over unobserved graphs. Estimating each node's latent
position is typically framed as a Bayesian inference problem, with Metropolis
within Gibbs being the most popular tool for approximating the posterior
distribution. However, it is well-known that Metropolis within Gibbs is
inefficient for large networks; the acceptance ratios are expensive to compute,
and the resultant posterior draws are highly correlated. In this article, we
propose an alternative Markov chain Monte Carlo strategy -- defined using a
combination of split Hamiltonian Monte Carlo and Firefly Monte Carlo -- that
leverages the posterior distribution's functional form for more efficient
posterior computation. We demonstrate that these strategies outperform
Metropolis within Gibbs and other algorithms on synthetic networks, as well as
on real information-sharing networks of teachers and staff in a school
district.
