Latent position models are widely used in statistical network analyses, with applications in the literature spanning biology, finance, computing, politics, and social interactions, amongst others. The theory of estimation of the latent positions is well developed in the literature, but uncertainty quantification has largely centred on asymptotics. For applications requiring critical decisions such as cyber-security, reliably quantifying uncertainty in practical, finite-sample settings could open up a range of new, network-wide analytical techniques; for example, in anomaly detection, nodes might be flagged not just for having clearly outlying estimated latent positions, but from apparent inliers actually being difficult to characterise; or in changepoint detection, assessing behavioural shifts from time-varying embedding paths. This talk explores the challenges in taking a Bayesian approach, focusing on a flexible indefinite dot product graph model.