No tension between pulsar timing array upper limits on the nano-Hertz gravitational wave background and assembly models of massive black hole binaries

Pulsar timing arrays provide a means to observe the nano-Hertz gravitational wave background from the population of merging massive black hole binaries. Observations are placing increasingly stringent upper limits on the gravitational wave background. Upper limits and future detections will enable the study of the properties of the merging population. Recent upper limits have cast doubt on current predictions of the gravitational wave background. Here we perform a Bayesian analysis comparing upper limits to astrophysical prediction. So far models are consistent with observation. These proceedings summarise previous work in Ref. [1].