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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 latentposition is typically framed as a Bayesian inference problem, with Metropoliswithin Gibbs being the most popular tool for approximating the posteriordistribution. However, it is well-known that Metropolis within Gibbs isinefficient for large networks; the acceptance ratios are expensive to compute,and the resultant posterior draws are highly correlated. In this article, wepropose an alternative Markov chain Monte Carlo strategy -- defined using acombination of split Hamiltonian Monte Carlo and Firefly Monte Carlo -- thatleverages the posterior distribution's functional form for more efficientposterior computation. We demonstrate that these strategies outperformMetropolis within Gibbs and other algorithms on synthetic networks, as well ason real information-sharing networks of teachers and staff in a schooldistrict.

Faster MCMC for Gaussian Latent Position Network Models